lst:=[[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x,3,-1/15*a*cos(f*x+e)*(c-c*sin(f*x+e))^(9/2)/c/f/sqrt(a+a*sin(f*x+e))-1/6*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/c/f,1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x,3,-1/10*a*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/c/f/sqrt(a+a*sin(f*x+e))-1/5*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/c/f,1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x,3,-1/6*a*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/c/f/sqrt(a+a*sin(f*x+e))-1/4*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/c/f,1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))*sqrt(c-c*sin(f*x+e)),x,3,-1/3*a*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/c/f/sqrt(a+a*sin(f*x+e))-1/3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/c/f,1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),x,2,1/2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/a/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x,5,-2*a*cos(f*x+e)*ln(1-sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x,5,cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c/f/(c-c*sin(f*x+e))^(3/2)+a*cos(f*x+e)*ln(1-sin(f*x+e))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x,2,1/4*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/a/c/f/(c-c*sin(f*x+e))^(5/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x,4,-4/105*a^2*cos(f*x+e)*(c-c*sin(f*x+e))^(9/2)/c/f/sqrt(a+a*sin(f*x+e))-2/21*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/c/f-1/7*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x,4,-1/15*a^2*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/c/f/sqrt(a+a*sin(f*x+e))-2/15*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/c/f-1/6*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x,4,-2/15*a^2*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/c/f/sqrt(a+a*sin(f*x+e))-1/5*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/c/f-1/5*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*sqrt(c-c*sin(f*x+e)),x,3,1/6*c*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/f/sqrt(c-c*sin(f*x+e))+1/4*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e)),x,2,1/3*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x,6,-4*a^2*cos(f*x+e)*ln(1-sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c/f/sqrt(c-c*sin(f*x+e))-1/2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x,6,cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c/f/(c-c*sin(f*x+e))^(3/2)+4*a^2*cos(f*x+e)*ln(1-sin(f*x+e))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^2/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x,6,1/2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c/f/(c-c*sin(f*x+e))^(5/2)-a*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^2/f/(c-c*sin(f*x+e))^(3/2)-a^2*cos(f*x+e)*ln(1-sin(f*x+e))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x,2,1/6*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/c/f/(c-c*sin(f*x+e))^(7/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x,3,1/8*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/c/f/(c-c*sin(f*x+e))^(9/2)+1/48*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/a/c^2/f/(c-c*sin(f*x+e))^(7/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x,5,-1/35*a^3*cos(f*x+e)*(c-c*sin(f*x+e))^(9/2)/c/f/sqrt(a+a*sin(f*x+e))-1/14*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/c/f-3/28*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/c/f-1/8*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(9/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x,5,-2/35*a^3*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/c/f/sqrt(a+a*sin(f*x+e))-4/35*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/c/f-1/7*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/c/f-1/7*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x,4,1/15*c^2*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/f/sqrt(c-c*sin(f*x+e))+2/15*c*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e))/a/f+1/6*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2)/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e)),x,3,1/10*c*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/f/sqrt(c-c*sin(f*x+e))+1/5*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e))/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e)),x,2,1/4*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x,7,-8*a^3*cos(f*x+e)*ln(1-sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-4*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c/f/sqrt(c-c*sin(f*x+e))-a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c/f/sqrt(c-c*sin(f*x+e))-1/3*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x,7,cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c/f/(c-c*sin(f*x+e))^(3/2)+12*a^3*cos(f*x+e)*ln(1-sin(f*x+e))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+6*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^2/f/sqrt(c-c*sin(f*x+e))+3/2*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^2/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x,7,1/2*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c/f/(c-c*sin(f*x+e))^(5/2)-3/2*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^2/f/(c-c*sin(f*x+e))^(3/2)-6*a^3*cos(f*x+e)*ln(1-sin(f*x+e))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-3*a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^3/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x,7,1/3*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c/f/(c-c*sin(f*x+e))^(7/2)-1/2*a*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^2/f/(c-c*sin(f*x+e))^(5/2)+a^2*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^3/f/(c-c*sin(f*x+e))^(3/2)+a^3*cos(f*x+e)*ln(1-sin(f*x+e))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x,2,1/8*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/c/f/(c-c*sin(f*x+e))^(9/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x,3,1/10*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/c/f/(c-c*sin(f*x+e))^(11/2)+1/80*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/a/c^2/f/(c-c*sin(f*x+e))^(9/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x,6,-4/315*a^4*cos(f*x+e)*(c-c*sin(f*x+e))^(11/2)/c/f/sqrt(a+a*sin(f*x+e))-4/105*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(11/2)/c/f-1/15*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(11/2)/c/f-4/45*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(11/2)/c/f-1/10*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(11/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x,6,-8/315*a^4*cos(f*x+e)*(c-c*sin(f*x+e))^(9/2)/c/f/sqrt(a+a*sin(f*x+e))-4/63*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/c/f-2/21*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/c/f-1/9*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(9/2)/c/f-1/9*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2)/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x,5,1/35*c^3*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/f/sqrt(c-c*sin(f*x+e))+1/14*c^2*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*sqrt(c-c*sin(f*x+e))/a/f+3/28*c*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*(c-c*sin(f*x+e))^(3/2)/a/f+1/8*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*(c-c*sin(f*x+e))^(5/2)/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x,4,4/105*c^2*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/f/sqrt(c-c*sin(f*x+e))+2/21*c*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*sqrt(c-c*sin(f*x+e))/a/f+1/7*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*(c-c*sin(f*x+e))^(3/2)/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e)),x,3,1/15*c*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/f/sqrt(c-c*sin(f*x+e))+1/6*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)*sqrt(c-c*sin(f*x+e))/a/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/sqrt(c-c*sin(f*x+e)),x,2,1/5*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x,8,-16*a^4*cos(f*x+e)*ln(1-sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-8*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c/f/sqrt(c-c*sin(f*x+e))-2*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c/f/sqrt(c-c*sin(f*x+e))-2/3*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c/f/sqrt(c-c*sin(f*x+e))-1/4*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/c/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x,8,cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/c/f/(c-c*sin(f*x+e))^(3/2)+32*a^4*cos(f*x+e)*ln(1-sin(f*x+e))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+16*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^2/f/sqrt(c-c*sin(f*x+e))+4*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^2/f/sqrt(c-c*sin(f*x+e))+4/3*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c^2/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x,8,1/2*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/c/f/(c-c*sin(f*x+e))^(5/2)-2*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c^2/f/(c-c*sin(f*x+e))^(3/2)-24*a^4*cos(f*x+e)*ln(1-sin(f*x+e))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-12*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^3/f/sqrt(c-c*sin(f*x+e))-3*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^3/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x,8,1/3*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/c/f/(c-c*sin(f*x+e))^(7/2)-2/3*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c^2/f/(c-c*sin(f*x+e))^(5/2)+2*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^3/f/(c-c*sin(f*x+e))^(3/2)+8*a^4*cos(f*x+e)*ln(1-sin(f*x+e))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+4*a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^4/f/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x,8,1/4*cos(f*x+e)*(a+a*sin(f*x+e))^(7/2)/c/f/(c-c*sin(f*x+e))^(9/2)-1/3*a*cos(f*x+e)*(a+a*sin(f*x+e))^(5/2)/c^2/f/(c-c*sin(f*x+e))^(7/2)+1/2*a^2*cos(f*x+e)*(a+a*sin(f*x+e))^(3/2)/c^3/f/(c-c*sin(f*x+e))^(5/2)-a^3*cos(f*x+e)*sqrt(a+a*sin(f*x+e))/c^4/f/(c-c*sin(f*x+e))^(3/2)-a^4*cos(f*x+e)*ln(1-sin(f*x+e))/c^5/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x,2,1/10*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c/f/(c-c*sin(f*x+e))^(11/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x,3,1/12*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c/f/(c-c*sin(f*x+e))^(13/2)+1/120*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c^2/f/(c-c*sin(f*x+e))^(11/2),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x,4,1/14*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c/f/(c-c*sin(f*x+e))^(15/2)+1/84*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c^2/f/(c-c*sin(f*x+e))^(13/2)+1/840*cos(f*x+e)*(a+a*sin(f*x+e))^(9/2)/a/c^3/f/(c-c*sin(f*x+e))^(11/2),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/sqrt(a+a*sin(f*x+e)),x,2,-1/4*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/c/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e)),x,2,-1/3*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/c/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2*sqrt(c-c*sin(f*x+e))/sqrt(a+a*sin(f*x+e)),x,2,-1/2*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/c/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),x,2,-cos(f*x+e)*sqrt(c-c*sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x,4,-cos(f*x+e)*ln(1-sin(f*x+e))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x,2,cos(f*x+e)/c/f/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x,8,16*c^4*cos(f*x+e)*ln(1+sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+8*c^3*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))+2*c^2*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a/f/sqrt(a+a*sin(f*x+e))+2/3*c*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/a/f/sqrt(a+a*sin(f*x+e))+1/4*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/a/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x,7,8*c^3*cos(f*x+e)*ln(1+sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+4*c^2*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))+c*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a/f/sqrt(a+a*sin(f*x+e))+1/3*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/a/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x,6,4*c^2*cos(f*x+e)*ln(1+sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*c*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))+1/2*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2*sqrt(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x,5,2*c*cos(f*x+e)*ln(1+sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e)),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e)),x,4,cos(f*x+e)*ln(1+sin(f*x+e))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x,3,arctanh(sin(f*x+e))*cos(f*x+e)/a/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x,4,1/2*cos(f*x+e)/a/c/f/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+1/2*arctanh(sin(f*x+e))*cos(f*x+e)/a/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x,9,-80*c^5*cos(f*x+e)*ln(1+sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-40*c^4*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))-10*c^3*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a^2/f/sqrt(a+a*sin(f*x+e))-10/3*c^2*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/a^2/f/sqrt(a+a*sin(f*x+e))-5/4*c*cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/a^2/f/sqrt(a+a*sin(f*x+e))-cos(f*x+e)*(c-c*sin(f*x+e))^(9/2)/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x,8,-32*c^4*cos(f*x+e)*ln(1+sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-16*c^3*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))-4*c^2*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a^2/f/sqrt(a+a*sin(f*x+e))-4/3*c*cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/a^2/f/sqrt(a+a*sin(f*x+e))-cos(f*x+e)*(c-c*sin(f*x+e))^(7/2)/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x,7,-12*c^3*cos(f*x+e)*ln(1+sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-6*c^2*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))-3/2*c*cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a^2/f/sqrt(a+a*sin(f*x+e))-cos(f*x+e)*(c-c*sin(f*x+e))^(5/2)/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x,6,-4*c^2*cos(f*x+e)*ln(1+sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2*c*cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))-cos(f*x+e)*(c-c*sin(f*x+e))^(3/2)/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2*sqrt(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x,5,-c*cos(f*x+e)*ln(1+sin(f*x+e))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-cos(f*x+e)*sqrt(c-c*sin(f*x+e))/a/f/(a+a*sin(f*x+e))^(3/2),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e)),x,2,-cos(f*x+e)/a/f/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x,4,-1/2*cos(f*x+e)/a/c/f/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))+1/2*arctanh(sin(f*x+e))*cos(f*x+e)/a^2/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x,5,-1/2*cos(f*x+e)/a/c/f/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2)+1/2*cos(f*x+e)/a^2/c/f/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+1/2*arctanh(sin(f*x+e))*cos(f*x+e)/a^2/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,4,2^(3/2+n)*cos(f*x+e)^3*hypergeom([3/2+m, -1/2-n],[5/2+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-3/2-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/(3+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x,3,-1/9*2^(3/2+m)*a^3*c^3*cos(f*x+e)^9*hypergeom([9/2, -1/2-m],[11/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^(-3+m)/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x,3,-1/7*2^(3/2+m)*a^2*c^2*cos(f*x+e)^7*hypergeom([7/2, -1/2-m],[9/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^(-2+m)/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x,3,-1/5*2^(3/2+m)*a*c*cos(f*x+e)^5*hypergeom([5/2, -1/2-m],[7/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^(-1+m)/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x,2,-1/3*2^(3/2+m)*cos(f*x+e)^3*hypergeom([3/2, -1/2-m],[5/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^m/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x,3,-2^(3/2+m)*cos(f*x+e)*hypergeom([1/2, -1/2-m],[3/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-1/2-m)*(a+a*sin(f*x+e))^m/c/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x,3,2^(3/2+m)*hypergeom([-1/2, -1/2-m],[1/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^(2+m)/a^2/c^2/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x,3,1/3*2^(3/2+m)*hypergeom([-3/2, -1/2-m],[-1/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)^3*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^(3+m)/a^3/c^3/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x,5,768*c^3*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/(7+2*m)/(9+2*m)/(4*m^2+16*m+15)/sqrt(c-c*sin(f*x+e))+192*c^2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*sqrt(c-c*sin(f*x+e))/a/f/(9+2*m)/(4*m^2+24*m+35)+24*c*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(3/2)/a/f/(4*m^2+32*m+63)+2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(5/2)/a/f/(9+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x,4,64*c^2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/(7+2*m)/(4*m^2+16*m+15)/sqrt(c-c*sin(f*x+e))+16*c*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*sqrt(c-c*sin(f*x+e))/a/f/(4*m^2+24*m+35)+2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(3/2)/a/f/(7+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*sqrt(c-c*sin(f*x+e)),x,3,8*c*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/(4*m^2+16*m+15)/sqrt(c-c*sin(f*x+e))+2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*sqrt(c-c*sin(f*x+e))/a/f/(5+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/sqrt(c-c*sin(f*x+e)),x,2,2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/(3+2*m)/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x,4,cos(f*x+e)*hypergeom([1, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(1+m)/a/c/f/(3+2*m)/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x,4,1/2*cos(f*x+e)*hypergeom([2, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(1+m)/a/c^2/f/(3+2*m)/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/sqrt(c-c*sin(f*x+e)),x,2,2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)/a/f/(3+2*m)/sqrt(c-c*sin(f*x+e)),1],
[cos(f*x+e)^2*(c+c*sin(f*x+e))^m/sqrt(a-a*sin(f*x+e)),x,2,2*cos(f*x+e)*(c+c*sin(f*x+e))^(1+m)/c/f/(3+2*m)/sqrt(a-a*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x,4,cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-4-m)/a/c/f/(7+2*m)+2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-3-m)/a/c^2/f/(4*m^2+24*m+35)+2*cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-2-m)/a/c^3/f/(7+2*m)/(4*m^2+16*m+15),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x,3,cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-3-m)/a/c/f/(5+2*m)+cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-2-m)/a/c^2/f/(4*m^2+16*m+15),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x,2,cos(f*x+e)*(a+a*sin(f*x+e))^(1+m)*(c-c*sin(f*x+e))^(-2-m)/a/c/f/(3+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x,4,2^(-1/2-m)*cos(f*x+e)^3*hypergeom([3/2+m, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(1/2+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m)/f/(3+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x,4,2^(1/2-m)*cos(f*x+e)^3*hypergeom([1/2+m, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1/2+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m)/f/(3+2*m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x,4,2^(3/2-m)*cos(f*x+e)^3*hypergeom([-1/2+m, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-3/2+m)*(a+a*sin(f*x+e))^m/f/(3+2*m)/((c-c*sin(f*x+e))^m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x,4,2^(5/2-m)*cos(f*x+e)^3*hypergeom([-3/2+m, 3/2+m],[5/2+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-5/2+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m)/f/(3+2*m),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x,8,2/3*a*c^4*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*a*c^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2/7*a*c^3*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))+10/77*a*c^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e))+2/33*a*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))-2/11*a*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2)/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x,7,22/45*a*c^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/15*a*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/105*a*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))+2/21*a*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e))-2/9*a*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x,6,2/5*a*c^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+6/5*a*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+6/35*a*c*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))-2/7*a*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))*sqrt(c-c*sin(f*x+e)),x,5,2/5*a*c*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+6/5*a*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2/5*a*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),x,4,-2/3*a*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*a*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x,4,4*a*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-6*a*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x,5,4/5*a*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-6/5*a*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+6/5*a*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x,6,4/9*a*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)-2/15*a*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-2/15*a*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+2/15*a*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x,7,4/13*a*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2)-2/39*a*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)-2/65*a*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-2/65*a*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+2/65*a*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x,8,14/45*a^2*c^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/15*a^2*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2/15*a^2*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))+2/33*a^2*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e))-14/99*a^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))-2/11*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x,7,14/45*a^2*c^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/15*a^2*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2/15*a^2*c*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))-2/9*a^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e))-2/9*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*sqrt(c-c*sin(f*x+e)),x,6,-2/5*a^2*c*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+6/5*a^2*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-6/35*a*c*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))+2/7*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e)),x,5,-14/15*a^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/5*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2/5*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x,5,4*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/(c-c*sin(f*x+e))^(3/2)+14/3*a^2*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-14*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x,5,4/5*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/(c-c*sin(f*x+e))^(5/2)-28/5*a^2*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+42/5*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x,6,4/9*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/(c-c*sin(f*x+e))^(7/2)-28/45*a^2*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+14/15*a^2*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-14/15*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x,7,4/13*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/(c-c*sin(f*x+e))^(9/2)-28/117*a^2*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+14/195*a^2*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+14/195*a^2*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-14/195*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x,8,4/17*a*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/(c-c*sin(f*x+e))^(11/2)-28/221*a^2*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2)+14/663*a^2*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+14/1105*a^2*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+14/1105*a^2*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-14/1105*a^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^5/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x,9,154/585*a^3*c^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+154/195*a^3*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/195*a^3*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))+2/39*a^3*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e))-14/117*a^3*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))-2/13*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/f/g-2/13*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x,8,-14/45*a^3*c^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/15*a^3*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2/15*a^2*c^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-2/33*a*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))+14/99*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e))+2/11*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e)),x,7,-22/45*a^3*c*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/15*a^3*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-22/105*a^2*c*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-2/21*a*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))+2/9*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e)),x,6,-22/15*a^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/5*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-22/35*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-2/7*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x,6,4*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(3/2)+154/15*a^3*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-154/5*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/5*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x,6,4/5*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(5/2)-44/5*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/(c-c*sin(f*x+e))^(3/2)-154/15*a^3*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+154/5*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x,6,4/9*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(7/2)-44/45*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/(c-c*sin(f*x+e))^(5/2)+308/45*a^3*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-154/15*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x,7,4/13*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(9/2)-44/117*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/(c-c*sin(f*x+e))^(7/2)+308/585*a^3*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-154/195*a^3*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+154/195*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x,8,4/17*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(11/2)-44/221*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/(c-c*sin(f*x+e))^(9/2)+308/1989*a^3*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)-154/3315*a^3*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-154/3315*a^3*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+154/3315*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^5/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x,9,4/21*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/(c-c*sin(f*x+e))^(13/2)-44/357*a^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/(c-c*sin(f*x+e))^(11/2)+44/663*a^3*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2)-22/1989*a^3*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)-22/3315*a^3*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)-22/3315*a^3*(g*cos(f*x+e))^(5/2)/c^5/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+22/3315*a^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^6/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x,10,-154/585*a^4*c^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+154/195*a^4*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-22/195*a^3*c^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-2/39*a^2*c^3*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))-14/585*a*c^3*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e))+14/195*c^3*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)/f/g/sqrt(c-c*sin(f*x+e))+22/195*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e))/f/g+2/15*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2)/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x,9,-14/39*a^4*c^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/13*a^4*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2/13*a^3*c^2*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-10/143*a^2*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))-14/429*a*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e))+14/143*c^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)/f/g/sqrt(c-c*sin(f*x+e))+2/13*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e))/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*sqrt(c-c*sin(f*x+e)),x,8,-2/3*a^4*c*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*a^4*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-2/7*a^3*c*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-10/77*a^2*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))-2/33*a*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e))+2/11*c*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(7/2)/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/sqrt(c-c*sin(f*x+e)),x,7,-22/9*a^4*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/3*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-22/21*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/f/g/sqrt(c-c*sin(f*x+e))-10/21*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/f/g/sqrt(c-c*sin(f*x+e))-2/9*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x,7,4*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(3/2)+22*a^4*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-66*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+66/7*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c/f/g/sqrt(c-c*sin(f*x+e))+30/7*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x,7,4/5*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(5/2)-12*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(3/2)-154/5*a^4*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+462/5*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-66/5*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x,7,4/9*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(7/2)-4/3*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(5/2)+44/3*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/(c-c*sin(f*x+e))^(3/2)+154/9*a^4*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-154/3*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x,7,4/13*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(9/2)-20/39*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(7/2)+44/39*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/(c-c*sin(f*x+e))^(5/2)-308/39*a^4*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)+154/13*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^4/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x,8,4/17*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(11/2)-60/221*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(9/2)+220/663*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/(c-c*sin(f*x+e))^(7/2)-308/663*a^4*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+154/221*a^4*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-154/221*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^5/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x,9,4/21*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(13/2)-20/119*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(11/2)+220/1547*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/(c-c*sin(f*x+e))^(9/2)-220/1989*a^4*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+22/663*a^4*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+22/663*a^4*(g*cos(f*x+e))^(5/2)/c^5/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-22/663*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^6/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x,10,4/25*a*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(5/2)/f/g/(c-c*sin(f*x+e))^(15/2)-4/35*a^2*(g*cos(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(3/2)/c/f/g/(c-c*sin(f*x+e))^(13/2)+44/595*a^3*(g*cos(f*x+e))^(5/2)*sqrt(a+a*sin(f*x+e))/c^2/f/g/(c-c*sin(f*x+e))^(11/2)-44/1105*a^4*(g*cos(f*x+e))^(5/2)/c^3/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2)+22/3315*a^4*(g*cos(f*x+e))^(5/2)/c^4/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+22/5525*a^4*(g*cos(f*x+e))^(5/2)/c^5/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+22/5525*a^4*(g*cos(f*x+e))^(5/2)/c^6/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-22/5525*a^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^7/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/sqrt(a+a*sin(f*x+e)),x,6,22/15*c^3*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/5*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+22/35*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e))+2/7*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e)),x,5,14/15*c^2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+14/5*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2/5*c*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/sqrt(a+a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(c-c*sin(f*x+e))/sqrt(a+a*sin(f*x+e)),x,4,2/3*c*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+2*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),x,3,2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x,4,2*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x,5,2/5*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+2/5*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-2/5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x,6,2/9*(g*cos(f*x+e))^(5/2)/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+2/15*(g*cos(f*x+e))^(5/2)/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+2/15*(g*cos(f*x+e))^(5/2)/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-2/15*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x,7,-22*c^4*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-66*c^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-66/7*c^3*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a/f/g/sqrt(a+a*sin(f*x+e))-30/7*c^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/a/f/g/sqrt(a+a*sin(f*x+e))-4*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x,6,-154/15*c^3*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-154/5*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-22/5*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a/f/g/sqrt(a+a*sin(f*x+e))-4*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/(a+a*sin(f*x+e))^(3/2),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x,5,-14/3*c^2*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-14*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-4*c*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/(a+a*sin(f*x+e))^(3/2),1],
[(g*cos(f*x+e))^(3/2)*sqrt(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x,4,-4*c*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))-6*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e)),x,4,-2*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))-2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x,5,-2*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2)+2*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x,6,-2*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2)+6/5*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+6/5*(g*cos(f*x+e))^(5/2)/a/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-6/5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x,7,-2*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2)+10/9*(g*cos(f*x+e))^(5/2)/a/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+2/3*(g*cos(f*x+e))^(5/2)/a/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+2/3*(g*cos(f*x+e))^(5/2)/a/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-2/3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x,8,418/5*c^5*(g*cos(f*x+e))^(5/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+1254/5*c^5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+1254/35*c^4*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a^2/f/g/sqrt(a+a*sin(f*x+e))+114/7*c^3*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))+76/5*c^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)-4/5*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2)/f/g/(a+a*sin(f*x+e))^(5/2),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x,7,154/5*c^4*(g*cos(f*x+e))^(5/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+462/5*c^4*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+66/5*c^3*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a^2/f/g/sqrt(a+a*sin(f*x+e))+12*c^2*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)-4/5*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x,6,154/15*c^3*(g*cos(f*x+e))^(5/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+154/5*c^3*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))+44/5*c^2*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/a/f/g/(a+a*sin(f*x+e))^(3/2)-4/5*c*(g*cos(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2)/f/g/(a+a*sin(f*x+e))^(5/2),1],
[(g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x,5,28/5*c^2*(g*cos(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))+42/5*c^2*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e))-4/5*c*(g*cos(f*x+e))^(5/2)*sqrt(c-c*sin(f*x+e))/f/g/(a+a*sin(f*x+e))^(5/2),1],
[(g*cos(f*x+e))^(3/2)*sqrt(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x,5,-4/5*c*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e))+6/5*c*(g*cos(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))+6/5*c*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e)),x,5,-2/5*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e))-2/5*(g*cos(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))-2/5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x,6,2*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2)-6/5*(g*cos(f*x+e))^(5/2)/c/f/g/(a+a*sin(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e))-6/5*(g*cos(f*x+e))^(5/2)/a/c/f/g/(a+a*sin(f*x+e))^(3/2)/sqrt(c-c*sin(f*x+e))-6/5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/c/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x,7,-2/5*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2)-2*(g*cos(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2)+6/5*(g*cos(f*x+e))^(5/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+6/5*(g*cos(f*x+e))^(5/2)/a^2/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-6/5*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/c^2/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x,8,-2/5*(g*cos(f*x+e))^(5/2)/f/g/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2)-14/5*(g*cos(f*x+e))^(5/2)/a/f/g/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2)+14/9*(g*cos(f*x+e))^(5/2)/a^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2)+14/15*(g*cos(f*x+e))^(5/2)/a^2/c/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)+14/15*(g*cos(f*x+e))^(5/2)/a^2/c^2/f/g/sqrt(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)-14/15*g*sqrt(cos(f*x+e))*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/c^3/f/sqrt(a+a*sin(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,3,2^(9/4+n)*(g*cos(f*x+e))^(5/2)*hypergeom([5/4+m, -1/4-n],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-5/4-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/g/(5+4*m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x,3,-1/17*2^(9/4+m)*a^3*c^3*(g*cos(f*x+e))^(17/2)*hypergeom([17/4, -1/4-m],[21/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(-3+m)/f/g^7,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x,3,-1/13*2^(9/4+m)*a^2*c^2*(g*cos(f*x+e))^(13/2)*hypergeom([13/4, -1/4-m],[17/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(-2+m)/f/g^5,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x,3,-1/9*2^(9/4+m)*a*c*(g*cos(f*x+e))^(9/2)*hypergeom([9/4, -1/4-m],[13/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(-1+m)/f/g^3,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x,2,-1/5*2^(9/4+m)*(g*cos(f*x+e))^(5/2)*hypergeom([5/4, -1/4-m],[9/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^m/f/g,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x,3,-2^(9/4+m)*g*sqrt(g*cos(f*x+e))*hypergeom([1/4, -1/4-m],[5/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(1+m)/a/c/f,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x,3,1/3*2^(9/4+m)*g^3*hypergeom([-3/4, -1/4-m],[1/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(2+m)/a^2/c^2/f/(g*cos(f*x+e))^(3/2),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x,3,1/7*2^(9/4+m)*g^5*hypergeom([-7/4, -1/4-m],[-3/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(3+m)/a^3/c^3/f/(g*cos(f*x+e))^(7/2),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x,3,-1/15*2^(9/4+m)*a^2*c^2*(g*cos(f*x+e))^(15/2)*hypergeom([15/4, -1/4-m],[19/4],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(-2+m)*sqrt(c-c*sin(f*x+e))/f/g^6,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x,3,-1/11*2^(9/4+m)*a*c*(g*cos(f*x+e))^(11/2)*hypergeom([11/4, -1/4-m],[15/4],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(-1+m)*sqrt(c-c*sin(f*x+e))/f/g^4,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*sqrt(c-c*sin(f*x+e)),x,3,-1/7*2^(9/4+m)*(g*cos(f*x+e))^(7/2)*hypergeom([7/4, -1/4-m],[11/4],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^m*sqrt(c-c*sin(f*x+e))/f/g^2,1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/sqrt(c-c*sin(f*x+e)),x,3,-1/3*2^(9/4+m)*cos(f*x+e)*(g*cos(f*x+e))^(3/2)*hypergeom([3/4, -1/4-m],[7/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^m/f/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x,3,2^(9/4+m)*g^2*cos(f*x+e)*hypergeom([-1/4, -1/4-m],[3/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(1+m)/a/c/f/sqrt(g*cos(f*x+e))/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x,3,1/5*2^(9/4+m)*g^4*cos(f*x+e)*hypergeom([-5/4, -1/4-m],[-1/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^(2+m)/a^2/c^2/f/(g*cos(f*x+e))^(5/2)/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/sqrt(c-c*sin(f*x+e)),x,3,-1/3*2^(9/4+m)*cos(f*x+e)*(g*cos(f*x+e))^(3/2)*hypergeom([3/4, -1/4-m],[7/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(a+a*sin(f*x+e))^m/f/sqrt(c-c*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/sqrt(a-a*sin(f*x+e)),x,3,-1/3*2^(9/4+m)*cos(f*x+e)*(g*cos(f*x+e))^(3/2)*hypergeom([3/4, -1/4-m],[7/4],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/4-m)*(c+c*sin(f*x+e))^m/f/sqrt(a-a*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x,3,2^(-3/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([5/4+m, 11/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(7/4+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m)/f/g/(5+4*m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x,3,2^(1/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([5/4+m, 7/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(3/4+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m)/f/g/(5+4*m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x,3,2^(5/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([3/4+m, 5/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1/4+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m)/f/g/(5+4*m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x,3,2^(9/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([-1/4+m, 5/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-5/4+m)*(a+a*sin(f*x+e))^m/f/g/(5+4*m)/((c-c*sin(f*x+e))^m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x,3,2^(13/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([-5/4+m, 5/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-9/4+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m)/f/g/(5+4*m),1],
[(g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x,3,2^(17/4-m)*(g*cos(f*x+e))^(5/2)*hypergeom([-9/4+m, 5/4+m],[9/4+m],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-13/4+m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m)/f/g/(5+4*m),1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,3,2^(1/2+n+1/2*p)*(g*cos(f*x+e))^(p+1)*hypergeom([1/2-n-1/2*p, 1/2+m+1/2*p],[3/2+m+1/2*p],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1/2-n-1/2*p)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/g/(1+2*m+p),1],
[(g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+m),x,4,-g*ln(1-sin(f*x+e))*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m/c/f/((g*cos(f*x+e))^(2*m)),1],
[(g*cos(f*x+e))^(5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,3,-8*a^3*(g*cos(f*x+e))^(6-2*m)*(a+a*sin(f*x+e))^(-3+m)*(c-c*sin(f*x+e))^n/f/g/(3-m+n)/(4-m+n)/(5-m+n)-4*a^2*(g*cos(f*x+e))^(6-2*m)*(a+a*sin(f*x+e))^(-2+m)*(c-c*sin(f*x+e))^n/f/g/(4-m+n)/(5-m+n)-a*(g*cos(f*x+e))^(6-2*m)*(a+a*sin(f*x+e))^(-1+m)*(c-c*sin(f*x+e))^n/f/g/(5-m+n),1],
[(g*cos(f*x+e))^(3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,2,-2*a^2*(g*cos(f*x+e))^(4-2*m)*(a+a*sin(f*x+e))^(-2+m)*(c-c*sin(f*x+e))^n/f/g/(2-m+n)/(3-m+n)-a*(g*cos(f*x+e))^(4-2*m)*(a+a*sin(f*x+e))^(-1+m)*(c-c*sin(f*x+e))^n/f/g/(3-m+n),1],
[(g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,1,-a*(g*cos(f*x+e))^(2-2*m)*(a+a*sin(f*x+e))^(-1+m)*(c-c*sin(f*x+e))^n/f/g/(1-m+n),1],
[(g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,4,1/2*hypergeom([1, -m+n],[1-m+n],1/2-1/2*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/g/(m-n)/((g*cos(f*x+e))^(2*m)),1],
[(g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,4,1/4*c*hypergeom([2, -1-m+n],[-m+n],1/2-1/2*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n)/f/g^3/(1+m-n)/((g*cos(f*x+e))^(2*m)),1],
[(g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,4,1/8*c^2*hypergeom([3, -2-m+n],[-1-m+n],1/2-1/2*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n)/f/g^5/(2+m-n)/((g*cos(f*x+e))^(2*m)),1],
[(g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x,3,arctanh(sin(f*x+e))*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m/f/g/((g*cos(f*x+e))^(2*m)),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n),x,3,2^(3-1/2*m+1/2*n)*(g*cos(f*x+e))^(-m-n)*hypergeom([-2+1/2*m-1/2*n, 1/2*m-1/2*n],[1+1/2*m-1/2*n],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-3+1/2*m-1/2*n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n)/f/g/(m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n),x,3,2^(2-1/2*m+1/2*n)*(g*cos(f*x+e))^(-m-n)*hypergeom([-1+1/2*m-1/2*n, 1/2*m-1/2*n],[1+1/2*m-1/2*n],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-2+1/2*m-1/2*n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n)/f/g/(m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n),x,3,2^(1-1/2*m+1/2*n)*(g*cos(f*x+e))^(-m-n)*hypergeom([1/2*m-1/2*n, 1/2*m-1/2*n],[1+1/2*m-1/2*n],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1+1/2*m-1/2*n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n)/f/g/(m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,1,(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/g/(m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n),x,2,(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n)/f/g/(2+m-n)+(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/c/f/g/(m-n)/(2+m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n),x,3,(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n)/f/g/(4+m-n)+2*(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n)/c/f/g/(2+m-n)/(4+m-n)+2*(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/c^2/f/g/(m-n)/(2+m-n)/(4+m-n),1],
[(g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n),x,4,(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n)/f/g/(6+m-n)+3*(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n)/c/f/g/(4+m-n)/(6+m-n)+6*(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n)/c^2/f/g/(2+m-n)/(4+m-n)/(6+m-n)+6*(g*cos(f*x+e))^(-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/c^3/f/g/(m-n)/(2+m-n)/(4+m-n)/(6+m-n),1],
[(g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x,4,2^(1/2+n-1/2*p)*cos(f*x+e)*hypergeom([1/2+m-1/2*p, 1/2-n+1/2*p],[3/2+m-1/2*p],1/2+1/2*sin(f*x+e))*(g*sec(f*x+e))^p*(1-sin(f*x+e))^(-1/2-n+1/2*p)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n/f/(1+2*m-p),1],
[cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,4,1/3*a*sin(d*x+c)^3/d+1/4*a*sin(d*x+c)^4/d,1],
[cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x,4,1/2*a*sin(d*x+c)^2/d+1/3*a*sin(d*x+c)^3/d,1],
[cot(d*x+c)*(a+a*sin(d*x+c)),x,3,a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d,1],
[cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,3,-1/2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2/a/d,1],
[cot(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,4,-1/2*a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d,1],
[cot(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,4,-1/3*a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d,1],
[cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,1/3*a^2*sin(d*x+c)^3/d+1/2*a^2*sin(d*x+c)^4/d+1/5*a^2*sin(d*x+c)^5/d,1],
[cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^2,x,4,1/2*a^2*sin(d*x+c)^2/d+2/3*a^2*sin(d*x+c)^3/d+1/4*a^2*sin(d*x+c)^4/d,1],
[cot(d*x+c)*(a+a*sin(d*x+c))^2,x,3,a^2*ln(sin(d*x+c))/d+2*a^2*sin(d*x+c)/d+1/2*a^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^2,x,4,-a^2*csc(d*x+c)/d+2*a^2*ln(sin(d*x+c))/d+a^2*sin(d*x+c)/d,1],
[cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,-2*a^2*csc(d*x+c)/d-1/2*a^2*csc(d*x+c)^2/d+a^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x,3,-1/3*csc(d*x+c)^3*(a+a*sin(d*x+c))^3/a/d,1],
[cot(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x,4,-1/2*a^2*csc(d*x+c)^2/d-2/3*a^2*csc(d*x+c)^3/d-1/4*a^2*csc(d*x+c)^4/d,1],
[cot(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x,4,-1/3*a^2*csc(d*x+c)^3/d-1/2*a^2*csc(d*x+c)^4/d-1/5*a^2*csc(d*x+c)^5/d,1],
[cot(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x,4,-1/4*a^2*csc(d*x+c)^4/d-2/5*a^2*csc(d*x+c)^5/d-1/6*a^2*csc(d*x+c)^6/d,1],
[cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x,4,1/4*a^3*sin(d*x+c)^4/d+3/5*a^3*sin(d*x+c)^5/d+1/2*a^3*sin(d*x+c)^6/d+1/7*a^3*sin(d*x+c)^7/d,1],
[cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,1/3*a^3*sin(d*x+c)^3/d+3/4*a^3*sin(d*x+c)^4/d+3/5*a^3*sin(d*x+c)^5/d+1/6*a^3*sin(d*x+c)^6/d,1],
[cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^3,x,4,-1/4*(a+a*sin(d*x+c))^4/a/d+1/5*(a+a*sin(d*x+c))^5/a^2/d,1],
[cot(d*x+c)*(a+a*sin(d*x+c))^3,x,3,a^3*ln(sin(d*x+c))/d+3*a^3*sin(d*x+c)/d+3/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^3,x,4,-a^3*csc(d*x+c)/d+3*a^3*ln(sin(d*x+c))/d+3*a^3*sin(d*x+c)/d+1/2*a^3*sin(d*x+c)^2/d,1],
[cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,-3*a^3*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d+3*a^3*ln(sin(d*x+c))/d+a^3*sin(d*x+c)/d,1],
[cot(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x,4,-3*a^3*csc(d*x+c)/d-3/2*a^3*csc(d*x+c)^2/d-1/3*a^3*csc(d*x+c)^3/d+a^3*ln(sin(d*x+c))/d,1],
[cot(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x,3,-1/4*csc(d*x+c)^4*(a+a*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x,4,1/20*csc(d*x+c)^4*(a+a*sin(d*x+c))^4/a/d-1/5*csc(d*x+c)^5*(a+a*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x,4,-1/3*a^3*csc(d*x+c)^3/d-3/4*a^3*csc(d*x+c)^4/d-3/5*a^3*csc(d*x+c)^5/d-1/6*a^3*csc(d*x+c)^6/d,1],
[cot(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x,4,-1/4*a^3*csc(d*x+c)^4/d-3/5*a^3*csc(d*x+c)^5/d-1/2*a^3*csc(d*x+c)^6/d-1/7*a^3*csc(d*x+c)^7/d,1],
[cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x,4,1/5*a^4*sin(d*x+c)^5/d+2/3*a^4*sin(d*x+c)^6/d+6/7*a^4*sin(d*x+c)^7/d+1/2*a^4*sin(d*x+c)^8/d+1/9*a^4*sin(d*x+c)^9/d,1],
[cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^4,x,4,1/4*a^4*sin(d*x+c)^4/d+4/5*a^4*sin(d*x+c)^5/d+a^4*sin(d*x+c)^6/d+4/7*a^4*sin(d*x+c)^7/d+1/8*a^4*sin(d*x+c)^8/d,1],
[cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x,4,1/5*(a+a*sin(d*x+c))^5/a/d-1/3*(a+a*sin(d*x+c))^6/a^2/d+1/7*(a+a*sin(d*x+c))^7/a^3/d,1],
[cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^4,x,4,-1/5*(a+a*sin(d*x+c))^5/a/d+1/6*(a+a*sin(d*x+c))^6/a^2/d,1],
[cot(d*x+c)*(a+a*sin(d*x+c))^4,x,3,a^4*ln(sin(d*x+c))/d+4*a^4*sin(d*x+c)/d+3*a^4*sin(d*x+c)^2/d+4/3*a^4*sin(d*x+c)^3/d+1/4*a^4*sin(d*x+c)^4/d,1],
[cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^4,x,4,-a^4*csc(d*x+c)/d+4*a^4*ln(sin(d*x+c))/d+6*a^4*sin(d*x+c)/d+2*a^4*sin(d*x+c)^2/d+1/3*a^4*sin(d*x+c)^3/d,1],
[cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x,4,-4*a^4*csc(d*x+c)/d-1/2*a^4*csc(d*x+c)^2/d+6*a^4*ln(sin(d*x+c))/d+4*a^4*sin(d*x+c)/d+1/2*a^4*sin(d*x+c)^2/d,1],
[cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,4,ln(1+sin(d*x+c))/a/d-sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d-1/3*sin(d*x+c)^3/a/d+1/4*sin(d*x+c)^4/a/d,1],
[cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,4,-ln(1+sin(d*x+c))/a/d+sin(d*x+c)/a/d-1/2*sin(d*x+c)^2/a/d+1/3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,4,ln(1+sin(d*x+c))/a/d-sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d,1],
[cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x,4,-ln(1+sin(d*x+c))/a/d+sin(d*x+c)/a/d,1],
[cot(d*x+c)/(a+a*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-ln(1+sin(d*x+c))/a/d,1],
[cot(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-ln(sin(d*x+c))/a/d+ln(1+sin(d*x+c))/a/d,1],
[cot(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,4,csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d+ln(sin(d*x+c))/a/d-ln(1+sin(d*x+c))/a/d,1],
[cot(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d+1/2*csc(d*x+c)^2/a/d-1/3*csc(d*x+c)^3/a/d-ln(sin(d*x+c))/a/d+ln(1+sin(d*x+c))/a/d,1],
[cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x,4,-4*ln(1+sin(d*x+c))/a^2/d+3*sin(d*x+c)/a^2/d-sin(d*x+c)^2/a^2/d+1/3*sin(d*x+c)^3/a^2/d-1/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,4,3*ln(1+sin(d*x+c))/a^2/d-2*sin(d*x+c)/a^2/d+1/2*sin(d*x+c)^2/a^2/d+1/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,-2*ln(1+sin(d*x+c))/a^2/d+sin(d*x+c)/a^2/d-1/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,4,ln(1+sin(d*x+c))/a^2/d+1/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)/(a+a*sin(d*x+c))^2,x,3,ln(sin(d*x+c))/a^2/d-ln(1+sin(d*x+c))/a^2/d+1/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,4,-csc(d*x+c)/a^2/d-2*ln(sin(d*x+c))/a^2/d+2*ln(1+sin(d*x+c))/a^2/d-1/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,2*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a^2/d+3*ln(sin(d*x+c))/a^2/d-3*ln(1+sin(d*x+c))/a^2/d+1/d/(a^2+a^2*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x,4,-3*csc(d*x+c)/a^2/d+csc(d*x+c)^2/a^2/d-1/3*csc(d*x+c)^3/a^2/d-4*ln(sin(d*x+c))/a^2/d+4*ln(1+sin(d*x+c))/a^2/d-1/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x,4,-10*ln(1+sin(d*x+c))/a^3/d+6*sin(d*x+c)/a^3/d-3/2*sin(d*x+c)^2/a^3/d+1/3*sin(d*x+c)^3/a^3/d+1/2/a/d/(a+a*sin(d*x+c))^2-5/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x,4,6*ln(1+sin(d*x+c))/a^3/d-3*sin(d*x+c)/a^3/d+1/2*sin(d*x+c)^2/a^3/d-1/2/a/d/(a+a*sin(d*x+c))^2+4/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,4,-3*ln(1+sin(d*x+c))/a^3/d+sin(d*x+c)/a^3/d+1/2/a/d/(a+a*sin(d*x+c))^2-3/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,4,ln(1+sin(d*x+c))/a^3/d-1/2/a/d/(a+a*sin(d*x+c))^2+2/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,3,1/2*sin(d*x+c)^2/a/d/(a+a*sin(d*x+c))^2,1],
[cot(d*x+c)/(a+a*sin(d*x+c))^3,x,3,ln(sin(d*x+c))/a^3/d-ln(1+sin(d*x+c))/a^3/d+1/2/a/d/(a+a*sin(d*x+c))^2+1/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^3,x,4,-csc(d*x+c)/a^3/d-3*ln(sin(d*x+c))/a^3/d+3*ln(1+sin(d*x+c))/a^3/d-1/2/a/d/(a+a*sin(d*x+c))^2-2/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x,4,3*csc(d*x+c)/a^3/d-1/2*csc(d*x+c)^2/a^3/d+6*ln(sin(d*x+c))/a^3/d-6*ln(1+sin(d*x+c))/a^3/d+1/2/a/d/(a+a*sin(d*x+c))^2+3/d/(a^3+a^3*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x,4,-6*csc(d*x+c)/a^3/d+3/2*csc(d*x+c)^2/a^3/d-1/3*csc(d*x+c)^3/a^3/d-10*ln(sin(d*x+c))/a^3/d+10*ln(1+sin(d*x+c))/a^3/d-1/2/a/d/(a+a*sin(d*x+c))^2-4/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^4,x,4,10*ln(1+sin(d*x+c))/a^4/d-4*sin(d*x+c)/a^4/d+1/2*sin(d*x+c)^2/a^4/d+1/3/a/d/(a+a*sin(d*x+c))^3-5/2/d/(a^2+a^2*sin(d*x+c))^2+10/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x,4,-4*ln(1+sin(d*x+c))/a^4/d+sin(d*x+c)/a^4/d-1/3/a/d/(a+a*sin(d*x+c))^3+2/d/(a^2+a^2*sin(d*x+c))^2-6/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x,4,ln(1+sin(d*x+c))/a^4/d+1/3/a/d/(a+a*sin(d*x+c))^3-3/2/d/(a^2+a^2*sin(d*x+c))^2+3/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x,3,1/3*sin(d*x+c)^3/a/d/(a+a*sin(d*x+c))^3,1],
[cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^4,x,4,1/3/a/d/(a+a*sin(d*x+c))^3-1/2/d/(a^2+a^2*sin(d*x+c))^2,1],
[cot(d*x+c)/(a+a*sin(d*x+c))^4,x,3,ln(sin(d*x+c))/a^4/d-ln(1+sin(d*x+c))/a^4/d+1/3/a/d/(a+a*sin(d*x+c))^3+1/2/d/(a^2+a^2*sin(d*x+c))^2+1/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^4,x,4,-csc(d*x+c)/a^4/d-4*ln(sin(d*x+c))/a^4/d+4*ln(1+sin(d*x+c))/a^4/d-1/3/a/d/(a+a*sin(d*x+c))^3-1/d/(a^2+a^2*sin(d*x+c))^2-3/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^4,x,4,4*csc(d*x+c)/a^4/d-1/2*csc(d*x+c)^2/a^4/d+10*ln(sin(d*x+c))/a^4/d-10*ln(1+sin(d*x+c))/a^4/d+1/3/a/d/(a+a*sin(d*x+c))^3+3/2/d/(a^2+a^2*sin(d*x+c))^2+6/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)*sqrt(a+a*sin(d*x+c)),x,4,-2*sqrt(a)*arctanh(sqrt(a+a*sin(d*x+c))/sqrt(a))/d+2*sqrt(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x,3,a^4*sin(d*x+c)^(1+n)/d/(1+n)+4*a^4*sin(d*x+c)^(2+n)/d/(2+n)+6*a^4*sin(d*x+c)^(3+n)/d/(3+n)+4*a^4*sin(d*x+c)^(4+n)/d/(4+n)+a^4*sin(d*x+c)^(5+n)/d/(5+n),1],
[cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x,3,a^3*sin(d*x+c)^(1+n)/d/(1+n)+3*a^3*sin(d*x+c)^(2+n)/d/(2+n)+3*a^3*sin(d*x+c)^(3+n)/d/(3+n)+a^3*sin(d*x+c)^(4+n)/d/(4+n),1],
[cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x,3,a^2*sin(d*x+c)^(1+n)/d/(1+n)+2*a^2*sin(d*x+c)^(2+n)/d/(2+n)+a^2*sin(d*x+c)^(3+n)/d/(3+n),1],
[cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x,3,a*sin(d*x+c)^(1+n)/d/(1+n)+a*sin(d*x+c)^(2+n)/d/(2+n),1],
[cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x,2,hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a/d/(1+n),1],
[cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x,2,hypergeom([2, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^2/d/(1+n),1],
[cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x,2,hypergeom([3, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^3/d/(1+n),1],
[cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x,2,hypergeom([4, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^4/d/(1+n),1],
[cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,8,1/16*a*x-1/3*a*cos(d*x+c)^3/d+1/5*a*cos(d*x+c)^5/d+1/16*a*cos(d*x+c)*sin(d*x+c)/d-1/8*a*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a*cos(d*x+c)^3*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,7,1/8*a*x-1/3*a*cos(d*x+c)^3/d+1/5*a*cos(d*x+c)^5/d+1/8*a*cos(d*x+c)*sin(d*x+c)/d-1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x,6,1/8*a*x-1/3*a*cos(d*x+c)^3/d+1/8*a*cos(d*x+c)*sin(d*x+c)/d-1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+a*sin(d*x+c)),x,6,1/2*a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c)),x,7,-a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d-a*cot(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c)),x,5,-a*x+1/2*a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,5,1/2*a*arctanh(cos(d*x+c))/d-1/3*a*cot(d*x+c)^3/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,6,1/8*a*arctanh(cos(d*x+c))/d-1/3*a*cot(d*x+c)^3/d+1/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,7,1/8*a*arctanh(cos(d*x+c))/d-1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d+1/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x,12,1/8*a^2*x-2/3*a^2*cos(d*x+c)^3/d+3/5*a^2*cos(d*x+c)^5/d-1/7*a^2*cos(d*x+c)^7/d+1/8*a^2*cos(d*x+c)*sin(d*x+c)/d-1/4*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/3*a^2*cos(d*x+c)^3*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x,5,3/16*a^2*x-1/10*a^2*cos(d*x+c)^5/d+3/16*a^2*cos(d*x+c)*sin(d*x+c)/d+1/8*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/6*cos(d*x+c)^3*(a+a*sin(d*x+c))^3/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x,5,1/4*a^2*x-2/3*a^2*cos(d*x+c)^3/d+1/5*a^2*cos(d*x+c)^5/d+1/4*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+a*sin(d*x+c))^2,x,9,a^2*x-a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d-1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x,8,-1/2*a^2*x-2*a^2*arctanh(cos(d*x+c))/d+2*a^2*cos(d*x+c)/d-a^2*cot(d*x+c)/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^2,x,7,-2*a^2*x-1/2*a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d-2*a^2*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x,8,-a^2*x+a^2*arctanh(cos(d*x+c))/d-a^2*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x,9,5/8*a^2*arctanh(cos(d*x+c))/d-2/3*a^2*cot(d*x+c)^3/d-3/8*a^2*cot(d*x+c)*csc(d*x+c)/d-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x,10,1/4*a^2*arctanh(cos(d*x+c))/d-2/3*a^2*cot(d*x+c)^3/d-1/5*a^2*cot(d*x+c)^5/d+1/4*a^2*cot(d*x+c)*csc(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x,12,3/16*a^2*arctanh(cos(d*x+c))/d-2/3*a^2*cot(d*x+c)^3/d-2/5*a^2*cot(d*x+c)^5/d+3/16*a^2*cot(d*x+c)*csc(d*x+c)/d-5/24*a^2*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^2*cot(d*x+c)*csc(d*x+c)^5/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x,15,5/16*a^3*x-4/3*a^3*cos(d*x+c)^3/d+a^3*cos(d*x+c)^5/d-1/7*a^3*cos(d*x+c)^7/d+5/16*a^3*cos(d*x+c)*sin(d*x+c)/d-5/8*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/2*a^3*cos(d*x+c)^3*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x,6,7/16*a^3*x-4/3*a^3*cos(d*x+c)^3/d+3/5*a^3*cos(d*x+c)^5/d+7/16*a^3*cos(d*x+c)*sin(d*x+c)/d-7/8*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a^3*cos(d*x+c)^3*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+a*sin(d*x+c))^3,x,12,13/8*a^3*x-a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d-a^3*cos(d*x+c)^3/d+13/8*a^3*cos(d*x+c)*sin(d*x+c)/d-1/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x,10,1/2*a^3*x-3*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d-1/3*a^3*cos(d*x+c)^3/d-a^3*cot(d*x+c)/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^3,x,10,-5/2*a^3*x-5/2*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d-3*a^3*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+1/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x,10,-3*a^3*x+1/2*a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d-3*a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^3*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x,11,-a^3*x+13/8*a^3*arctanh(cos(d*x+c))/d-a^3*cot(d*x+c)/d-a^3*cot(d*x+c)^3/d-11/8*a^3*cot(d*x+c)*csc(d*x+c)/d-1/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x,12,7/8*a^3*arctanh(cos(d*x+c))/d-4/3*a^3*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d-1/8*a^3*cot(d*x+c)*csc(d*x+c)/d-3/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x,14,7/16*a^3*arctanh(cos(d*x+c))/d-4/3*a^3*cot(d*x+c)^3/d-3/5*a^3*cot(d*x+c)^5/d+7/16*a^3*cot(d*x+c)*csc(d*x+c)/d-17/24*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^3*cot(d*x+c)*csc(d*x+c)^5/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^4,x,6,21/16*a^4*x-7/8*a^4*cos(d*x+c)^3/d+21/16*a^4*cos(d*x+c)*sin(d*x+c)/d-1/6*a*cos(d*x+c)^3*(a+a*sin(d*x+c))^3/d-3/10*cos(d*x+c)^3*(a^2+a^2*sin(d*x+c))^2/d-21/40*cos(d*x+c)^3*(a^4+a^4*sin(d*x+c))/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+a*sin(d*x+c))^4,x,15,5/2*a^4*x-a^4*arctanh(cos(d*x+c))/d+a^4*cos(d*x+c)/d-7/3*a^4*cos(d*x+c)^3/d+1/5*a^4*cos(d*x+c)^5/d+5/2*a^4*cos(d*x+c)*sin(d*x+c)/d-a^4*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^4,x,12,17/8*a^4*x-4*a^4*arctanh(cos(d*x+c))/d+4*a^4*cos(d*x+c)/d-4/3*a^4*cos(d*x+c)^3/d-a^4*cot(d*x+c)/d+23/8*a^4*cos(d*x+c)*sin(d*x+c)/d+1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,6,3/8*x/a+cos(d*x+c)/a/d-2/3*cos(d*x+c)^3/a/d+1/5*cos(d*x+c)^5/a/d-3/8*cos(d*x+c)*sin(d*x+c)/a/d-1/4*cos(d*x+c)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,6,-3/8*x/a-cos(d*x+c)/a/d+1/3*cos(d*x+c)^3/a/d+3/8*cos(d*x+c)*sin(d*x+c)/a/d+1/4*cos(d*x+c)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,5,1/2*x/a+cos(d*x+c)/a/d-1/3*cos(d*x+c)^3/a/d-1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x,4,-1/2*x/a-cos(d*x+c)/a/d+1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)/(a+a*sin(d*x+c)),x,3,-x/a-arctanh(cos(d*x+c))/a/d,1],
[cot(d*x+c)^2/(a+a*sin(d*x+c)),x,4,arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x,5,-1/2*arctanh(cos(d*x+c))/a/d+cot(d*x+c)/a/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,5,1/2*arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d-1/3*cot(d*x+c)^3/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,6,-3/8*arctanh(cos(d*x+c))/a/d+cot(d*x+c)/a/d+1/3*cot(d*x+c)^3/a/d-3/8*cot(d*x+c)*csc(d*x+c)/a/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c)),x,6,3/8*arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d-2/3*cot(d*x+c)^3/a/d-1/5*cot(d*x+c)^5/a/d+3/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x,12,-27/8*x/a^2-4*cos(d*x+c)/a^2/d+2/3*cos(d*x+c)^3/a^2/d+11/8*cos(d*x+c)*sin(d*x+c)/a^2/d+1/4*cos(d*x+c)*sin(d*x+c)^3/a^2/d-2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,9,3*x/a^2+3*cos(d*x+c)/a^2/d-1/3*cos(d*x+c)^3/a^2/d-cos(d*x+c)*sin(d*x+c)/a^2/d+2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,8,-5/2*x/a^2-2*cos(d*x+c)/a^2/d+1/2*cos(d*x+c)*sin(d*x+c)/a^2/d-2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,3,2*x/a^2+cos(d*x+c)/a^2/d+2*cos(d*x+c)/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)/(a+a*sin(d*x+c))^2,x,5,-arctanh(cos(d*x+c))/a^2/d+2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cot(d*x+c)^2/(a+a*sin(d*x+c))^2,x,7,2*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a^2/d-2*cot(d*x+c)/a^2/d/(1+csc(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,9,-5/2*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x,11,3*arctanh(cos(d*x+c))/a^2/d-3*cot(d*x+c)/a^2/d-1/3*cot(d*x+c)^3/a^2/d+cot(d*x+c)*csc(d*x+c)/a^2/d-2*cos(d*x+c)/a^2/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,9,-11/2*x/a^3-3*cos(d*x+c)/a^3/d+1/2*cos(d*x+c)*sin(d*x+c)/a^3/d+2/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c))^2-19/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,4,3*x/a^3+3*cos(d*x+c)/a^3/d-1/3*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^3+2*cos(d*x+c)^3/a/d/(a+a*sin(d*x+c))^2,1],
[cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,3,-x/a^3-7/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c))+2/3*cos(d*x+c)/a/d/(a+a*sin(d*x+c))^2,1],
[cos(d*x+c)*cot(d*x+c)/(a+a*sin(d*x+c))^3,x,7,-arctanh(cos(d*x+c))/a^3/d+2/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c))^2+5/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cot(d*x+c)^2/(a+a*sin(d*x+c))^3,x,10,3*arctanh(cos(d*x+c))/a^3/d-cot(d*x+c)/a^3/d+2/3*cot(d*x+c)/a^3/d/(1+csc(d*x+c))^2-13/3*cot(d*x+c)/a^3/d/(1+csc(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^3,x,11,-11/2*arctanh(cos(d*x+c))/a^3/d+3*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d+2/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c))^2+17/3*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(f*x+e)^2*sin(f*x+e)/(a+a*sin(f*x+e))^6,x,5,2/9*cos(f*x+e)/a/f/(a+a*sin(f*x+e))^5-19/63*cos(f*x+e)/a^2/f/(a+a*sin(f*x+e))^4+2/105*cos(f*x+e)/f/(a^2+a^2*sin(f*x+e))^3+4/315*cos(f*x+e)/f/(a^3+a^3*sin(f*x+e))^2+4/315*cos(f*x+e)/f/(a^6+a^6*sin(f*x+e)),1],
[cos(d*x+c)^2*sin(d*x+c)^3*sqrt(a+a*sin(d*x+c)),x,7,-76/495*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-38/693*a*cos(d*x+c)*sin(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+2/99*a*cos(d*x+c)*sin(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))+152/3465*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d+2/11*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+a*sin(d*x+c))/d-76/1155*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,4,-8/63*a^2*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-2/21*a*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+4/21*cos(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d-2/9*cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2)/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)*sqrt(a+a*sin(d*x+c)),x,3,-8/105*a^2*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-2/35*a*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-2/7*cos(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)*cot(d*x+c)*sqrt(a+a*sin(d*x+c)),x,5,-2*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+2/3*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+2/3*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,4,-sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+3*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-cot(d*x+c)*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^2*csc(d*x+c)*sqrt(a+a*sin(d*x+c)),x,5,5/4*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-1/4*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,6,3/8*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+3/8*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/12*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x,8,-1724/6435*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-862/9009*a^2*cos(d*x+c)*sin(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-38/1287*a^2*cos(d*x+c)*sin(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))+3448/45045*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d+6/143*a*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+a*sin(d*x+c))/d-1724/15015*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d+2/13*cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^(3/2)/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,5,-64/385*a^3*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-48/385*a^2*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-6/77*a*cos(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d+4/33*cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2)/d-2/11*cos(d*x+c)^3*(a+a*sin(d*x+c))^(5/2)/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,4,-64/315*a^3*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-16/105*a^2*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-2/21*a*cos(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d-2/9*cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2)/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,6,-2*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-2/5*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+2/5*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d+2/5*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,5,-3*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+11/3*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+5/3*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-cot(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,6,1/4*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+13/4*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-3/4*a*cot(d*x+c)*sqrt(a+a*sin(d*x+c))/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,6,13/8*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+5/24*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/4*a*cot(d*x+c)*csc(d*x+c)*sqrt(a+a*sin(d*x+c))/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2)/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3/sqrt(a+a*sin(d*x+c)),x,6,-4/45*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/63*cos(d*x+c)*sin(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+2/9*cos(d*x+c)*sin(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))+8/315*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a/d-4/105*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/a^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,4,-22/105*a*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)+12/35*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-2/7*cos(d*x+c)^3*sqrt(a+a*sin(d*x+c))/a/d,1],
[cos(d*x+c)^2*sin(d*x+c)/sqrt(a+a*sin(d*x+c)),x,2,2/15*a*cos(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-2/5*cos(d*x+c)^3/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)/sqrt(a+a*sin(d*x+c)),x,4,-2*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,4,arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d-cot(d*x+c)/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/sqrt(a+a*sin(d*x+c)),x,5,1/4*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+1/4*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,6,1/8*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+1/8*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+1/12*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x,8,2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-344/105*cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-16/35*cos(d*x+c)*sin(d*x+c)^2/a/d/sqrt(a+a*sin(d*x+c))+2/7*cos(d*x+c)*sin(d*x+c)^3/a/d/sqrt(a+a*sin(d*x+c))+76/105*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,5,-2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+18/5*cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-2/5*cos(d*x+c)^3/a/d/sqrt(a+a*sin(d*x+c))-4/5*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,4,2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-10/3*cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))+2/3*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,6,-2*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d,1],
[cot(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,6,3*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,8,-11/4*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+5/4*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,9,23/8*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-2*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-9/8*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))+7/12*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^3*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,4,1/4*a*sin(d*x+c)^4/d+1/5*a*sin(d*x+c)^5/d-1/6*a*sin(d*x+c)^6/d-1/7*a*sin(d*x+c)^7/d,1],
[cos(d*x+c)^3*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,4,1/3*a*sin(d*x+c)^3/d+1/4*a*sin(d*x+c)^4/d-1/5*a*sin(d*x+c)^5/d-1/6*a*sin(d*x+c)^6/d,1],
[cos(d*x+c)^3*sin(d*x+c)*(a+a*sin(d*x+c)),x,6,-1/4*a*cos(d*x+c)^4/d+1/3*a*sin(d*x+c)^3/d-1/5*a*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c)),x,3,2/3*(a+a*sin(d*x+c))^3/a^2/d-1/4*(a+a*sin(d*x+c))^4/a^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)*(a+a*sin(d*x+c)),x,4,a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d-1/2*a*sin(d*x+c)^2/d-1/3*a*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^2*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d-1/2*a*sin(d*x+c)^2/d,1],
[cot(d*x+c)^3*(a+a*sin(d*x+c)),x,3,-a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d,1],
[cos(d*x+c)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,4,1/3*sin(d*x+c)^3/a/d-1/4*sin(d*x+c)^4/a/d,1],
[cos(d*x+c)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x,5,1/2*sin(d*x+c)^2/a/d-1/3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^3/(a+a*sin(d*x+c)),x,2,-1/2*(a-a*sin(d*x+c))^2/a^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)/(a+a*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-ln(sin(d*x+c))/a/d,1],
[cot(d*x+c)^3/(a+a*sin(d*x+c)),x,5,csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d,1],
[cot(d*x+c)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x,4,1/2*csc(d*x+c)^2/a/d-1/3*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,4,1/3*csc(d*x+c)^3/a/d-1/4*csc(d*x+c)^4/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x,9,3/128*a*x-1/5*a*cos(d*x+c)^5/d+2/7*a*cos(d*x+c)^7/d-1/9*a*cos(d*x+c)^9/d+3/128*a*cos(d*x+c)*sin(d*x+c)/d+1/64*a*cos(d*x+c)^3*sin(d*x+c)/d-1/16*a*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,9,3/128*a*x-1/5*a*cos(d*x+c)^5/d+1/7*a*cos(d*x+c)^7/d+3/128*a*cos(d*x+c)*sin(d*x+c)/d+1/64*a*cos(d*x+c)^3*sin(d*x+c)/d-1/16*a*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,8,1/16*a*x-1/5*a*cos(d*x+c)^5/d+1/7*a*cos(d*x+c)^7/d+1/16*a*cos(d*x+c)*sin(d*x+c)/d+1/24*a*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x,7,1/16*a*x-1/5*a*cos(d*x+c)^5/d+1/16*a*cos(d*x+c)*sin(d*x+c)/d+1/24*a*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+a*sin(d*x+c)),x,8,3/8*a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d+3/8*a*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+a*sin(d*x+c)),x,10,-3/2*a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d-a*cot(d*x+c)/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+a*sin(d*x+c)),x,11,-3/2*a*x+3/2*a*arctanh(cos(d*x+c))/d-a*cos(d*x+c)/d-a*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c)),x,10,a*x+3/2*a*arctanh(cos(d*x+c))/d-a*cos(d*x+c)/d+a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c)),x,7,a*x-3/8*a*arctanh(cos(d*x+c))/d+a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d+3/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)^3*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,6,-3/8*a*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d+3/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)^3*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,7,-1/16*a*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d-1/16*a*cot(d*x+c)*csc(d*x+c)/d+1/8*a*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,8,-1/16*a*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d-1/7*a*cot(d*x+c)^7/d-1/16*a*cot(d*x+c)*csc(d*x+c)/d+1/8*a*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c)),x,9,-3/128*a*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d-1/7*a*cot(d*x+c)^7/d-3/128*a*cot(d*x+c)*csc(d*x+c)/d-1/64*a*cot(d*x+c)*csc(d*x+c)^3/d+1/16*a*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x,16,9/256*a^2*x-2/5*a^2*cos(d*x+c)^5/d+4/7*a^2*cos(d*x+c)^7/d-2/9*a^2*cos(d*x+c)^9/d+9/256*a^2*cos(d*x+c)*sin(d*x+c)/d+3/128*a^2*cos(d*x+c)^3*sin(d*x+c)/d-3/32*a^2*cos(d*x+c)^5*sin(d*x+c)/d-3/16*a^2*cos(d*x+c)^5*sin(d*x+c)^3/d-1/10*a^2*cos(d*x+c)^5*sin(d*x+c)^5/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x,13,3/64*a^2*x-2/5*a^2*cos(d*x+c)^5/d+3/7*a^2*cos(d*x+c)^7/d-1/9*a^2*cos(d*x+c)^9/d+3/64*a^2*cos(d*x+c)*sin(d*x+c)/d+1/32*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/8*a^2*cos(d*x+c)^5*sin(d*x+c)/d-1/4*a^2*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x,14,11/128*a^2*x-2/5*a^2*cos(d*x+c)^5/d+2/7*a^2*cos(d*x+c)^7/d+11/128*a^2*cos(d*x+c)*sin(d*x+c)/d+11/192*a^2*cos(d*x+c)^3*sin(d*x+c)/d-11/48*a^2*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a^2*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x,6,1/8*a^2*x-1/15*a^2*cos(d*x+c)^5/d+1/8*a^2*cos(d*x+c)*sin(d*x+c)/d+1/12*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/7*cos(d*x+c)^5*(a+a*sin(d*x+c))^2/d-1/21*cos(d*x+c)^5*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+a*sin(d*x+c))^2,x,11,3/4*a^2*x-a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)^3/d-1/5*a^2*cos(d*x+c)^5/d+3/4*a^2*cos(d*x+c)*sin(d*x+c)/d+1/2*a^2*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x,13,-9/8*a^2*x-2*a^2*arctanh(cos(d*x+c))/d+2*a^2*cos(d*x+c)/d+2/3*a^2*cos(d*x+c)^3/d-a^2*cot(d*x+c)/d+1/8*a^2*cos(d*x+c)*sin(d*x+c)/d-1/4*a^2*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x,12,-3*a^2*x+1/2*a^2*arctanh(cos(d*x+c))/d+1/3*a^2*cos(d*x+c)^3/d-2*a^2*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d-a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x,12,-1/2*a^2*x+3*a^2*arctanh(cos(d*x+c))/d-2*a^2*cos(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)*csc(d*x+c)/d-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^2,x,13,2*a^2*x+9/8*a^2*arctanh(cos(d*x+c))/d-a^2*cos(d*x+c)/d+2*a^2*cot(d*x+c)/d-2/3*a^2*cot(d*x+c)^3/d+1/8*a^2*cot(d*x+c)*csc(d*x+c)/d-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x,10,a^2*x-3/4*a^2*arctanh(cos(d*x+c))/d+a^2*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-1/5*a^2*cot(d*x+c)^5/d+3/4*a^2*cot(d*x+c)*csc(d*x+c)/d-1/2*a^2*cot(d*x+c)^3*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x,11,-7/16*a^2*arctanh(cos(d*x+c))/d-2/5*a^2*cot(d*x+c)^5/d+5/16*a^2*cot(d*x+c)*csc(d*x+c)/d-1/4*a^2*cot(d*x+c)^3*csc(d*x+c)/d+1/8*a^2*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^2*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x,14,-11/128*a^2*arctanh(cos(d*x+c))/d-2/5*a^2*cot(d*x+c)^5/d-2/7*a^2*cot(d*x+c)^7/d-11/128*a^2*cot(d*x+c)*csc(d*x+c)/d+7/64*a^2*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^2*cot(d*x+c)^3*csc(d*x+c)^3/d+1/16*a^2*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cot(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x,13,-3/64*a^2*arctanh(cos(d*x+c))/d-2/5*a^2*cot(d*x+c)^5/d-3/7*a^2*cot(d*x+c)^7/d-1/9*a^2*cot(d*x+c)^9/d-3/64*a^2*cot(d*x+c)*csc(d*x+c)/d-1/32*a^2*cot(d*x+c)*csc(d*x+c)^3/d+1/8*a^2*cot(d*x+c)*csc(d*x+c)^5/d-1/4*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cot(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x,16,-9/256*a^2*arctanh(cos(d*x+c))/d-2/5*a^2*cot(d*x+c)^5/d-4/7*a^2*cot(d*x+c)^7/d-2/9*a^2*cot(d*x+c)^9/d-9/256*a^2*cot(d*x+c)*csc(d*x+c)/d-3/128*a^2*cot(d*x+c)*csc(d*x+c)^3/d+9/160*a^2*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d+3/80*a^2*cot(d*x+c)*csc(d*x+c)^7/d-1/10*a^2*cot(d*x+c)^3*csc(d*x+c)^7/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x,19,15/256*a^3*x-4/5*a^3*cos(d*x+c)^5/d+9/7*a^3*cos(d*x+c)^7/d-2/3*a^3*cos(d*x+c)^9/d+1/11*a^3*cos(d*x+c)^11/d+15/256*a^3*cos(d*x+c)*sin(d*x+c)/d+5/128*a^3*cos(d*x+c)^3*sin(d*x+c)/d-5/32*a^3*cos(d*x+c)^5*sin(d*x+c)/d-5/16*a^3*cos(d*x+c)^5*sin(d*x+c)^3/d-3/10*a^3*cos(d*x+c)^5*sin(d*x+c)^5/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x,19,21/256*a^3*x-4/5*a^3*cos(d*x+c)^5/d+a^3*cos(d*x+c)^7/d-1/3*a^3*cos(d*x+c)^9/d+21/256*a^3*cos(d*x+c)*sin(d*x+c)/d+7/128*a^3*cos(d*x+c)^3*sin(d*x+c)/d-7/32*a^3*cos(d*x+c)^5*sin(d*x+c)/d-7/16*a^3*cos(d*x+c)^5*sin(d*x+c)^3/d-1/10*a^3*cos(d*x+c)^5*sin(d*x+c)^5/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x,17,17/128*a^3*x-4/5*a^3*cos(d*x+c)^5/d+5/7*a^3*cos(d*x+c)^7/d-1/9*a^3*cos(d*x+c)^9/d+17/128*a^3*cos(d*x+c)*sin(d*x+c)/d+17/192*a^3*cos(d*x+c)^3*sin(d*x+c)/d-17/48*a^3*cos(d*x+c)^5*sin(d*x+c)/d-3/8*a^3*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x,7,27/128*a^3*x-9/80*a^3*cos(d*x+c)^5/d+27/128*a^3*cos(d*x+c)*sin(d*x+c)/d+9/64*a^3*cos(d*x+c)^3*sin(d*x+c)/d-3/56*a*cos(d*x+c)^5*(a+a*sin(d*x+c))^2/d-1/8*cos(d*x+c)^5*(a+a*sin(d*x+c))^3/d-9/112*cos(d*x+c)^5*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+a*sin(d*x+c))^3,x,15,19/16*a^3*x-a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d-3/5*a^3*cos(d*x+c)^5/d+19/16*a^3*cos(d*x+c)*sin(d*x+c)/d+19/24*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a^3*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x,15,-3/8*a^3*x-3*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d+a^3*cos(d*x+c)^3/d-1/5*a^3*cos(d*x+c)^5/d-a^3*cot(d*x+c)/d+11/8*a^3*cos(d*x+c)*sin(d*x+c)/d-3/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x,15,-33/8*a^3*x-3/2*a^3*arctanh(cos(d*x+c))/d+2*a^3*cos(d*x+c)/d+a^3*cos(d*x+c)^3/d-3*a^3*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d-7/8*a^3*cos(d*x+c)*sin(d*x+c)/d-1/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^3,x,14,-7/2*a^3*x+7/2*a^3*arctanh(cos(d*x+c))/d-2*a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d-2*a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^3*cot(d*x+c)*csc(d*x+c)/d-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^3,x,15,3/2*a^3*x+33/8*a^3*arctanh(cos(d*x+c))/d-3*a^3*cos(d*x+c)/d+2*a^3*cot(d*x+c)/d-a^3*cot(d*x+c)^3/d-7/8*a^3*cot(d*x+c)*csc(d*x+c)/d-1/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x,15,3*a^3*x+3/8*a^3*arctanh(cos(d*x+c))/d-a^3*cos(d*x+c)/d+3*a^3*cot(d*x+c)/d-a^3*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d+11/8*a^3*cot(d*x+c)*csc(d*x+c)/d-3/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x,14,a^3*x-19/16*a^3*arctanh(cos(d*x+c))/d+a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/5*a^3*cot(d*x+c)^5/d+17/16*a^3*cot(d*x+c)*csc(d*x+c)/d-3/4*a^3*cot(d*x+c)^3*csc(d*x+c)/d+1/8*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x,14,-9/16*a^3*arctanh(cos(d*x+c))/d-4/5*a^3*cot(d*x+c)^5/d-1/7*a^3*cot(d*x+c)^7/d+3/16*a^3*cot(d*x+c)*csc(d*x+c)/d-1/4*a^3*cot(d*x+c)^3*csc(d*x+c)/d+3/8*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/2*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x,16,-27/128*a^3*arctanh(cos(d*x+c))/d-4/5*a^3*cot(d*x+c)^5/d-3/7*a^3*cot(d*x+c)^7/d-27/128*a^3*cot(d*x+c)*csc(d*x+c)/d+23/64*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/2*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d+1/16*a^3*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cot(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x,17,-17/128*a^3*arctanh(cos(d*x+c))/d-4/5*a^3*cot(d*x+c)^5/d-5/7*a^3*cot(d*x+c)^7/d-1/9*a^3*cot(d*x+c)^9/d-17/128*a^3*cot(d*x+c)*csc(d*x+c)/d+5/64*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d+3/16*a^3*cot(d*x+c)*csc(d*x+c)^5/d-3/8*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cot(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x,19,-21/256*a^3*arctanh(cos(d*x+c))/d-4/5*a^3*cot(d*x+c)^5/d-a^3*cot(d*x+c)^7/d-1/3*a^3*cot(d*x+c)^9/d-21/256*a^3*cot(d*x+c)*csc(d*x+c)/d-7/128*a^3*cot(d*x+c)*csc(d*x+c)^3/d+29/160*a^3*cot(d*x+c)*csc(d*x+c)^5/d-3/8*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d+3/80*a^3*cot(d*x+c)*csc(d*x+c)^7/d-1/10*a^3*cot(d*x+c)^3*csc(d*x+c)^7/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x,8,55/256*a^4*x-11/112*a^4*cos(d*x+c)^7/d+55/256*a^4*cos(d*x+c)*sin(d*x+c)/d+55/384*a^4*cos(d*x+c)^3*sin(d*x+c)/d+11/96*a^4*cos(d*x+c)^5*sin(d*x+c)/d-1/10*cos(d*x+c)^5*(a+a*sin(d*x+c))^5/a/d-1/18*cos(d*x+c)^7*(a^2+a^2*sin(d*x+c))^2/d-11/144*cos(d*x+c)^7*(a^4+a^4*sin(d*x+c))/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x,17,-61/8*a^4*x+2*a^4*arctanh(cos(d*x+c))/d+4/3*a^4*cos(d*x+c)^3/d-5*a^4*cot(d*x+c)/d-1/3*a^4*cot(d*x+c)^3/d-2*a^4*cot(d*x+c)*csc(d*x+c)/d-19/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,8,1/16*x/a+1/3*cos(d*x+c)^3/a/d-2/5*cos(d*x+c)^5/a/d+1/7*cos(d*x+c)^7/a/d+1/16*cos(d*x+c)*sin(d*x+c)/a/d-1/8*cos(d*x+c)^3*sin(d*x+c)/a/d-1/6*cos(d*x+c)^3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,8,-1/16*x/a-1/3*cos(d*x+c)^3/a/d+1/5*cos(d*x+c)^5/a/d-1/16*cos(d*x+c)*sin(d*x+c)/a/d+1/8*cos(d*x+c)^3*sin(d*x+c)/a/d+1/6*cos(d*x+c)^3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,7,1/8*x/a+1/3*cos(d*x+c)^3/a/d-1/5*cos(d*x+c)^5/a/d+1/8*cos(d*x+c)*sin(d*x+c)/a/d-1/4*cos(d*x+c)^3*sin(d*x+c)/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x,6,-1/8*x/a-1/3*cos(d*x+c)^3/a/d-1/8*cos(d*x+c)*sin(d*x+c)/a/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a/d,1],
[cos(d*x+c)^3*cot(d*x+c)/(a+a*sin(d*x+c)),x,6,-1/2*x/a-arctanh(cos(d*x+c))/a/d+cos(d*x+c)/a/d-1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,6,-x/a+arctanh(cos(d*x+c))/a/d-cos(d*x+c)/a/d-cot(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3/(a+a*sin(d*x+c)),x,5,x/a+1/2*arctanh(cos(d*x+c))/a/d+cot(d*x+c)/a/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^4/(a+a*sin(d*x+c)),x,5,-1/2*arctanh(cos(d*x+c))/a/d-1/3*cot(d*x+c)^3/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c)),x,6,1/8*arctanh(cos(d*x+c))/a/d+1/3*cot(d*x+c)^3/a/d+1/8*cot(d*x+c)*csc(d*x+c)/a/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,7,-1/8*arctanh(cos(d*x+c))/a/d-1/3*cot(d*x+c)^3/a/d-1/5*cot(d*x+c)^5/a/d-1/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,8,1/16*arctanh(cos(d*x+c))/a/d+1/3*cot(d*x+c)^3/a/d+1/5*cot(d*x+c)^5/a/d+1/16*cot(d*x+c)*csc(d*x+c)/a/d+1/24*cot(d*x+c)*csc(d*x+c)^3/a/d-1/6*cot(d*x+c)*csc(d*x+c)^5/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x,11,-5/8*x/a^2-2*cos(d*x+c)/a^2/d+5/3*cos(d*x+c)^3/a^2/d-4/5*cos(d*x+c)^5/a^2/d+1/7*cos(d*x+c)^7/a^2/d+5/8*cos(d*x+c)*sin(d*x+c)/a^2/d+5/12*cos(d*x+c)*sin(d*x+c)^3/a^2/d+1/3*cos(d*x+c)*sin(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x,12,11/16*x/a^2+2*cos(d*x+c)/a^2/d-4/3*cos(d*x+c)^3/a^2/d+2/5*cos(d*x+c)^5/a^2/d-11/16*cos(d*x+c)*sin(d*x+c)/a^2/d-11/24*cos(d*x+c)*sin(d*x+c)^3/a^2/d-1/6*cos(d*x+c)*sin(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,10,-3/4*x/a^2-2*cos(d*x+c)/a^2/d+cos(d*x+c)^3/a^2/d-1/5*cos(d*x+c)^5/a^2/d+3/4*cos(d*x+c)*sin(d*x+c)/a^2/d+1/2*cos(d*x+c)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,10,7/8*x/a^2+2*cos(d*x+c)/a^2/d-2/3*cos(d*x+c)^3/a^2/d-7/8*cos(d*x+c)*sin(d*x+c)/a^2/d-1/4*cos(d*x+c)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,4,-x/a^2-2/3*cos(d*x+c)^3/a^2/d-cos(d*x+c)*sin(d*x+c)/a^2/d-cos(d*x+c)^5/d/(a+a*sin(d*x+c))^2,1],
[cos(d*x+c)^3*cot(d*x+c)/(a+a*sin(d*x+c))^2,x,4,-2*x/a^2-arctanh(cos(d*x+c))/a^2/d-cos(d*x+c)/a^2/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+a*sin(d*x+c))^2,x,6,x/a^2+2*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x,8,-3/2*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d,1],
[cot(d*x+c)^4/(a+a*sin(d*x+c))^2,x,9,arctanh(cos(d*x+c))/a^2/d-2*cot(d*x+c)/a^2/d-1/3*cot(d*x+c)^3/a^2/d+cot(d*x+c)*csc(d*x+c)/a^2/d,1],
[cot(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,10,-7/8*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d+2/3*cot(d*x+c)^3/a^2/d-7/8*cot(d*x+c)*csc(d*x+c)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^2/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x,10,3/4*arctanh(cos(d*x+c))/a^2/d-2*cot(d*x+c)/a^2/d-cot(d*x+c)^3/a^2/d-1/5*cot(d*x+c)^5/a^2/d+3/4*cot(d*x+c)*csc(d*x+c)/a^2/d+1/2*cot(d*x+c)*csc(d*x+c)^3/a^2/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x,12,-11/16*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d+4/3*cot(d*x+c)^3/a^2/d+2/5*cot(d*x+c)^5/a^2/d-11/16*cot(d*x+c)*csc(d*x+c)/a^2/d-11/24*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,12,51/8*x/a^3+7*cos(d*x+c)/a^3/d-cos(d*x+c)^3/a^3/d-19/8*cos(d*x+c)*sin(d*x+c)/a^3/d-1/4*cos(d*x+c)*sin(d*x+c)^3/a^3/d+4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,9,-11/2*x/a^3-5*cos(d*x+c)/a^3/d+1/3*cos(d*x+c)^3/a^3/d+3/2*cos(d*x+c)*sin(d*x+c)/a^3/d-4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,4,9/2*x/a^3+9/2*cos(d*x+c)/a^3/d+cos(d*x+c)^5/d/(a+a*sin(d*x+c))^3+3/2*cos(d*x+c)^3/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)/(a+a*sin(d*x+c))^3,x,5,x/a^3-arctanh(cos(d*x+c))/a^3/d+4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+a*sin(d*x+c))^3,x,7,3*arctanh(cos(d*x+c))/a^3/d-cot(d*x+c)/a^3/d-4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x,9,-9/2*arctanh(cos(d*x+c))/a^3/d+3*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d+4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cot(d*x+c)^4/(a+a*sin(d*x+c))^3,x,11,11/2*arctanh(cos(d*x+c))/a^3/d-5*cot(d*x+c)/a^3/d-1/3*cot(d*x+c)^3/a^3/d+3/2*cot(d*x+c)*csc(d*x+c)/a^3/d-4*cot(d*x+c)/a^3/d/(1+csc(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^3,x,14,-51/8*arctanh(cos(d*x+c))/a^3/d+7*cot(d*x+c)/a^3/d+cot(d*x+c)^3/a^3/d-19/8*cot(d*x+c)*csc(d*x+c)/a^3/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^3/d+4*cos(d*x+c)/a^3/d/(1+sin(d*x+c)),1],
[cos(f*x+e)^4*sin(f*x+e)/(a+a*sin(f*x+e))^6,x,2,1/7*cos(f*x+e)^5/f/(a+a*sin(f*x+e))^6-6/35*cos(f*x+e)^5/a/f/(a+a*sin(f*x+e))^5,1],
[cos(f*x+e)^4*sin(f*x+e)^2/(a+a*sin(f*x+e))^7,x,18,-1/18*a*cos(f*x+e)^7/f/(a+a*sin(f*x+e))^8+25/126*cos(f*x+e)^5/a/f/(a+a*sin(f*x+e))^6-47/315*cos(f*x+e)^5/a^2/f/(a+a*sin(f*x+e))^5,1],
[cos(f*x+e)^4*sin(f*x+e)^3/(a+a*sin(f*x+e))^8,x,24,4/11*cos(f*x+e)/a^8/f/(1+sin(f*x+e))^6-52/33*cos(f*x+e)/a^8/f/(1+sin(f*x+e))^5+617/231*cos(f*x+e)/a^8/f/(1+sin(f*x+e))^4-846/385*cos(f*x+e)/a^8/f/(1+sin(f*x+e))^3+1003/1155*cos(f*x+e)/a^8/f/(1+sin(f*x+e))^2-152/1155*cos(f*x+e)/a^8/f/(1+sin(f*x+e)),1],
[cos(d*x+c)^4*sin(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,5,-1472/45045*a^3*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-368/9009*a^2*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-46/1287*a*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))+20/143*cos(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d-2/13*cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2)/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)*sqrt(a+a*sin(d*x+c)),x,4,-64/3465*a^3*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-16/693*a^2*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-2/99*a*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))-2/11*cos(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)^3*cot(d*x+c)*sqrt(a+a*sin(d*x+c)),x,9,-2*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+8/15*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/7*a*cos(d*x+c)*sin(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+164/105*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-12/35*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,8,-sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+61/15*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+4/15*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-cot(d*x+c)*sqrt(a+a*sin(d*x+c))/d-2/5*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3*sqrt(a+a*sin(d*x+c)),x,7,13/4*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-2/3*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/4*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/3*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-1/2*cot(d*x+c)*csc(d*x+c)*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^4*sqrt(a+a*sin(d*x+c)),x,7,11/8*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-2*a*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+11/8*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/12*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^4*csc(d*x+c)*sqrt(a+a*sin(d*x+c)),x,9,-67/64*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+61/64*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+61/96*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/24*a*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c)),x,11,-31/128*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-31/128*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+97/192*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+97/240*a*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))-1/40*a*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-1/5*cot(d*x+c)*csc(d*x+c)^4*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*sqrt(a+a*sin(d*x+c)),x,13,-55/512*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-55/512*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-55/768*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+329/960*a*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+47/160*a*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-1/60*a*cot(d*x+c)*csc(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))-1/6*cot(d*x+c)*csc(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*sqrt(a+a*sin(d*x+c)),x,15,-61/1024*sqrt(a)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-61/1024*a*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-61/1536*a*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-61/1920*a*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+579/2240*a*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+193/840*a*cot(d*x+c)*csc(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))-1/84*a*cot(d*x+c)*csc(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))-1/7*cot(d*x+c)*csc(d*x+c)^6*sqrt(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,6,-256/6435*a^4*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-64/1287*a^3*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-56/1287*a^2*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))-14/429*a*cos(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d+4/39*cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2)/d-2/15*cos(d*x+c)^5*(a+a*sin(d*x+c))^(5/2)/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,5,-256/5005*a^4*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-64/1001*a^3*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-8/143*a^2*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))-6/143*a*cos(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d-2/13*cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2)/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,12,-2*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-14/45*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-34/63*a^2*cos(d*x+c)*sin(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-2/9*a^2*cos(d*x+c)*sin(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))+388/315*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d+16/105*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,10,-3*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+171/35*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+69/35*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d+4/35*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d-cot(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d-2/7*cos(d*x+c)*(a+a*sin(d*x+c))^(5/2)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x,9,9/4*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+73/20*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/5*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-3/4*a*cot(d*x+c)*sqrt(a+a*sin(d*x+c))/d-2/5*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x,8,37/8*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-8/3*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+29/24*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/3*a*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/d-1/4*a*cot(d*x+c)*csc(d*x+c)*sqrt(a+a*sin(d*x+c))/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x,11,21/64*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-2*a^2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+149/64*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+19/32*a^2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/8*a*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c))/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x,12,-165/128*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d+91/128*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+73/64*a^2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+31/80*a^2*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))-3/40*a*cot(d*x+c)*csc(d*x+c)^3*sqrt(a+a*sin(d*x+c))/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x,14,-179/512*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-179/512*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+111/256*a^2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+239/320*a^2*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+137/480*a^2*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-1/20*a*cot(d*x+c)*csc(d*x+c)^4*sqrt(a+a*sin(d*x+c))/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^(3/2)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x,16,-171/1024*a^(3/2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/d-171/1024*a^2*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-57/512*a^2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+199/640*a^2*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+1237/2240*a^2*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))+9/40*a^2*cot(d*x+c)*csc(d*x+c)^4/d/sqrt(a+a*sin(d*x+c))-1/28*a*cot(d*x+c)*csc(d*x+c)^5*sqrt(a+a*sin(d*x+c))/d-1/7*cot(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^(3/2)/d,1],
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[cos(d*x+c)^4*sin(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,5,-152/3465*a^2*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-38/693*a*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)+20/99*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c))-2/11*cos(d*x+c)^5*sqrt(a+a*sin(d*x+c))/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)/sqrt(a+a*sin(d*x+c)),x,3,8/315*a^2*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)+2/63*a*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-2/9*cos(d*x+c)^5/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)/sqrt(a+a*sin(d*x+c)),x,13,-2*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+32/15*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/5*cos(d*x+c)*sin(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+2/15*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,11,arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+4/3*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))-cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-2/3*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3/sqrt(a+a*sin(d*x+c)),x,11,9/4*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d-2*cos(d*x+c)/d/sqrt(a+a*sin(d*x+c))+1/4*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^4/sqrt(a+a*sin(d*x+c)),x,11,-7/8*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d+9/8*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+1/12*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/sqrt(a+a*sin(d*x+c)),x,15,-11/64*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d-11/64*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))+53/96*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+1/24*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^2/sqrt(a+a*sin(d*x+c)),x,17,-9/128*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/sqrt(a)/d-9/128*cot(d*x+c)/d/sqrt(a+a*sin(d*x+c))-3/64*cot(d*x+c)*csc(d*x+c)/d/sqrt(a+a*sin(d*x+c))+29/80*cot(d*x+c)*csc(d*x+c)^2/d/sqrt(a+a*sin(d*x+c))+1/40*cot(d*x+c)*csc(d*x+c)^3/d/sqrt(a+a*sin(d*x+c))-1/5*cot(d*x+c)*csc(d*x+c)^4/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x,12,-4/165*cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-2/231*cos(d*x+c)*sin(d*x+c)^3/a/d/sqrt(a+a*sin(d*x+c))+14/33*cos(d*x+c)*sin(d*x+c)^4/a/d/sqrt(a+a*sin(d*x+c))+8/1155*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d-2/11*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+a*sin(d*x+c))/a^2/d-4/385*cos(d*x+c)*(a+a*sin(d*x+c))^(3/2)/a^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,4,-46/315*a*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)+20/63*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)-2/9*cos(d*x+c)^5/a/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,2,6/35*a*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-2/7*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2),1],
[cos(d*x+c)^3*cot(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,6,-2*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+10/3*cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-2/3*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,9,3*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-cos(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-cot(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x,8,-3/4*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d+7/4*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cot(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x,10,-1/8*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-1/8*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))+11/12*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cot(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x,12,-3/64*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-3/64*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/32*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))+5/8*cot(d*x+c)*csc(d*x+c)^2/a/d/sqrt(a+a*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x,14,-3/128*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(3/2)/d-3/128*cot(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/64*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))-1/80*cot(d*x+c)*csc(d*x+c)^2/a/d/sqrt(a+a*sin(d*x+c))+19/40*cot(d*x+c)*csc(d*x+c)^3/a/d/sqrt(a+a*sin(d*x+c))-1/5*cot(d*x+c)*csc(d*x+c)^4*sqrt(a+a*sin(d*x+c))/a^2/d,1],
[cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x,18,-4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+4496/693*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))+200/231*cos(d*x+c)*sin(d*x+c)^2/a^2/d/sqrt(a+a*sin(d*x+c))-424/693*cos(d*x+c)*sin(d*x+c)^3/a^2/d/sqrt(a+a*sin(d*x+c))+46/99*cos(d*x+c)*sin(d*x+c)^4/a^2/d/sqrt(a+a*sin(d*x+c))-2/11*cos(d*x+c)*sin(d*x+c)^5/a^2/d/sqrt(a+a*sin(d*x+c))-1048/693*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x,16,4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-2048/315*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))-92/105*cos(d*x+c)*sin(d*x+c)^2/a^2/d/sqrt(a+a*sin(d*x+c))+38/63*cos(d*x+c)*sin(d*x+c)^3/a^2/d/sqrt(a+a*sin(d*x+c))-2/9*cos(d*x+c)*sin(d*x+c)^4/a^2/d/sqrt(a+a*sin(d*x+c))+472/315*cos(d*x+c)*sqrt(a+a*sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x,6,-4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+4/7*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)+2/3*cos(d*x+c)^3/a/d/(a+a*sin(d*x+c))^(3/2)-2/7*cos(d*x+c)^5/a/d/(a+a*sin(d*x+c))^(3/2)+4*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x,5,4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-2/5*cos(d*x+c)^5/d/(a+a*sin(d*x+c))^(5/2)-2/3*cos(d*x+c)^3/a/d/(a+a*sin(d*x+c))^(3/2)-4*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)/(a+a*sin(d*x+c))^(5/2),x,9,-2*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-2*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x,12,5*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-cot(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x,14,-23/4*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+9/4*cot(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x,16,45/8*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d-19/8*cot(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))+13/12*cot(d*x+c)*csc(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x,18,-363/64*arctanh(sqrt(a)*cos(d*x+c)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+149/64*cot(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))-107/96*cot(d*x+c)*csc(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))+17/24*cot(d*x+c)*csc(d*x+c)^2/a^2/d/sqrt(a+a*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x,5,a^2*cos(d*x+c)*hypergeom([-3/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+2*a^2*cos(d*x+c)*hypergeom([-3/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2)+a^2*cos(d*x+c)*hypergeom([-3/2, 3/2+1/2*n],[5/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(3+n)/d/(3+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x,3,a*cos(d*x+c)*hypergeom([-3/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+a*cos(d*x+c)*hypergeom([-3/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x,3,cos(d*x+c)*hypergeom([-1/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/a/d/(1+n)/sqrt(cos(d*x+c)^2)-cos(d*x+c)*hypergeom([-1/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/a/d/(2+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x,5,-cos(d*x+c)*sin(d*x+c)^(1+n)/a^2/d/(2+n)+(3+2*n)*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/a^2/d/(1+n)/(2+n)/sqrt(cos(d*x+c)^2)-2*cos(d*x+c)*hypergeom([1/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/a^2/d/(2+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x,4,1/6*a*sin(d*x+c)^6/d+1/7*a*sin(d*x+c)^7/d-1/4*a*sin(d*x+c)^8/d-2/9*a*sin(d*x+c)^9/d+1/10*a*sin(d*x+c)^10/d+1/11*a*sin(d*x+c)^11/d,1],
[cos(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x,4,1/5*a*sin(d*x+c)^5/d+1/6*a*sin(d*x+c)^6/d-2/7*a*sin(d*x+c)^7/d-1/4*a*sin(d*x+c)^8/d+1/9*a*sin(d*x+c)^9/d+1/10*a*sin(d*x+c)^10/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,8,-1/6*a*cos(d*x+c)^6/d+1/8*a*cos(d*x+c)^8/d+1/5*a*sin(d*x+c)^5/d-2/7*a*sin(d*x+c)^7/d+1/9*a*sin(d*x+c)^9/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,8,-1/6*a*cos(d*x+c)^6/d+1/8*a*cos(d*x+c)^8/d+1/3*a*sin(d*x+c)^3/d-2/5*a*sin(d*x+c)^5/d+1/7*a*sin(d*x+c)^7/d,1],
[cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x,6,-1/6*a*cos(d*x+c)^6/d+1/3*a*sin(d*x+c)^3/d-2/5*a*sin(d*x+c)^5/d+1/7*a*sin(d*x+c)^7/d,1],
[cos(d*x+c)^4*cot(d*x+c)*(a+a*sin(d*x+c)),x,4,a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d-a*sin(d*x+c)^2/d-2/3*a*sin(d*x+c)^3/d+1/4*a*sin(d*x+c)^4/d+1/5*a*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+a*ln(sin(d*x+c))/d-2*a*sin(d*x+c)/d-a*sin(d*x+c)^2/d+1/3*a*sin(d*x+c)^3/d+1/4*a*sin(d*x+c)^4/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-2*a*ln(sin(d*x+c))/d-2*a*sin(d*x+c)/d+1/2*a*sin(d*x+c)^2/d+1/3*a*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+a*sin(d*x+c)),x,4,2*a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-2*a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d+1/2*a*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*(a+a*sin(d*x+c)),x,3,2*a*csc(d*x+c)/d+a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d+a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+a*csc(d*x+c)^2/d+2/3*a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d-1/5*a*csc(d*x+c)^5/d+a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,6,-1/6*a*cot(d*x+c)^6/d-a*csc(d*x+c)/d+2/3*a*csc(d*x+c)^3/d-1/5*a*csc(d*x+c)^5/d,1],
[cot(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,6,-1/6*a*cot(d*x+c)^6/d-1/3*a*csc(d*x+c)^3/d+2/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d,1],
[cot(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,8,-1/6*a*cot(d*x+c)^6/d-1/8*a*cot(d*x+c)^8/d-1/3*a*csc(d*x+c)^3/d+2/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d,1],
[cot(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c)),x,8,-1/6*a*cot(d*x+c)^6/d-1/8*a*cot(d*x+c)^8/d-1/5*a*csc(d*x+c)^5/d+2/7*a*csc(d*x+c)^7/d-1/9*a*csc(d*x+c)^9/d,1],
[cot(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c)),x,4,-1/5*a*csc(d*x+c)^5/d-1/6*a*csc(d*x+c)^6/d+2/7*a*csc(d*x+c)^7/d+1/4*a*csc(d*x+c)^8/d-1/9*a*csc(d*x+c)^9/d-1/10*a*csc(d*x+c)^10/d,1],
[cot(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c)),x,4,-1/6*a*csc(d*x+c)^6/d-1/7*a*csc(d*x+c)^7/d+1/4*a*csc(d*x+c)^8/d+2/9*a*csc(d*x+c)^9/d-1/10*a*csc(d*x+c)^10/d-1/11*a*csc(d*x+c)^11/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x,4,1/4*a^2*sin(d*x+c)^4/d+2/5*a^2*sin(d*x+c)^5/d-1/6*a^2*sin(d*x+c)^6/d-4/7*a^2*sin(d*x+c)^7/d-1/8*a^2*sin(d*x+c)^8/d+2/9*a^2*sin(d*x+c)^9/d+1/10*a^2*sin(d*x+c)^10/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,4/5*(a+a*sin(d*x+c))^5/a^3/d-2*(a+a*sin(d*x+c))^6/a^4/d+13/7*(a+a*sin(d*x+c))^7/a^5/d-3/4*(a+a*sin(d*x+c))^8/a^6/d+1/9*(a+a*sin(d*x+c))^9/a^7/d,1],
[cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x,4,-4/5*(a+a*sin(d*x+c))^5/a^3/d+4/3*(a+a*sin(d*x+c))^6/a^4/d-5/7*(a+a*sin(d*x+c))^7/a^5/d+1/8*(a+a*sin(d*x+c))^8/a^6/d,1],
[cos(d*x+c)^4*cot(d*x+c)*(a+a*sin(d*x+c))^2,x,4,a^2*ln(sin(d*x+c))/d+2*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d-4/3*a^2*sin(d*x+c)^3/d-1/4*a^2*sin(d*x+c)^4/d+2/5*a^2*sin(d*x+c)^5/d+1/6*a^2*sin(d*x+c)^6/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,-a^2*csc(d*x+c)/d+2*a^2*ln(sin(d*x+c))/d-a^2*sin(d*x+c)/d-2*a^2*sin(d*x+c)^2/d-1/3*a^2*sin(d*x+c)^3/d+1/2*a^2*sin(d*x+c)^4/d+1/5*a^2*sin(d*x+c)^5/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x,4,-2*a^2*csc(d*x+c)/d-1/2*a^2*csc(d*x+c)^2/d-a^2*ln(sin(d*x+c))/d-4*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d+2/3*a^2*sin(d*x+c)^3/d+1/4*a^2*sin(d*x+c)^4/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x,4,a^2*csc(d*x+c)/d-a^2*csc(d*x+c)^2/d-1/3*a^2*csc(d*x+c)^3/d-4*a^2*ln(sin(d*x+c))/d-a^2*sin(d*x+c)/d+a^2*sin(d*x+c)^2/d+1/3*a^2*sin(d*x+c)^3/d,1],
[cot(d*x+c)^5*(a+a*sin(d*x+c))^2,x,3,4*a^2*csc(d*x+c)/d+1/2*a^2*csc(d*x+c)^2/d-2/3*a^2*csc(d*x+c)^3/d-1/4*a^2*csc(d*x+c)^4/d-a^2*ln(sin(d*x+c))/d+2*a^2*sin(d*x+c)/d+1/2*a^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^2,x,4,a^2*csc(d*x+c)/d+2*a^2*csc(d*x+c)^2/d+1/3*a^2*csc(d*x+c)^3/d-1/2*a^2*csc(d*x+c)^4/d-1/5*a^2*csc(d*x+c)^5/d+2*a^2*ln(sin(d*x+c))/d+a^2*sin(d*x+c)/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,-2*a^2*csc(d*x+c)/d+1/2*a^2*csc(d*x+c)^2/d+4/3*a^2*csc(d*x+c)^3/d+1/4*a^2*csc(d*x+c)^4/d-2/5*a^2*csc(d*x+c)^5/d-1/6*a^2*csc(d*x+c)^6/d+a^2*ln(sin(d*x+c))/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,2/3*(a+a*sin(d*x+c))^6/a^3/d-12/7*(a+a*sin(d*x+c))^7/a^4/d+13/8*(a+a*sin(d*x+c))^8/a^5/d-2/3*(a+a*sin(d*x+c))^9/a^6/d+1/10*(a+a*sin(d*x+c))^10/a^7/d,1],
[cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x,4,-2/3*(a+a*sin(d*x+c))^6/a^3/d+8/7*(a+a*sin(d*x+c))^7/a^4/d-5/8*(a+a*sin(d*x+c))^8/a^5/d+1/9*(a+a*sin(d*x+c))^9/a^6/d,1],
[cos(d*x+c)^4*cot(d*x+c)*(a+a*sin(d*x+c))^3,x,4,a^3*ln(sin(d*x+c))/d+3*a^3*sin(d*x+c)/d+1/2*a^3*sin(d*x+c)^2/d-5/3*a^3*sin(d*x+c)^3/d-5/4*a^3*sin(d*x+c)^4/d+1/5*a^3*sin(d*x+c)^5/d+1/2*a^3*sin(d*x+c)^6/d+1/7*a^3*sin(d*x+c)^7/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,-a^3*csc(d*x+c)/d+3*a^3*ln(sin(d*x+c))/d+a^3*sin(d*x+c)/d-5/2*a^3*sin(d*x+c)^2/d-5/3*a^3*sin(d*x+c)^3/d+1/4*a^3*sin(d*x+c)^4/d+3/5*a^3*sin(d*x+c)^5/d+1/6*a^3*sin(d*x+c)^6/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x,4,-3*a^3*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d+a^3*ln(sin(d*x+c))/d-5*a^3*sin(d*x+c)/d-5/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d+3/4*a^3*sin(d*x+c)^4/d+1/5*a^3*sin(d*x+c)^5/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+a*sin(d*x+c))^3,x,4,-a^3*csc(d*x+c)/d-3/2*a^3*csc(d*x+c)^2/d-1/3*a^3*csc(d*x+c)^3/d-5*a^3*ln(sin(d*x+c))/d-5*a^3*sin(d*x+c)/d+1/2*a^3*sin(d*x+c)^2/d+a^3*sin(d*x+c)^3/d+1/4*a^3*sin(d*x+c)^4/d,1],
[cot(d*x+c)^5*(a+a*sin(d*x+c))^3,x,3,5*a^3*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d-a^3*csc(d*x+c)^3/d-1/4*a^3*csc(d*x+c)^4/d-5*a^3*ln(sin(d*x+c))/d+a^3*sin(d*x+c)/d+3/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^3,x,4,5*a^3*csc(d*x+c)/d+5/2*a^3*csc(d*x+c)^2/d-1/3*a^3*csc(d*x+c)^3/d-3/4*a^3*csc(d*x+c)^4/d-1/5*a^3*csc(d*x+c)^5/d+a^3*ln(sin(d*x+c))/d+3*a^3*sin(d*x+c)/d+1/2*a^3*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,-a^3*csc(d*x+c)/d+5/2*a^3*csc(d*x+c)^2/d+5/3*a^3*csc(d*x+c)^3/d-1/4*a^3*csc(d*x+c)^4/d-3/5*a^3*csc(d*x+c)^5/d-1/6*a^3*csc(d*x+c)^6/d+3*a^3*ln(sin(d*x+c))/d+a^3*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x,4,-4*a^4*csc(d*x+c)/d-2*a^4*csc(d*x+c)^2/d-1/3*a^4*csc(d*x+c)^3/d-4*a^4*ln(sin(d*x+c))/d-10*a^4*sin(d*x+c)/d-2*a^4*sin(d*x+c)^2/d+4/3*a^4*sin(d*x+c)^3/d+a^4*sin(d*x+c)^4/d+1/5*a^4*sin(d*x+c)^5/d,1],
[cot(d*x+c)^5*(a+a*sin(d*x+c))^4,x,3,4*a^4*csc(d*x+c)/d-2*a^4*csc(d*x+c)^2/d-4/3*a^4*csc(d*x+c)^3/d-1/4*a^4*csc(d*x+c)^4/d-10*a^4*ln(sin(d*x+c))/d-4*a^4*sin(d*x+c)/d+2*a^4*sin(d*x+c)^2/d+4/3*a^4*sin(d*x+c)^3/d+1/4*a^4*sin(d*x+c)^4/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^4,x,4,10*a^4*csc(d*x+c)/d+2*a^4*csc(d*x+c)^2/d-4/3*a^4*csc(d*x+c)^3/d-a^4*csc(d*x+c)^4/d-1/5*a^4*csc(d*x+c)^5/d-4*a^4*ln(sin(d*x+c))/d+4*a^4*sin(d*x+c)/d+2*a^4*sin(d*x+c)^2/d+1/3*a^4*sin(d*x+c)^3/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,4,1/4*sin(d*x+c)^4/a/d-1/5*sin(d*x+c)^5/a/d-1/6*sin(d*x+c)^6/a/d+1/7*sin(d*x+c)^7/a/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,8,1/3*sin(d*x+c)^3/a/d-1/4*sin(d*x+c)^4/a/d-1/5*sin(d*x+c)^5/a/d+1/6*sin(d*x+c)^6/a/d,1],
[cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c)),x,6,-1/4*cos(d*x+c)^4/a/d-1/3*sin(d*x+c)^3/a/d+1/5*sin(d*x+c)^5/a/d,1],
[cos(d*x+c)^4*cot(d*x+c)/(a+a*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d-1/2*sin(d*x+c)^2/a/d+1/3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3/(a+a*sin(d*x+c)),x,4,csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d-ln(sin(d*x+c))/a/d+sin(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^4/(a+a*sin(d*x+c)),x,4,csc(d*x+c)/a/d+1/2*csc(d*x+c)^2/a/d-1/3*csc(d*x+c)^3/a/d+ln(sin(d*x+c))/a/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c)),x,5,-1/4*cot(d*x+c)^4/a/d-csc(d*x+c)/a/d+1/3*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c)),x,6,1/4*cot(d*x+c)^4/a/d+1/3*csc(d*x+c)^3/a/d-1/5*csc(d*x+c)^5/a/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,4,-1/3*csc(d*x+c)^3/a/d+1/4*csc(d*x+c)^4/a/d+1/5*csc(d*x+c)^5/a/d-1/6*csc(d*x+c)^6/a/d,1],
[cot(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,4,-1/4*csc(d*x+c)^4/a/d+1/5*csc(d*x+c)^5/a/d+1/6*csc(d*x+c)^6/a/d-1/7*csc(d*x+c)^7/a/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,4,1/4*sin(d*x+c)^4/a^2/d-2/5*sin(d*x+c)^5/a^2/d+1/6*sin(d*x+c)^6/a^2/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,1/3*sin(d*x+c)^3/a^2/d-1/2*sin(d*x+c)^4/a^2/d+1/5*sin(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,4,1/2*sin(d*x+c)^2/a^2/d-2/3*sin(d*x+c)^3/a^2/d+1/4*sin(d*x+c)^4/a^2/d,1],
[cos(d*x+c)^4*cot(d*x+c)/(a+a*sin(d*x+c))^2,x,4,ln(sin(d*x+c))/a^2/d-2*sin(d*x+c)/a^2/d+1/2*sin(d*x+c)^2/a^2/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,-csc(d*x+c)/a^2/d-2*ln(sin(d*x+c))/a^2/d+sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x,4,2*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a^2/d+ln(sin(d*x+c))/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^4/(a+a*sin(d*x+c))^2,x,3,-1/3*csc(d*x+c)^3*(a-a*sin(d*x+c))^3/a^5/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x,3,-1/2*csc(d*x+c)^2/a^2/d+2/3*csc(d*x+c)^3/a^2/d-1/4*csc(d*x+c)^4/a^2/d,1],
[cot(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,4,-1/3*csc(d*x+c)^3/a^2/d+1/2*csc(d*x+c)^4/a^2/d-1/5*csc(d*x+c)^5/a^2/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,-1/4*csc(d*x+c)^4/a^2/d+2/5*csc(d*x+c)^5/a^2/d-1/6*csc(d*x+c)^6/a^2/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,4,-4*ln(1+sin(d*x+c))/a^3/d+4*sin(d*x+c)/a^3/d-2*sin(d*x+c)^2/a^3/d+4/3*sin(d*x+c)^3/a^3/d-3/4*sin(d*x+c)^4/a^3/d+1/5*sin(d*x+c)^5/a^3/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,4,4*ln(1+sin(d*x+c))/a^3/d-4*sin(d*x+c)/a^3/d+2*sin(d*x+c)^2/a^3/d-sin(d*x+c)^3/a^3/d+1/4*sin(d*x+c)^4/a^3/d,1],
[cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,4,-4*ln(1+sin(d*x+c))/a^3/d+4*sin(d*x+c)/a^3/d-3/2*sin(d*x+c)^2/a^3/d+1/3*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^4*cot(d*x+c)/(a+a*sin(d*x+c))^3,x,4,ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d+sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2/(a+a*sin(d*x+c))^3,x,4,-csc(d*x+c)/a^3/d-3*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x,4,3*csc(d*x+c)/a^3/d-1/2*csc(d*x+c)^2/a^3/d+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d,1],
[cos(d*x+c)*cot(d*x+c)^4/(a+a*sin(d*x+c))^3,x,4,-4*csc(d*x+c)/a^3/d+3/2*csc(d*x+c)^2/a^3/d-1/3*csc(d*x+c)^3/a^3/d-4*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x,3,4*csc(d*x+c)/a^3/d-2*csc(d*x+c)^2/a^3/d+csc(d*x+c)^3/a^3/d-1/4*csc(d*x+c)^4/a^3/d+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d,1],
[cot(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^3,x,4,-4*csc(d*x+c)/a^3/d+2*csc(d*x+c)^2/a^3/d-4/3*csc(d*x+c)^3/a^3/d+3/4*csc(d*x+c)^4/a^3/d-1/5*csc(d*x+c)^5/a^3/d-4*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d,1],
[cot(d*x+c)^5/(a+a*sin(d*x+c))^4,x,3,12*csc(d*x+c)/a^4/d-4*csc(d*x+c)^2/a^4/d+4/3*csc(d*x+c)^3/a^4/d-1/4*csc(d*x+c)^4/a^4/d+16*ln(sin(d*x+c))/a^4/d-16*ln(1+sin(d*x+c))/a^4/d+4/d/(a^4+a^4*sin(d*x+c)),1],
[cot(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^4,x,4,-16*csc(d*x+c)/a^4/d+6*csc(d*x+c)^2/a^4/d-8/3*csc(d*x+c)^3/a^4/d+csc(d*x+c)^4/a^4/d-1/5*csc(d*x+c)^5/a^4/d-20*ln(sin(d*x+c))/a^4/d+20*ln(1+sin(d*x+c))/a^4/d-4/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x,3,a^3*sin(d*x+c)^(1+n)/d/(1+n)+3*a^3*sin(d*x+c)^(2+n)/d/(2+n)+a^3*sin(d*x+c)^(3+n)/d/(3+n)-5*a^3*sin(d*x+c)^(4+n)/d/(4+n)-5*a^3*sin(d*x+c)^(5+n)/d/(5+n)+a^3*sin(d*x+c)^(6+n)/d/(6+n)+3*a^3*sin(d*x+c)^(7+n)/d/(7+n)+a^3*sin(d*x+c)^(8+n)/d/(8+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x,3,a^2*sin(d*x+c)^(1+n)/d/(1+n)+2*a^2*sin(d*x+c)^(2+n)/d/(2+n)-a^2*sin(d*x+c)^(3+n)/d/(3+n)-4*a^2*sin(d*x+c)^(4+n)/d/(4+n)-a^2*sin(d*x+c)^(5+n)/d/(5+n)+2*a^2*sin(d*x+c)^(6+n)/d/(6+n)+a^2*sin(d*x+c)^(7+n)/d/(7+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x,3,a*sin(d*x+c)^(1+n)/d/(1+n)+a*sin(d*x+c)^(2+n)/d/(2+n)-2*a*sin(d*x+c)^(3+n)/d/(3+n)-2*a*sin(d*x+c)^(4+n)/d/(4+n)+a*sin(d*x+c)^(5+n)/d/(5+n)+a*sin(d*x+c)^(6+n)/d/(6+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x,3,sin(d*x+c)^(1+n)/a/d/(1+n)-sin(d*x+c)^(2+n)/a/d/(2+n)-sin(d*x+c)^(3+n)/a/d/(3+n)+sin(d*x+c)^(4+n)/a/d/(4+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x,3,sin(d*x+c)^(1+n)/a^2/d/(1+n)-2*sin(d*x+c)^(2+n)/a^2/d/(2+n)+sin(d*x+c)^(3+n)/a^2/d/(3+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x,4,-3*sin(d*x+c)^(1+n)/a^3/d/(1+n)+4*hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^3/d/(1+n)+sin(d*x+c)^(2+n)/a^3/d/(2+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x,4,sin(d*x+c)^(1+n)/a^4/d/(1+n)-4*hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^4/d+4*sin(d*x+c)^(1+n)/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c)),x,10,3/256*a*x-1/7*a*cos(d*x+c)^7/d+2/9*a*cos(d*x+c)^9/d-1/11*a*cos(d*x+c)^11/d+3/256*a*cos(d*x+c)*sin(d*x+c)/d+1/128*a*cos(d*x+c)^3*sin(d*x+c)/d+1/160*a*cos(d*x+c)^5*sin(d*x+c)/d-3/80*a*cos(d*x+c)^7*sin(d*x+c)/d-1/10*a*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,10,3/256*a*x-1/7*a*cos(d*x+c)^7/d+1/9*a*cos(d*x+c)^9/d+3/256*a*cos(d*x+c)*sin(d*x+c)/d+1/128*a*cos(d*x+c)^3*sin(d*x+c)/d+1/160*a*cos(d*x+c)^5*sin(d*x+c)/d-3/80*a*cos(d*x+c)^7*sin(d*x+c)/d-1/10*a*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,9,5/128*a*x-1/7*a*cos(d*x+c)^7/d+1/9*a*cos(d*x+c)^9/d+5/128*a*cos(d*x+c)*sin(d*x+c)/d+5/192*a*cos(d*x+c)^3*sin(d*x+c)/d+1/48*a*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a*cos(d*x+c)^7*sin(d*x+c)/d,1],
[cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c)),x,8,5/128*a*x-1/7*a*cos(d*x+c)^7/d+5/128*a*cos(d*x+c)*sin(d*x+c)/d+5/192*a*cos(d*x+c)^3*sin(d*x+c)/d+1/48*a*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a*cos(d*x+c)^7*sin(d*x+c)/d,1],
[cos(d*x+c)^5*cot(d*x+c)*(a+a*sin(d*x+c)),x,9,5/16*a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d+1/5*a*cos(d*x+c)^5/d+5/16*a*cos(d*x+c)*sin(d*x+c)/d+5/24*a*cos(d*x+c)^3*sin(d*x+c)/d+1/6*a*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2*(a+a*sin(d*x+c)),x,11,-15/8*a*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d+1/5*a*cos(d*x+c)^5/d-a*cot(d*x+c)/d-9/8*a*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3*(a+a*sin(d*x+c)),x,12,-15/8*a*x+5/2*a*arctanh(cos(d*x+c))/d-2*a*cos(d*x+c)/d-1/3*a*cos(d*x+c)^3/d-a*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d-9/8*a*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4*(a+a*sin(d*x+c)),x,11,5/2*a*x+5/2*a*arctanh(cos(d*x+c))/d-2*a*cos(d*x+c)/d-1/3*a*cos(d*x+c)^3/d+2*a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)^5*(a+a*sin(d*x+c)),x,12,5/2*a*x-15/8*a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+2*a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d+9/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*(a+a*sin(d*x+c)),x,12,-a*x-15/8*a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d-a*cot(d*x+c)/d+1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d+9/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c)),x,9,-a*x+5/16*a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d+1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d-5/16*a*cot(d*x+c)*csc(d*x+c)/d+5/24*a*cot(d*x+c)^3*csc(d*x+c)/d-1/6*a*cot(d*x+c)^5*csc(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,7,5/16*a*arctanh(cos(d*x+c))/d-1/7*a*cot(d*x+c)^7/d-5/16*a*cot(d*x+c)*csc(d*x+c)/d+5/24*a*cot(d*x+c)^3*csc(d*x+c)/d-1/6*a*cot(d*x+c)^5*csc(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,8,5/128*a*arctanh(cos(d*x+c))/d-1/7*a*cot(d*x+c)^7/d+5/128*a*cot(d*x+c)*csc(d*x+c)/d-5/64*a*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,9,5/128*a*arctanh(cos(d*x+c))/d-1/7*a*cot(d*x+c)^7/d-1/9*a*cot(d*x+c)^9/d+5/128*a*cot(d*x+c)*csc(d*x+c)/d-5/64*a*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c)),x,10,3/256*a*arctanh(cos(d*x+c))/d-1/7*a*cot(d*x+c)^7/d-1/9*a*cot(d*x+c)^9/d+3/256*a*cot(d*x+c)*csc(d*x+c)/d+1/128*a*cot(d*x+c)*csc(d*x+c)^3/d-1/32*a*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c)),x,10,3/256*a*arctanh(cos(d*x+c))/d-1/7*a*cot(d*x+c)^7/d-2/9*a*cot(d*x+c)^9/d-1/11*a*cot(d*x+c)^11/d+3/256*a*cot(d*x+c)*csc(d*x+c)/d+1/128*a*cot(d*x+c)*csc(d*x+c)^3/d-1/32*a*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x,18,17/1024*a^2*x-2/7*a^2*cos(d*x+c)^7/d+4/9*a^2*cos(d*x+c)^9/d-2/11*a^2*cos(d*x+c)^11/d+17/1024*a^2*cos(d*x+c)*sin(d*x+c)/d+17/1536*a^2*cos(d*x+c)^3*sin(d*x+c)/d+17/1920*a^2*cos(d*x+c)^5*sin(d*x+c)/d-17/320*a^2*cos(d*x+c)^7*sin(d*x+c)/d-17/120*a^2*cos(d*x+c)^7*sin(d*x+c)^3/d-1/12*a^2*cos(d*x+c)^7*sin(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x,14,3/128*a^2*x-2/7*a^2*cos(d*x+c)^7/d+1/3*a^2*cos(d*x+c)^9/d-1/11*a^2*cos(d*x+c)^11/d+3/128*a^2*cos(d*x+c)*sin(d*x+c)/d+1/64*a^2*cos(d*x+c)^3*sin(d*x+c)/d+1/80*a^2*cos(d*x+c)^5*sin(d*x+c)/d-3/40*a^2*cos(d*x+c)^7*sin(d*x+c)/d-1/5*a^2*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x,16,13/256*a^2*x-2/7*a^2*cos(d*x+c)^7/d+2/9*a^2*cos(d*x+c)^9/d+13/256*a^2*cos(d*x+c)*sin(d*x+c)/d+13/384*a^2*cos(d*x+c)^3*sin(d*x+c)/d+13/480*a^2*cos(d*x+c)^5*sin(d*x+c)/d-13/80*a^2*cos(d*x+c)^7*sin(d*x+c)/d-1/10*a^2*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^2,x,7,5/64*a^2*x-1/28*a^2*cos(d*x+c)^7/d+5/64*a^2*cos(d*x+c)*sin(d*x+c)/d+5/96*a^2*cos(d*x+c)^3*sin(d*x+c)/d+1/24*a^2*cos(d*x+c)^5*sin(d*x+c)/d-1/9*cos(d*x+c)^7*(a+a*sin(d*x+c))^2/d-1/36*cos(d*x+c)^7*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^5*cot(d*x+c)*(a+a*sin(d*x+c))^2,x,12,5/8*a^2*x-a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)^3/d+1/5*a^2*cos(d*x+c)^5/d-1/7*a^2*cos(d*x+c)^7/d+5/8*a^2*cos(d*x+c)*sin(d*x+c)/d+5/12*a^2*cos(d*x+c)^3*sin(d*x+c)/d+1/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x,17,-25/16*a^2*x-2*a^2*arctanh(cos(d*x+c))/d+2*a^2*cos(d*x+c)/d+2/3*a^2*cos(d*x+c)^3/d+2/5*a^2*cos(d*x+c)^5/d-a^2*cot(d*x+c)/d-7/16*a^2*cos(d*x+c)*sin(d*x+c)/d-7/24*a^2*cos(d*x+c)*sin(d*x+c)^3/d+1/6*a^2*cos(d*x+c)*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x,16,-15/4*a^2*x+3/2*a^2*arctanh(cos(d*x+c))/d-a^2*cos(d*x+c)/d+1/5*a^2*cos(d*x+c)^5/d-2*a^2*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d-9/4*a^2*cos(d*x+c)*sin(d*x+c)/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x,17,5/8*a^2*x+5*a^2*arctanh(cos(d*x+c))/d-4*a^2*cos(d*x+c)/d-2/3*a^2*cos(d*x+c)^3/d+a^2*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)*csc(d*x+c)/d-5/8*a^2*cos(d*x+c)*sin(d*x+c)/d+1/4*a^2*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^5*(a+a*sin(d*x+c))^2,x,16,5*a^2*x+5/8*a^2*arctanh(cos(d*x+c))/d-a^2*cos(d*x+c)/d-1/3*a^2*cos(d*x+c)^3/d+4*a^2*cot(d*x+c)/d-2/3*a^2*cot(d*x+c)^3/d+5/8*a^2*cot(d*x+c)*csc(d*x+c)/d-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d+a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*(a+a*sin(d*x+c))^2,x,15,3/2*a^2*x-15/4*a^2*arctanh(cos(d*x+c))/d+2*a^2*cos(d*x+c)/d+a^2*cot(d*x+c)/d-1/5*a^2*cot(d*x+c)^5/d+9/4*a^2*cot(d*x+c)*csc(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)^3/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^2,x,17,-2*a^2*x-25/16*a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d-2*a^2*cot(d*x+c)/d+2/3*a^2*cot(d*x+c)^3/d-2/5*a^2*cot(d*x+c)^5/d+7/16*a^2*cot(d*x+c)*csc(d*x+c)/d+7/24*a^2*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^2*cot(d*x+c)*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x,12,-a^2*x+5/8*a^2*arctanh(cos(d*x+c))/d-a^2*cot(d*x+c)/d+1/3*a^2*cot(d*x+c)^3/d-1/5*a^2*cot(d*x+c)^5/d-1/7*a^2*cot(d*x+c)^7/d-5/8*a^2*cot(d*x+c)*csc(d*x+c)/d+5/12*a^2*cot(d*x+c)^3*csc(d*x+c)/d-1/3*a^2*cot(d*x+c)^5*csc(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x,13,45/128*a^2*arctanh(cos(d*x+c))/d-2/7*a^2*cot(d*x+c)^7/d-35/128*a^2*cot(d*x+c)*csc(d*x+c)/d+5/24*a^2*cot(d*x+c)^3*csc(d*x+c)/d-1/6*a^2*cot(d*x+c)^5*csc(d*x+c)/d-5/64*a^2*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a^2*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a^2*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x,12,5/64*a^2*arctanh(cos(d*x+c))/d-2/7*a^2*cot(d*x+c)^7/d-1/9*a^2*cot(d*x+c)^9/d+5/64*a^2*cot(d*x+c)*csc(d*x+c)/d-5/32*a^2*cot(d*x+c)*csc(d*x+c)^3/d+5/24*a^2*cot(d*x+c)^3*csc(d*x+c)^3/d-1/4*a^2*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x,16,13/256*a^2*arctanh(cos(d*x+c))/d-2/7*a^2*cot(d*x+c)^7/d-2/9*a^2*cot(d*x+c)^9/d+13/256*a^2*cot(d*x+c)*csc(d*x+c)/d-9/128*a^2*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a^2*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a^2*cot(d*x+c)^5*csc(d*x+c)^3/d-1/32*a^2*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a^2*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x,14,3/128*a^2*arctanh(cos(d*x+c))/d-2/7*a^2*cot(d*x+c)^7/d-1/3*a^2*cot(d*x+c)^9/d-1/11*a^2*cot(d*x+c)^11/d+3/128*a^2*cot(d*x+c)*csc(d*x+c)/d+1/64*a^2*cot(d*x+c)*csc(d*x+c)^3/d-1/16*a^2*cot(d*x+c)*csc(d*x+c)^5/d+1/8*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d-1/5*a^2*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x,18,17/1024*a^2*arctanh(cos(d*x+c))/d-2/7*a^2*cot(d*x+c)^7/d-4/9*a^2*cot(d*x+c)^9/d-2/11*a^2*cot(d*x+c)^11/d+17/1024*a^2*cot(d*x+c)*csc(d*x+c)/d+17/1536*a^2*cot(d*x+c)*csc(d*x+c)^3/d-11/384*a^2*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a^2*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a^2*cot(d*x+c)^5*csc(d*x+c)^5/d-1/64*a^2*cot(d*x+c)*csc(d*x+c)^7/d+1/24*a^2*cot(d*x+c)^3*csc(d*x+c)^7/d-1/12*a^2*cot(d*x+c)^5*csc(d*x+c)^7/d,1],
[cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x,21,27/1024*a^3*x-4/7*a^3*cos(d*x+c)^7/d+a^3*cos(d*x+c)^9/d-6/11*a^3*cos(d*x+c)^11/d+1/13*a^3*cos(d*x+c)^13/d+27/1024*a^3*cos(d*x+c)*sin(d*x+c)/d+9/512*a^3*cos(d*x+c)^3*sin(d*x+c)/d+9/640*a^3*cos(d*x+c)^5*sin(d*x+c)/d-27/320*a^3*cos(d*x+c)^7*sin(d*x+c)/d-9/40*a^3*cos(d*x+c)^7*sin(d*x+c)^3/d-1/4*a^3*cos(d*x+c)^7*sin(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x,21,41/1024*a^3*x-4/7*a^3*cos(d*x+c)^7/d+7/9*a^3*cos(d*x+c)^9/d-3/11*a^3*cos(d*x+c)^11/d+41/1024*a^3*cos(d*x+c)*sin(d*x+c)/d+41/1536*a^3*cos(d*x+c)^3*sin(d*x+c)/d+41/1920*a^3*cos(d*x+c)^5*sin(d*x+c)/d-41/320*a^3*cos(d*x+c)^7*sin(d*x+c)/d-41/120*a^3*cos(d*x+c)^7*sin(d*x+c)^3/d-1/12*a^3*cos(d*x+c)^7*sin(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x,19,19/256*a^3*x-4/7*a^3*cos(d*x+c)^7/d+5/9*a^3*cos(d*x+c)^9/d-1/11*a^3*cos(d*x+c)^11/d+19/256*a^3*cos(d*x+c)*sin(d*x+c)/d+19/384*a^3*cos(d*x+c)^3*sin(d*x+c)/d+19/480*a^3*cos(d*x+c)^5*sin(d*x+c)/d-19/80*a^3*cos(d*x+c)^7*sin(d*x+c)/d-3/10*a^3*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^3,x,8,33/256*a^3*x-33/560*a^3*cos(d*x+c)^7/d+33/256*a^3*cos(d*x+c)*sin(d*x+c)/d+11/128*a^3*cos(d*x+c)^3*sin(d*x+c)/d+11/160*a^3*cos(d*x+c)^5*sin(d*x+c)/d-1/30*a*cos(d*x+c)^7*(a+a*sin(d*x+c))^2/d-1/10*cos(d*x+c)^7*(a+a*sin(d*x+c))^3/d-11/240*cos(d*x+c)^7*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^5*cot(d*x+c)*(a+a*sin(d*x+c))^3,x,17,125/128*a^3*x-a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d+1/5*a^3*cos(d*x+c)^5/d-3/7*a^3*cos(d*x+c)^7/d+125/128*a^3*cos(d*x+c)*sin(d*x+c)/d+125/192*a^3*cos(d*x+c)^3*sin(d*x+c)/d+25/48*a^3*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a^3*cos(d*x+c)^7*sin(d*x+c)/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x,19,-15/16*a^3*x-3*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d+a^3*cos(d*x+c)^3/d+3/5*a^3*cos(d*x+c)^5/d-1/7*a^3*cos(d*x+c)^7/d-a^3*cot(d*x+c)/d+15/16*a^3*cos(d*x+c)*sin(d*x+c)/d-11/8*a^3*cos(d*x+c)*sin(d*x+c)^3/d+1/2*a^3*cos(d*x+c)*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x,17,-85/16*a^3*x-1/2*a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d+2/3*a^3*cos(d*x+c)^3/d+3/5*a^3*cos(d*x+c)^5/d-3*a^3*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d-43/16*a^3*cos(d*x+c)*sin(d*x+c)/d+5/24*a^3*cos(d*x+c)*sin(d*x+c)^3/d+1/6*a^3*cos(d*x+c)*sin(d*x+c)^5/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4*(a+a*sin(d*x+c))^3,x,15,-25/8*a^3*x+13/2*a^3*arctanh(cos(d*x+c))/d-5*a^3*cos(d*x+c)/d-2/3*a^3*cos(d*x+c)^3/d+1/5*a^3*cos(d*x+c)^5/d-a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^3*cot(d*x+c)*csc(d*x+c)/d-23/8*a^3*cos(d*x+c)*sin(d*x+c)/d+3/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^5*(a+a*sin(d*x+c))^3,x,16,45/8*a^3*x+45/8*a^3*arctanh(cos(d*x+c))/d-5*a^3*cos(d*x+c)/d-a^3*cos(d*x+c)^3/d+5*a^3*cot(d*x+c)/d-a^3*cot(d*x+c)^3/d-3/8*a^3*cot(d*x+c)*csc(d*x+c)/d-1/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d+3/8*a^3*cos(d*x+c)*sin(d*x+c)/d+1/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cot(d*x+c)^6*(a+a*sin(d*x+c))^3,x,16,13/2*a^3*x-25/8*a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d-1/3*a^3*cos(d*x+c)^3/d+5*a^3*cot(d*x+c)/d-2/3*a^3*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d+23/8*a^3*cot(d*x+c)*csc(d*x+c)/d-3/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^3,x,18,-1/2*a^3*x-85/16*a^3*arctanh(cos(d*x+c))/d+3*a^3*cos(d*x+c)/d-a^3*cot(d*x+c)/d+2/3*a^3*cot(d*x+c)^3/d-3/5*a^3*cot(d*x+c)^5/d+43/16*a^3*cot(d*x+c)*csc(d*x+c)/d-5/24*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^3*cot(d*x+c)*csc(d*x+c)^5/d+1/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x,18,-3*a^3*x-15/16*a^3*arctanh(cos(d*x+c))/d+a^3*cos(d*x+c)/d-3*a^3*cot(d*x+c)/d+a^3*cot(d*x+c)^3/d-3/5*a^3*cot(d*x+c)^5/d-1/7*a^3*cot(d*x+c)^7/d-15/16*a^3*cot(d*x+c)*csc(d*x+c)/d+11/8*a^3*cot(d*x+c)*csc(d*x+c)^3/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x,17,-a^3*x+125/128*a^3*arctanh(cos(d*x+c))/d-a^3*cot(d*x+c)/d+1/3*a^3*cot(d*x+c)^3/d-1/5*a^3*cot(d*x+c)^5/d-3/7*a^3*cot(d*x+c)^7/d-115/128*a^3*cot(d*x+c)*csc(d*x+c)/d+5/8*a^3*cot(d*x+c)^3*csc(d*x+c)/d-1/2*a^3*cot(d*x+c)^5*csc(d*x+c)/d-5/64*a^3*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a^3*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x,16,55/128*a^3*arctanh(cos(d*x+c))/d-4/7*a^3*cot(d*x+c)^7/d-1/9*a^3*cot(d*x+c)^9/d-25/128*a^3*cot(d*x+c)*csc(d*x+c)/d+5/24*a^3*cot(d*x+c)^3*csc(d*x+c)/d-1/6*a^3*cot(d*x+c)^5*csc(d*x+c)/d-15/64*a^3*cot(d*x+c)*csc(d*x+c)^3/d+5/16*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d-3/8*a^3*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x,18,33/256*a^3*arctanh(cos(d*x+c))/d-4/7*a^3*cot(d*x+c)^7/d-1/3*a^3*cot(d*x+c)^9/d+33/256*a^3*cot(d*x+c)*csc(d*x+c)/d-29/128*a^3*cot(d*x+c)*csc(d*x+c)^3/d+5/16*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d-3/8*a^3*cot(d*x+c)^5*csc(d*x+c)^3/d-1/32*a^3*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a^3*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x,19,19/256*a^3*arctanh(cos(d*x+c))/d-4/7*a^3*cot(d*x+c)^7/d-5/9*a^3*cot(d*x+c)^9/d-1/11*a^3*cot(d*x+c)^11/d+19/256*a^3*cot(d*x+c)*csc(d*x+c)/d-7/128*a^3*cot(d*x+c)*csc(d*x+c)^3/d+5/48*a^3*cot(d*x+c)^3*csc(d*x+c)^3/d-1/8*a^3*cot(d*x+c)^5*csc(d*x+c)^3/d-3/32*a^3*cot(d*x+c)*csc(d*x+c)^5/d+3/16*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d-3/10*a^3*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x,21,41/1024*a^3*arctanh(cos(d*x+c))/d-4/7*a^3*cot(d*x+c)^7/d-7/9*a^3*cot(d*x+c)^9/d-3/11*a^3*cot(d*x+c)^11/d+41/1024*a^3*cot(d*x+c)*csc(d*x+c)/d+41/1536*a^3*cot(d*x+c)*csc(d*x+c)^3/d-35/384*a^3*cot(d*x+c)*csc(d*x+c)^5/d+3/16*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d-3/10*a^3*cot(d*x+c)^5*csc(d*x+c)^5/d-1/64*a^3*cot(d*x+c)*csc(d*x+c)^7/d+1/24*a^3*cot(d*x+c)^3*csc(d*x+c)^7/d-1/12*a^3*cot(d*x+c)^5*csc(d*x+c)^7/d,1],
[cot(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x,21,27/1024*a^3*arctanh(cos(d*x+c))/d-4/7*a^3*cot(d*x+c)^7/d-a^3*cot(d*x+c)^9/d-6/11*a^3*cot(d*x+c)^11/d-1/13*a^3*cot(d*x+c)^13/d+27/1024*a^3*cot(d*x+c)*csc(d*x+c)/d+9/512*a^3*cot(d*x+c)*csc(d*x+c)^3/d-3/128*a^3*cot(d*x+c)*csc(d*x+c)^5/d+1/16*a^3*cot(d*x+c)^3*csc(d*x+c)^5/d-1/10*a^3*cot(d*x+c)^5*csc(d*x+c)^5/d-3/64*a^3*cot(d*x+c)*csc(d*x+c)^7/d+1/8*a^3*cot(d*x+c)^3*csc(d*x+c)^7/d-1/4*a^3*cot(d*x+c)^5*csc(d*x+c)^7/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x,22,-135/16*a^4*x+6*a^4*arctanh(cos(d*x+c))/d-4*a^4*cos(d*x+c)/d+4/5*a^4*cos(d*x+c)^5/d-4*a^4*cot(d*x+c)/d-1/3*a^4*cot(d*x+c)^3/d-2*a^4*cot(d*x+c)*csc(d*x+c)/d-89/16*a^4*cos(d*x+c)*sin(d*x+c)/d+23/24*a^4*cos(d*x+c)*sin(d*x+c)^3/d+1/6*a^4*cos(d*x+c)*sin(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,9,3/128*x/a+1/5*cos(d*x+c)^5/a/d-2/7*cos(d*x+c)^7/a/d+1/9*cos(d*x+c)^9/a/d+3/128*cos(d*x+c)*sin(d*x+c)/a/d+1/64*cos(d*x+c)^3*sin(d*x+c)/a/d-1/16*cos(d*x+c)^5*sin(d*x+c)/a/d-1/8*cos(d*x+c)^5*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,9,-3/128*x/a-1/5*cos(d*x+c)^5/a/d+1/7*cos(d*x+c)^7/a/d-3/128*cos(d*x+c)*sin(d*x+c)/a/d-1/64*cos(d*x+c)^3*sin(d*x+c)/a/d+1/16*cos(d*x+c)^5*sin(d*x+c)/a/d+1/8*cos(d*x+c)^5*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,8,1/16*x/a+1/5*cos(d*x+c)^5/a/d-1/7*cos(d*x+c)^7/a/d+1/16*cos(d*x+c)*sin(d*x+c)/a/d+1/24*cos(d*x+c)^3*sin(d*x+c)/a/d-1/6*cos(d*x+c)^5*sin(d*x+c)/a/d,1],
[cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c)),x,7,-1/16*x/a-1/5*cos(d*x+c)^5/a/d-1/16*cos(d*x+c)*sin(d*x+c)/a/d-1/24*cos(d*x+c)^3*sin(d*x+c)/a/d+1/6*cos(d*x+c)^5*sin(d*x+c)/a/d,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+a*sin(d*x+c)),x,8,-3/8*x/a-arctanh(cos(d*x+c))/a/d+cos(d*x+c)/a/d+1/3*cos(d*x+c)^3/a/d-3/8*cos(d*x+c)*sin(d*x+c)/a/d-1/4*cos(d*x+c)^3*sin(d*x+c)/a/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,10,-3/2*x/a+arctanh(cos(d*x+c))/a/d-cos(d*x+c)/a/d-1/3*cos(d*x+c)^3/a/d-cot(d*x+c)/a/d-1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+a*sin(d*x+c)),x,11,3/2*x/a+3/2*arctanh(cos(d*x+c))/a/d-cos(d*x+c)/a/d+cot(d*x+c)/a/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d+1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+a*sin(d*x+c)),x,9,x/a-3/2*arctanh(cos(d*x+c))/a/d+cos(d*x+c)/a/d+cot(d*x+c)/a/d-1/3*cot(d*x+c)^3/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^5/(a+a*sin(d*x+c)),x,7,-x/a-3/8*arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d+1/3*cot(d*x+c)^3/a/d+3/8*cot(d*x+c)*csc(d*x+c)/a/d-1/4*cot(d*x+c)^3*csc(d*x+c)/a/d,1],
[cot(d*x+c)^6/(a+a*sin(d*x+c)),x,6,3/8*arctanh(cos(d*x+c))/a/d-1/5*cot(d*x+c)^5/a/d-3/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)^3*csc(d*x+c)/a/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,13,-1/8*x/a^2-2/3*cos(d*x+c)^3/a^2/d+3/5*cos(d*x+c)^5/a^2/d-1/7*cos(d*x+c)^7/a^2/d-1/8*cos(d*x+c)*sin(d*x+c)/a^2/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a^2/d+1/3*cos(d*x+c)^3*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,6,3/16*x/a^2+1/10*cos(d*x+c)^5/a^2/d+3/16*cos(d*x+c)*sin(d*x+c)/a^2/d+1/8*cos(d*x+c)^3*sin(d*x+c)/a^2/d+1/6*cos(d*x+c)^3*(a-a*sin(d*x+c))^3/a^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,5,-1/4*x/a^2-2/15*cos(d*x+c)^5/a^2/d-1/4*cos(d*x+c)*sin(d*x+c)/a^2/d-1/6*cos(d*x+c)^3*sin(d*x+c)/a^2/d-1/3*cos(d*x+c)^7/d/(a+a*sin(d*x+c))^2,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+a*sin(d*x+c))^2,x,10,-x/a^2-arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/a^2/d-1/3*cos(d*x+c)^3/a^2/d-cos(d*x+c)*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+a*sin(d*x+c))^2,x,9,-1/2*x/a^2+2*arctanh(cos(d*x+c))/a^2/d-2*cos(d*x+c)/a^2/d-cot(d*x+c)/a^2/d+1/2*cos(d*x+c)*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x,8,2*x/a^2-1/2*arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+a*sin(d*x+c))^2,x,9,-x/a^2-arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a^2/d-1/3*cot(d*x+c)^3/a^2/d+cot(d*x+c)*csc(d*x+c)/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x,10,5/8*arctanh(cos(d*x+c))/a^2/d+2/3*cot(d*x+c)^3/a^2/d-3/8*cot(d*x+c)*csc(d*x+c)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^2/d,1],
[cot(d*x+c)^6/(a+a*sin(d*x+c))^2,x,11,-1/4*arctanh(cos(d*x+c))/a^2/d-2/3*cot(d*x+c)^3/a^2/d-1/5*cot(d*x+c)^5/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)/a^2/d+1/2*cot(d*x+c)*csc(d*x+c)^3/a^2/d,1],
[cot(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,13,3/16*arctanh(cos(d*x+c))/a^2/d+2/3*cot(d*x+c)^3/a^2/d+2/5*cot(d*x+c)^5/a^2/d+3/16*cot(d*x+c)*csc(d*x+c)/a^2/d-5/24*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,14,-23/16*x/a^3-4*cos(d*x+c)/a^3/d+7/3*cos(d*x+c)^3/a^3/d-3/5*cos(d*x+c)^5/a^3/d+23/16*cos(d*x+c)*sin(d*x+c)/a^3/d+23/24*cos(d*x+c)*sin(d*x+c)^3/a^3/d+1/6*cos(d*x+c)*sin(d*x+c)^5/a^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,12,13/8*x/a^3+4*cos(d*x+c)/a^3/d-5/3*cos(d*x+c)^3/a^3/d+1/5*cos(d*x+c)^5/a^3/d-13/8*cos(d*x+c)*sin(d*x+c)/a^3/d-3/4*cos(d*x+c)*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,5,-15/8*x/a^3-4*cos(d*x+c)/a^3/d+cos(d*x+c)^3/a^3/d+15/8*cos(d*x+c)*sin(d*x+c)/a^3/d+1/4*cos(d*x+c)*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+a*sin(d*x+c))^3,x,7,-7/2*x/a^3-arctanh(cos(d*x+c))/a^3/d-3*cos(d*x+c)/a^3/d+1/2*cos(d*x+c)*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+a*sin(d*x+c))^3,x,7,3*x/a^3+3*arctanh(cos(d*x+c))/a^3/d+cos(d*x+c)/a^3/d-cot(d*x+c)/a^3/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x,8,-x/a^3-7/2*arctanh(cos(d*x+c))/a^3/d+3*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+a*sin(d*x+c))^3,x,10,5/2*arctanh(cos(d*x+c))/a^3/d-4*cot(d*x+c)/a^3/d-1/3*cot(d*x+c)^3/a^3/d+3/2*cot(d*x+c)*csc(d*x+c)/a^3/d,1],
[cos(d*x+c)*cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x,12,-15/8*arctanh(cos(d*x+c))/a^3/d+4*cot(d*x+c)/a^3/d+cot(d*x+c)^3/a^3/d-15/8*cot(d*x+c)*csc(d*x+c)/a^3/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^3/d,1],
[cot(d*x+c)^6/(a+a*sin(d*x+c))^3,x,12,13/8*arctanh(cos(d*x+c))/a^3/d-4*cot(d*x+c)/a^3/d-5/3*cot(d*x+c)^3/a^3/d-1/5*cot(d*x+c)^5/a^3/d+13/8*cot(d*x+c)*csc(d*x+c)/a^3/d+3/4*cot(d*x+c)*csc(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x,6,a^3*cos(d*x+c)*hypergeom([-5/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+3*a^3*cos(d*x+c)*hypergeom([-5/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2)+3*a^3*cos(d*x+c)*hypergeom([-5/2, 3/2+1/2*n],[5/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(3+n)/d/(3+n)/sqrt(cos(d*x+c)^2)+a^3*cos(d*x+c)*hypergeom([-5/2, 2+1/2*n],[3+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(4+n)/d/(4+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x,5,a^2*cos(d*x+c)*hypergeom([-5/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+2*a^2*cos(d*x+c)*hypergeom([-5/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2)+a^2*cos(d*x+c)*hypergeom([-5/2, 3/2+1/2*n],[5/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(3+n)/d/(3+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x,3,a*cos(d*x+c)*hypergeom([-5/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+a*cos(d*x+c)*hypergeom([-5/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^7*sin(d*x+c)^6*(a+a*sin(d*x+c)),x,4,1/7*a*sin(d*x+c)^7/d+1/8*a*sin(d*x+c)^8/d-1/3*a*sin(d*x+c)^9/d-3/10*a*sin(d*x+c)^10/d+3/11*a*sin(d*x+c)^11/d+1/4*a*sin(d*x+c)^12/d-1/13*a*sin(d*x+c)^13/d-1/14*a*sin(d*x+c)^14/d,1],
[cos(d*x+c)^7*sin(d*x+c)^5*(a+a*sin(d*x+c)),x,8,-1/8*a*cos(d*x+c)^8/d+1/5*a*cos(d*x+c)^10/d-1/12*a*cos(d*x+c)^12/d+1/7*a*sin(d*x+c)^7/d-1/3*a*sin(d*x+c)^9/d+3/11*a*sin(d*x+c)^11/d-1/13*a*sin(d*x+c)^13/d,1],
[cos(d*x+c)^7*sin(d*x+c)^4*(a+a*sin(d*x+c)),x,8,-1/8*a*cos(d*x+c)^8/d+1/5*a*cos(d*x+c)^10/d-1/12*a*cos(d*x+c)^12/d+1/5*a*sin(d*x+c)^5/d-3/7*a*sin(d*x+c)^7/d+1/3*a*sin(d*x+c)^9/d-1/11*a*sin(d*x+c)^11/d,1],
[cos(d*x+c)^7*sin(d*x+c)^3*(a+a*sin(d*x+c)),x,8,-1/8*a*cos(d*x+c)^8/d+1/10*a*cos(d*x+c)^10/d+1/5*a*sin(d*x+c)^5/d-3/7*a*sin(d*x+c)^7/d+1/3*a*sin(d*x+c)^9/d-1/11*a*sin(d*x+c)^11/d,1],
[cos(d*x+c)^7*sin(d*x+c)^2*(a+a*sin(d*x+c)),x,8,-1/8*a*cos(d*x+c)^8/d+1/10*a*cos(d*x+c)^10/d+1/3*a*sin(d*x+c)^3/d-3/5*a*sin(d*x+c)^5/d+3/7*a*sin(d*x+c)^7/d-1/9*a*sin(d*x+c)^9/d,1],
[cos(d*x+c)^7*sin(d*x+c)*(a+a*sin(d*x+c)),x,6,-1/8*a*cos(d*x+c)^8/d+1/3*a*sin(d*x+c)^3/d-3/5*a*sin(d*x+c)^5/d+3/7*a*sin(d*x+c)^7/d-1/9*a*sin(d*x+c)^9/d,1],
[cos(d*x+c)^6*cot(d*x+c)*(a+a*sin(d*x+c)),x,4,a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d-3/2*a*sin(d*x+c)^2/d-a*sin(d*x+c)^3/d+3/4*a*sin(d*x+c)^4/d+3/5*a*sin(d*x+c)^5/d-1/6*a*sin(d*x+c)^6/d-1/7*a*sin(d*x+c)^7/d,1],
[cos(d*x+c)^5*cot(d*x+c)^2*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+a*ln(sin(d*x+c))/d-3*a*sin(d*x+c)/d-3/2*a*sin(d*x+c)^2/d+a*sin(d*x+c)^3/d+3/4*a*sin(d*x+c)^4/d-1/5*a*sin(d*x+c)^5/d-1/6*a*sin(d*x+c)^6/d,1],
[cos(d*x+c)^4*cot(d*x+c)^3*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-3*a*ln(sin(d*x+c))/d-3*a*sin(d*x+c)/d+3/2*a*sin(d*x+c)^2/d+a*sin(d*x+c)^3/d-1/4*a*sin(d*x+c)^4/d-1/5*a*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*cot(d*x+c)^4*(a+a*sin(d*x+c)),x,4,3*a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-3*a*ln(sin(d*x+c))/d+3*a*sin(d*x+c)/d+3/2*a*sin(d*x+c)^2/d-1/3*a*sin(d*x+c)^3/d-1/4*a*sin(d*x+c)^4/d,1],
[cos(d*x+c)^2*cot(d*x+c)^5*(a+a*sin(d*x+c)),x,4,3*a*csc(d*x+c)/d+3/2*a*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d+3*a*ln(sin(d*x+c))/d+3*a*sin(d*x+c)/d-1/2*a*sin(d*x+c)^2/d-1/3*a*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^6*(a+a*sin(d*x+c)),x,4,-3*a*csc(d*x+c)/d+3/2*a*csc(d*x+c)^2/d+a*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d-1/5*a*csc(d*x+c)^5/d+3*a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d-1/2*a*sin(d*x+c)^2/d,1],
[cot(d*x+c)^7*(a+a*sin(d*x+c)),x,3,-3*a*csc(d*x+c)/d-3/2*a*csc(d*x+c)^2/d+a*csc(d*x+c)^3/d+3/4*a*csc(d*x+c)^4/d-1/5*a*csc(d*x+c)^5/d-1/6*a*csc(d*x+c)^6/d-a*ln(sin(d*x+c))/d-a*sin(d*x+c)/d,1],
[cot(d*x+c)^7*csc(d*x+c)*(a+a*sin(d*x+c)),x,4,a*csc(d*x+c)/d-3/2*a*csc(d*x+c)^2/d-a*csc(d*x+c)^3/d+3/4*a*csc(d*x+c)^4/d+3/5*a*csc(d*x+c)^5/d-1/6*a*csc(d*x+c)^6/d-1/7*a*csc(d*x+c)^7/d-a*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^7*csc(d*x+c)^2*(a+a*sin(d*x+c)),x,6,-1/8*a*cot(d*x+c)^8/d+a*csc(d*x+c)/d-a*csc(d*x+c)^3/d+3/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d,1],
[cot(d*x+c)^7*csc(d*x+c)^3*(a+a*sin(d*x+c)),x,6,-1/8*a*cot(d*x+c)^8/d+1/3*a*csc(d*x+c)^3/d-3/5*a*csc(d*x+c)^5/d+3/7*a*csc(d*x+c)^7/d-1/9*a*csc(d*x+c)^9/d,1],
[cot(d*x+c)^7*csc(d*x+c)^4*(a+a*sin(d*x+c)),x,8,-1/8*a*cot(d*x+c)^8/d-1/10*a*cot(d*x+c)^10/d+1/3*a*csc(d*x+c)^3/d-3/5*a*csc(d*x+c)^5/d+3/7*a*csc(d*x+c)^7/d-1/9*a*csc(d*x+c)^9/d,1],
[cot(d*x+c)^7*csc(d*x+c)^5*(a+a*sin(d*x+c)),x,8,-1/8*a*cot(d*x+c)^8/d-1/10*a*cot(d*x+c)^10/d+1/5*a*csc(d*x+c)^5/d-3/7*a*csc(d*x+c)^7/d+1/3*a*csc(d*x+c)^9/d-1/11*a*csc(d*x+c)^11/d,1],
[cot(d*x+c)^7*csc(d*x+c)^6*(a+a*sin(d*x+c)),x,8,-1/8*a*cot(d*x+c)^8/d-1/5*a*cot(d*x+c)^10/d-1/12*a*cot(d*x+c)^12/d+1/5*a*csc(d*x+c)^5/d-3/7*a*csc(d*x+c)^7/d+1/3*a*csc(d*x+c)^9/d-1/11*a*csc(d*x+c)^11/d,1],
[cot(d*x+c)^7*csc(d*x+c)^7*(a+a*sin(d*x+c)),x,8,-1/8*a*cot(d*x+c)^8/d-1/5*a*cot(d*x+c)^10/d-1/12*a*cot(d*x+c)^12/d+1/7*a*csc(d*x+c)^7/d-1/3*a*csc(d*x+c)^9/d+3/11*a*csc(d*x+c)^11/d-1/13*a*csc(d*x+c)^13/d,1],
[cot(d*x+c)^7*csc(d*x+c)^8*(a+a*sin(d*x+c)),x,4,1/7*a*csc(d*x+c)^7/d+1/8*a*csc(d*x+c)^8/d-1/3*a*csc(d*x+c)^9/d-3/10*a*csc(d*x+c)^10/d+3/11*a*csc(d*x+c)^11/d+1/4*a*csc(d*x+c)^12/d-1/13*a*csc(d*x+c)^13/d-1/14*a*csc(d*x+c)^14/d,1],
[cos(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x,4,1/7*sin(d*x+c)^7/a/d-1/8*sin(d*x+c)^8/a/d-2/9*sin(d*x+c)^9/a/d+1/5*sin(d*x+c)^10/a/d+1/11*sin(d*x+c)^11/a/d-1/12*sin(d*x+c)^12/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x,4,1/6*sin(d*x+c)^6/a/d-1/7*sin(d*x+c)^7/a/d-1/4*sin(d*x+c)^8/a/d+2/9*sin(d*x+c)^9/a/d+1/10*sin(d*x+c)^10/a/d-1/11*sin(d*x+c)^11/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,4,1/5*sin(d*x+c)^5/a/d-1/6*sin(d*x+c)^6/a/d-2/7*sin(d*x+c)^7/a/d+1/4*sin(d*x+c)^8/a/d+1/9*sin(d*x+c)^9/a/d-1/10*sin(d*x+c)^10/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,8,-1/6*cos(d*x+c)^6/a/d+1/8*cos(d*x+c)^8/a/d-1/5*sin(d*x+c)^5/a/d+2/7*sin(d*x+c)^7/a/d-1/9*sin(d*x+c)^9/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,8,1/6*cos(d*x+c)^6/a/d-1/8*cos(d*x+c)^8/a/d+1/3*sin(d*x+c)^3/a/d-2/5*sin(d*x+c)^5/a/d+1/7*sin(d*x+c)^7/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x,6,-1/6*cos(d*x+c)^6/a/d-1/3*sin(d*x+c)^3/a/d+2/5*sin(d*x+c)^5/a/d-1/7*sin(d*x+c)^7/a/d,1],
[cos(d*x+c)^7/(a+a*sin(d*x+c)),x,3,-(a-a*sin(d*x+c))^4/a^5/d+4/5*(a-a*sin(d*x+c))^5/a^6/d-1/6*(a-a*sin(d*x+c))^6/a^7/d,1],
[cos(d*x+c)^6*cot(d*x+c)/(a+a*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d-sin(d*x+c)^2/a/d+2/3*sin(d*x+c)^3/a/d+1/4*sin(d*x+c)^4/a/d-1/5*sin(d*x+c)^5/a/d,1],
[cos(d*x+c)^5*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-ln(sin(d*x+c))/a/d-2*sin(d*x+c)/a/d+sin(d*x+c)^2/a/d+1/3*sin(d*x+c)^3/a/d-1/4*sin(d*x+c)^4/a/d,1],
[cos(d*x+c)^4*cot(d*x+c)^3/(a+a*sin(d*x+c)),x,4,csc(d*x+c)/a/d-1/2*csc(d*x+c)^2/a/d-2*ln(sin(d*x+c))/a/d+2*sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d-1/3*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^3*cot(d*x+c)^4/(a+a*sin(d*x+c)),x,4,2*csc(d*x+c)/a/d+1/2*csc(d*x+c)^2/a/d-1/3*csc(d*x+c)^3/a/d+2*ln(sin(d*x+c))/a/d+sin(d*x+c)/a/d-1/2*sin(d*x+c)^2/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^5/(a+a*sin(d*x+c)),x,4,-2*csc(d*x+c)/a/d+csc(d*x+c)^2/a/d+1/3*csc(d*x+c)^3/a/d-1/4*csc(d*x+c)^4/a/d+ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^6/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-csc(d*x+c)^2/a/d+2/3*csc(d*x+c)^3/a/d+1/4*csc(d*x+c)^4/a/d-1/5*csc(d*x+c)^5/a/d-ln(sin(d*x+c))/a/d,1],
[cot(d*x+c)^7/(a+a*sin(d*x+c)),x,6,-1/6*cot(d*x+c)^6/a/d+csc(d*x+c)/a/d-2/3*csc(d*x+c)^3/a/d+1/5*csc(d*x+c)^5/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)/(a+a*sin(d*x+c)),x,6,1/6*cot(d*x+c)^6/a/d-1/3*csc(d*x+c)^3/a/d+2/5*csc(d*x+c)^5/a/d-1/7*csc(d*x+c)^7/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,8,-1/6*cot(d*x+c)^6/a/d-1/8*cot(d*x+c)^8/a/d+1/3*csc(d*x+c)^3/a/d-2/5*csc(d*x+c)^5/a/d+1/7*csc(d*x+c)^7/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,8,1/6*cot(d*x+c)^6/a/d+1/8*cot(d*x+c)^8/a/d-1/5*csc(d*x+c)^5/a/d+2/7*csc(d*x+c)^7/a/d-1/9*csc(d*x+c)^9/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)^4/(a+a*sin(d*x+c)),x,4,1/5*csc(d*x+c)^5/a/d-1/6*csc(d*x+c)^6/a/d-2/7*csc(d*x+c)^7/a/d+1/4*csc(d*x+c)^8/a/d+1/9*csc(d*x+c)^9/a/d-1/10*csc(d*x+c)^10/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)^5/(a+a*sin(d*x+c)),x,4,1/6*csc(d*x+c)^6/a/d-1/7*csc(d*x+c)^7/a/d-1/4*csc(d*x+c)^8/a/d+2/9*csc(d*x+c)^9/a/d+1/10*csc(d*x+c)^10/a/d-1/11*csc(d*x+c)^11/a/d,1],
[cot(d*x+c)^7*csc(d*x+c)^6/(a+a*sin(d*x+c)),x,4,1/7*csc(d*x+c)^7/a/d-1/8*csc(d*x+c)^8/a/d-2/9*csc(d*x+c)^9/a/d+1/5*csc(d*x+c)^10/a/d+1/11*csc(d*x+c)^11/a/d-1/12*csc(d*x+c)^12/a/d,1],
[cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x,3,a^3*sin(d*x+c)^(1+n)/d/(1+n)+3*a^3*sin(d*x+c)^(2+n)/d/(2+n)-8*a^3*sin(d*x+c)^(4+n)/d/(4+n)-6*a^3*sin(d*x+c)^(5+n)/d/(5+n)+6*a^3*sin(d*x+c)^(6+n)/d/(6+n)+8*a^3*sin(d*x+c)^(7+n)/d/(7+n)-3*a^3*sin(d*x+c)^(9+n)/d/(9+n)-a^3*sin(d*x+c)^(10+n)/d/(10+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x,3,a^2*sin(d*x+c)^(1+n)/d/(1+n)+2*a^2*sin(d*x+c)^(2+n)/d/(2+n)-2*a^2*sin(d*x+c)^(3+n)/d/(3+n)-6*a^2*sin(d*x+c)^(4+n)/d/(4+n)+6*a^2*sin(d*x+c)^(6+n)/d/(6+n)+2*a^2*sin(d*x+c)^(7+n)/d/(7+n)-2*a^2*sin(d*x+c)^(8+n)/d/(8+n)-a^2*sin(d*x+c)^(9+n)/d/(9+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x,3,a*sin(d*x+c)^(1+n)/d/(1+n)+a*sin(d*x+c)^(2+n)/d/(2+n)-3*a*sin(d*x+c)^(3+n)/d/(3+n)-3*a*sin(d*x+c)^(4+n)/d/(4+n)+3*a*sin(d*x+c)^(5+n)/d/(5+n)+3*a*sin(d*x+c)^(6+n)/d/(6+n)-a*sin(d*x+c)^(7+n)/d/(7+n)-a*sin(d*x+c)^(8+n)/d/(8+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x,3,sin(d*x+c)^(1+n)/a/d/(1+n)-sin(d*x+c)^(2+n)/a/d/(2+n)-2*sin(d*x+c)^(3+n)/a/d/(3+n)+2*sin(d*x+c)^(4+n)/a/d/(4+n)+sin(d*x+c)^(5+n)/a/d/(5+n)-sin(d*x+c)^(6+n)/a/d/(6+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x,3,sin(d*x+c)^(1+n)/a^2/d/(1+n)-2*sin(d*x+c)^(2+n)/a^2/d/(2+n)+2*sin(d*x+c)^(4+n)/a^2/d/(4+n)-sin(d*x+c)^(5+n)/a^2/d/(5+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x,3,sin(d*x+c)^(1+n)/a^3/d/(1+n)-3*sin(d*x+c)^(2+n)/a^3/d/(2+n)+3*sin(d*x+c)^(3+n)/a^3/d/(3+n)-sin(d*x+c)^(4+n)/a^3/d/(4+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x,8,-7*sin(d*x+c)^(1+n)/a^4/d/(1+n)+8*hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^4/d/(1+n)+4*sin(d*x+c)^(2+n)/a^4/d/(2+n)-sin(d*x+c)^(3+n)/a^4/d/(3+n),1],
[cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x,5,(7+2*n)*sin(d*x+c)^(1+n)/a^5/d/(1+n)/(2+n)-4*(3+2*n)*hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/a^5/d/(1+n)-sin(d*x+c)^(1+n)*(a-a*sin(d*x+c))^2/a^7/d/(2+n)/(1+sin(d*x+c))+4*(5+2*n)*sin(d*x+c)^(1+n)/d/(2+n)/(a^5+a^5*sin(d*x+c)),1],
[cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c)),x,11,-5/1024*x/a-1/7*cos(d*x+c)^7/a/d+2/9*cos(d*x+c)^9/a/d-1/11*cos(d*x+c)^11/a/d-5/1024*cos(d*x+c)*sin(d*x+c)/a/d-5/1536*cos(d*x+c)^3*sin(d*x+c)/a/d-1/384*cos(d*x+c)^5*sin(d*x+c)/a/d+1/64*cos(d*x+c)^7*sin(d*x+c)/a/d+1/24*cos(d*x+c)^7*sin(d*x+c)^3/a/d+1/12*cos(d*x+c)^7*sin(d*x+c)^5/a/d,1],
[cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c)),x,10,3/256*x/a+1/7*cos(d*x+c)^7/a/d-2/9*cos(d*x+c)^9/a/d+1/11*cos(d*x+c)^11/a/d+3/256*cos(d*x+c)*sin(d*x+c)/a/d+1/128*cos(d*x+c)^3*sin(d*x+c)/a/d+1/160*cos(d*x+c)^5*sin(d*x+c)/a/d-3/80*cos(d*x+c)^7*sin(d*x+c)/a/d-1/10*cos(d*x+c)^7*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c)),x,10,-3/256*x/a-1/7*cos(d*x+c)^7/a/d+1/9*cos(d*x+c)^9/a/d-3/256*cos(d*x+c)*sin(d*x+c)/a/d-1/128*cos(d*x+c)^3*sin(d*x+c)/a/d-1/160*cos(d*x+c)^5*sin(d*x+c)/a/d+3/80*cos(d*x+c)^7*sin(d*x+c)/a/d+1/10*cos(d*x+c)^7*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c)),x,9,5/128*x/a+1/7*cos(d*x+c)^7/a/d-1/9*cos(d*x+c)^9/a/d+5/128*cos(d*x+c)*sin(d*x+c)/a/d+5/192*cos(d*x+c)^3*sin(d*x+c)/a/d+1/48*cos(d*x+c)^5*sin(d*x+c)/a/d-1/8*cos(d*x+c)^7*sin(d*x+c)/a/d,1],
[cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c)),x,8,-5/128*x/a-1/7*cos(d*x+c)^7/a/d-5/128*cos(d*x+c)*sin(d*x+c)/a/d-5/192*cos(d*x+c)^3*sin(d*x+c)/a/d-1/48*cos(d*x+c)^5*sin(d*x+c)/a/d+1/8*cos(d*x+c)^7*sin(d*x+c)/a/d,1],
[cos(d*x+c)^7*cot(d*x+c)/(a+a*sin(d*x+c)),x,9,-5/16*x/a-arctanh(cos(d*x+c))/a/d+cos(d*x+c)/a/d+1/3*cos(d*x+c)^3/a/d+1/5*cos(d*x+c)^5/a/d-5/16*cos(d*x+c)*sin(d*x+c)/a/d-5/24*cos(d*x+c)^3*sin(d*x+c)/a/d-1/6*cos(d*x+c)^5*sin(d*x+c)/a/d,1],
[cos(d*x+c)^6*cot(d*x+c)^2/(a+a*sin(d*x+c)),x,11,-15/8*x/a+arctanh(cos(d*x+c))/a/d-cos(d*x+c)/a/d-1/3*cos(d*x+c)^3/a/d-1/5*cos(d*x+c)^5/a/d-cot(d*x+c)/a/d-9/8*cos(d*x+c)*sin(d*x+c)/a/d+1/4*cos(d*x+c)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^5*cot(d*x+c)^3/(a+a*sin(d*x+c)),x,12,15/8*x/a+5/2*arctanh(cos(d*x+c))/a/d-2*cos(d*x+c)/a/d-1/3*cos(d*x+c)^3/a/d+cot(d*x+c)/a/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d+9/8*cos(d*x+c)*sin(d*x+c)/a/d-1/4*cos(d*x+c)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^4*cot(d*x+c)^4/(a+a*sin(d*x+c)),x,11,5/2*x/a-5/2*arctanh(cos(d*x+c))/a/d+2*cos(d*x+c)/a/d+1/3*cos(d*x+c)^3/a/d+2*cot(d*x+c)/a/d-1/3*cot(d*x+c)^3/a/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d+1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^3*cot(d*x+c)^5/(a+a*sin(d*x+c)),x,12,-5/2*x/a-15/8*arctanh(cos(d*x+c))/a/d+cos(d*x+c)/a/d-2*cot(d*x+c)/a/d+1/3*cot(d*x+c)^3/a/d+9/8*cot(d*x+c)*csc(d*x+c)/a/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d-1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*cot(d*x+c)^6/(a+a*sin(d*x+c)),x,11,-x/a+15/8*arctanh(cos(d*x+c))/a/d-cos(d*x+c)/a/d-cot(d*x+c)/a/d+1/3*cot(d*x+c)^3/a/d-1/5*cot(d*x+c)^5/a/d-9/8*cot(d*x+c)*csc(d*x+c)/a/d+1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cos(d*x+c)*cot(d*x+c)^7/(a+a*sin(d*x+c)),x,9,x/a+5/16*arctanh(cos(d*x+c))/a/d+cot(d*x+c)/a/d-1/3*cot(d*x+c)^3/a/d+1/5*cot(d*x+c)^5/a/d-5/16*cot(d*x+c)*csc(d*x+c)/a/d+5/24*cot(d*x+c)^3*csc(d*x+c)/a/d-1/6*cot(d*x+c)^5*csc(d*x+c)/a/d,1],
[cot(d*x+c)^8/(a+a*sin(d*x+c)),x,7,-5/16*arctanh(cos(d*x+c))/a/d-1/7*cot(d*x+c)^7/a/d+5/16*cot(d*x+c)*csc(d*x+c)/a/d-5/24*cot(d*x+c)^3*csc(d*x+c)/a/d+1/6*cot(d*x+c)^5*csc(d*x+c)/a/d,1],
[cot(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c)),x,8,5/128*arctanh(cos(d*x+c))/a/d+1/7*cot(d*x+c)^7/a/d+5/128*cot(d*x+c)*csc(d*x+c)/a/d-5/64*cot(d*x+c)*csc(d*x+c)^3/a/d+5/48*cot(d*x+c)^3*csc(d*x+c)^3/a/d-1/8*cot(d*x+c)^5*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c)),x,9,-5/128*arctanh(cos(d*x+c))/a/d-1/7*cot(d*x+c)^7/a/d-1/9*cot(d*x+c)^9/a/d-5/128*cot(d*x+c)*csc(d*x+c)/a/d+5/64*cot(d*x+c)*csc(d*x+c)^3/a/d-5/48*cot(d*x+c)^3*csc(d*x+c)^3/a/d+1/8*cot(d*x+c)^5*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c)),x,10,3/256*arctanh(cos(d*x+c))/a/d+1/7*cot(d*x+c)^7/a/d+1/9*cot(d*x+c)^9/a/d+3/256*cot(d*x+c)*csc(d*x+c)/a/d+1/128*cot(d*x+c)*csc(d*x+c)^3/a/d-1/32*cot(d*x+c)*csc(d*x+c)^5/a/d+1/16*cot(d*x+c)^3*csc(d*x+c)^5/a/d-1/10*cot(d*x+c)^5*csc(d*x+c)^5/a/d,1],
[cot(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c)),x,10,-3/256*arctanh(cos(d*x+c))/a/d-1/7*cot(d*x+c)^7/a/d-2/9*cot(d*x+c)^9/a/d-1/11*cot(d*x+c)^11/a/d-3/256*cot(d*x+c)*csc(d*x+c)/a/d-1/128*cot(d*x+c)*csc(d*x+c)^3/a/d+1/32*cot(d*x+c)*csc(d*x+c)^5/a/d-1/16*cot(d*x+c)^3*csc(d*x+c)^5/a/d+1/10*cot(d*x+c)^5*csc(d*x+c)^5/a/d,1],
[cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x,15,-3/128*x/a^2-2/5*cos(d*x+c)^5/a^2/d+5/7*cos(d*x+c)^7/a^2/d-4/9*cos(d*x+c)^9/a^2/d+1/11*cos(d*x+c)^11/a^2/d-3/128*cos(d*x+c)*sin(d*x+c)/a^2/d-1/64*cos(d*x+c)^3*sin(d*x+c)/a^2/d+1/16*cos(d*x+c)^5*sin(d*x+c)/a^2/d+1/8*cos(d*x+c)^5*sin(d*x+c)^3/a^2/d+1/5*cos(d*x+c)^5*sin(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x,17,9/256*x/a^2+2/5*cos(d*x+c)^5/a^2/d-4/7*cos(d*x+c)^7/a^2/d+2/9*cos(d*x+c)^9/a^2/d+9/256*cos(d*x+c)*sin(d*x+c)/a^2/d+3/128*cos(d*x+c)^3*sin(d*x+c)/a^2/d-3/32*cos(d*x+c)^5*sin(d*x+c)/a^2/d-3/16*cos(d*x+c)^5*sin(d*x+c)^3/a^2/d-1/10*cos(d*x+c)^5*sin(d*x+c)^5/a^2/d,1],
[cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x,14,-3/64*x/a^2-2/5*cos(d*x+c)^5/a^2/d+3/7*cos(d*x+c)^7/a^2/d-1/9*cos(d*x+c)^9/a^2/d-3/64*cos(d*x+c)*sin(d*x+c)/a^2/d-1/32*cos(d*x+c)^3*sin(d*x+c)/a^2/d+1/8*cos(d*x+c)^5*sin(d*x+c)/a^2/d+1/4*cos(d*x+c)^5*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x,15,11/128*x/a^2+2/5*cos(d*x+c)^5/a^2/d-2/7*cos(d*x+c)^7/a^2/d+11/128*cos(d*x+c)*sin(d*x+c)/a^2/d+11/192*cos(d*x+c)^3*sin(d*x+c)/a^2/d-11/48*cos(d*x+c)^5*sin(d*x+c)/a^2/d-1/8*cos(d*x+c)^5*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^2,x,6,-1/8*x/a^2-2/35*cos(d*x+c)^7/a^2/d-1/8*cos(d*x+c)*sin(d*x+c)/a^2/d-1/12*cos(d*x+c)^3*sin(d*x+c)/a^2/d-1/15*cos(d*x+c)^5*sin(d*x+c)/a^2/d-1/5*cos(d*x+c)^9/d/(a+a*sin(d*x+c))^2,1],
[cos(d*x+c)^7*cot(d*x+c)/(a+a*sin(d*x+c))^2,x,12,-3/4*x/a^2-arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/a^2/d+1/3*cos(d*x+c)^3/a^2/d-1/5*cos(d*x+c)^5/a^2/d-3/4*cos(d*x+c)*sin(d*x+c)/a^2/d-1/2*cos(d*x+c)^3*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^6*cot(d*x+c)^2/(a+a*sin(d*x+c))^2,x,14,-9/8*x/a^2+2*arctanh(cos(d*x+c))/a^2/d-2*cos(d*x+c)/a^2/d-2/3*cos(d*x+c)^3/a^2/d-cot(d*x+c)/a^2/d+1/8*cos(d*x+c)*sin(d*x+c)/a^2/d-1/4*cos(d*x+c)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^5*cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x,13,3*x/a^2+1/2*arctanh(cos(d*x+c))/a^2/d+1/3*cos(d*x+c)^3/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+cos(d*x+c)*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^4*cot(d*x+c)^4/(a+a*sin(d*x+c))^2,x,13,-1/2*x/a^2-3*arctanh(cos(d*x+c))/a^2/d+2*cos(d*x+c)/a^2/d-1/3*cot(d*x+c)^3/a^2/d+cot(d*x+c)*csc(d*x+c)/a^2/d-1/2*cos(d*x+c)*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^3*cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x,14,-2*x/a^2+9/8*arctanh(cos(d*x+c))/a^2/d-cos(d*x+c)/a^2/d-2*cot(d*x+c)/a^2/d+2/3*cot(d*x+c)^3/a^2/d+1/8*cot(d*x+c)*csc(d*x+c)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^2*cot(d*x+c)^6/(a+a*sin(d*x+c))^2,x,11,x/a^2+3/4*arctanh(cos(d*x+c))/a^2/d+cot(d*x+c)/a^2/d-1/3*cot(d*x+c)^3/a^2/d-1/5*cot(d*x+c)^5/a^2/d-3/4*cot(d*x+c)*csc(d*x+c)/a^2/d+1/2*cot(d*x+c)^3*csc(d*x+c)/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^7/(a+a*sin(d*x+c))^2,x,12,-7/16*arctanh(cos(d*x+c))/a^2/d+2/5*cot(d*x+c)^5/a^2/d+5/16*cot(d*x+c)*csc(d*x+c)/a^2/d-1/4*cot(d*x+c)^3*csc(d*x+c)/a^2/d+1/8*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/6*cot(d*x+c)^3*csc(d*x+c)^3/a^2/d,1],
[cot(d*x+c)^8/(a+a*sin(d*x+c))^2,x,19,1/8*arctanh(cos(d*x+c))/a^2/d-2/5*cot(d*x+c)^5/a^2/d-1/7*cot(d*x+c)^7/a^2/d+1/8*cot(d*x+c)*csc(d*x+c)/a^2/d-7/12*cot(d*x+c)*csc(d*x+c)^3/a^2/d+1/3*cot(d*x+c)*csc(d*x+c)^5/a^2/d,1],
[cot(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^2,x,15,-11/128*arctanh(cos(d*x+c))/a^2/d+2/5*cot(d*x+c)^5/a^2/d+2/7*cot(d*x+c)^7/a^2/d-11/128*cot(d*x+c)*csc(d*x+c)/a^2/d+7/64*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/6*cot(d*x+c)^3*csc(d*x+c)^3/a^2/d+1/16*cot(d*x+c)*csc(d*x+c)^5/a^2/d-1/8*cot(d*x+c)^3*csc(d*x+c)^5/a^2/d,1],
[cot(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x,14,3/64*arctanh(cos(d*x+c))/a^2/d-2/5*cot(d*x+c)^5/a^2/d-3/7*cot(d*x+c)^7/a^2/d-1/9*cot(d*x+c)^9/a^2/d+3/64*cot(d*x+c)*csc(d*x+c)/a^2/d+1/32*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/8*cot(d*x+c)*csc(d*x+c)^5/a^2/d+1/4*cot(d*x+c)^3*csc(d*x+c)^5/a^2/d,1],
[cot(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x,17,-9/256*arctanh(cos(d*x+c))/a^2/d+2/5*cot(d*x+c)^5/a^2/d+4/7*cot(d*x+c)^7/a^2/d+2/9*cot(d*x+c)^9/a^2/d-9/256*cot(d*x+c)*csc(d*x+c)/a^2/d-3/128*cot(d*x+c)*csc(d*x+c)^3/a^2/d+9/160*cot(d*x+c)*csc(d*x+c)^5/a^2/d-1/8*cot(d*x+c)^3*csc(d*x+c)^5/a^2/d+3/80*cot(d*x+c)*csc(d*x+c)^7/a^2/d-1/10*cot(d*x+c)^3*csc(d*x+c)^7/a^2/d,1],
[cot(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x,15,3/128*arctanh(cos(d*x+c))/a^2/d-2/5*cot(d*x+c)^5/a^2/d-5/7*cot(d*x+c)^7/a^2/d-4/9*cot(d*x+c)^9/a^2/d-1/11*cot(d*x+c)^11/a^2/d+3/128*cot(d*x+c)*csc(d*x+c)/a^2/d+1/64*cot(d*x+c)*csc(d*x+c)^3/a^2/d+1/80*cot(d*x+c)*csc(d*x+c)^5/a^2/d-3/40*cot(d*x+c)*csc(d*x+c)^7/a^2/d+1/5*cot(d*x+c)^3*csc(d*x+c)^7/a^2/d,1],
[cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x,18,-29/128*x/a^3-4/3*cos(d*x+c)^3/a^3/d+7/5*cos(d*x+c)^5/a^3/d-3/7*cos(d*x+c)^7/a^3/d-29/128*cos(d*x+c)*sin(d*x+c)/a^3/d+29/64*cos(d*x+c)^3*sin(d*x+c)/a^3/d+29/48*cos(d*x+c)^3*sin(d*x+c)^3/a^3/d+1/8*cos(d*x+c)^3*sin(d*x+c)^5/a^3/d,1],
[cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x,16,5/16*x/a^3+4/3*cos(d*x+c)^3/a^3/d-cos(d*x+c)^5/a^3/d+1/7*cos(d*x+c)^7/a^3/d+5/16*cos(d*x+c)*sin(d*x+c)/a^3/d-5/8*cos(d*x+c)^3*sin(d*x+c)/a^3/d-1/2*cos(d*x+c)^3*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^3,x,6,-7/16*x/a^3-7/30*cos(d*x+c)^5/a^3/d-7/16*cos(d*x+c)*sin(d*x+c)/a^3/d-7/24*cos(d*x+c)^3*sin(d*x+c)/a^3/d-1/3*cos(d*x+c)^9/d/(a+a*sin(d*x+c))^3-1/6*cos(d*x+c)^7/d/(a^3+a^3*sin(d*x+c)),1],
[cos(d*x+c)^7*cot(d*x+c)/(a+a*sin(d*x+c))^3,x,13,-13/8*x/a^3-arctanh(cos(d*x+c))/a^3/d+cos(d*x+c)/a^3/d-cos(d*x+c)^3/a^3/d-13/8*cos(d*x+c)*sin(d*x+c)/a^3/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^6*cot(d*x+c)^2/(a+a*sin(d*x+c))^3,x,11,1/2*x/a^3+3*arctanh(cos(d*x+c))/a^3/d-3*cos(d*x+c)/a^3/d+1/3*cos(d*x+c)^3/a^3/d-cot(d*x+c)/a^3/d+3/2*cos(d*x+c)*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^5*cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x,11,5/2*x/a^3-5/2*arctanh(cos(d*x+c))/a^3/d+3*cos(d*x+c)/a^3/d+3*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d-1/2*cos(d*x+c)*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^4*cot(d*x+c)^4/(a+a*sin(d*x+c))^3,x,11,-3*x/a^3-1/2*arctanh(cos(d*x+c))/a^3/d-cos(d*x+c)/a^3/d-3*cot(d*x+c)/a^3/d-1/3*cot(d*x+c)^3/a^3/d+3/2*cot(d*x+c)*csc(d*x+c)/a^3/d,1],
[cos(d*x+c)^3*cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x,12,x/a^3+13/8*arctanh(cos(d*x+c))/a^3/d+cot(d*x+c)/a^3/d+cot(d*x+c)^3/a^3/d-11/8*cot(d*x+c)*csc(d*x+c)/a^3/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^6/(a+a*sin(d*x+c))^3,x,13,-7/8*arctanh(cos(d*x+c))/a^3/d-4/3*cot(d*x+c)^3/a^3/d-1/5*cot(d*x+c)^5/a^3/d+1/8*cot(d*x+c)*csc(d*x+c)/a^3/d+3/4*cot(d*x+c)*csc(d*x+c)^3/a^3/d,1],
[cos(d*x+c)*cot(d*x+c)^7/(a+a*sin(d*x+c))^3,x,15,7/16*arctanh(cos(d*x+c))/a^3/d+4/3*cot(d*x+c)^3/a^3/d+3/5*cot(d*x+c)^5/a^3/d+7/16*cot(d*x+c)*csc(d*x+c)/a^3/d-17/24*cot(d*x+c)*csc(d*x+c)^3/a^3/d-1/6*cot(d*x+c)*csc(d*x+c)^5/a^3/d,1],
[cot(d*x+c)^8/(a+a*sin(d*x+c))^3,x,17,-5/16*arctanh(cos(d*x+c))/a^3/d-4/3*cot(d*x+c)^3/a^3/d-cot(d*x+c)^5/a^3/d-1/7*cot(d*x+c)^7/a^3/d-5/16*cot(d*x+c)*csc(d*x+c)/a^3/d+1/8*cot(d*x+c)*csc(d*x+c)^3/a^3/d+1/2*cot(d*x+c)*csc(d*x+c)^5/a^3/d,1],
[cot(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^3,x,18,29/128*arctanh(cos(d*x+c))/a^3/d+4/3*cot(d*x+c)^3/a^3/d+7/5*cot(d*x+c)^5/a^3/d+3/7*cot(d*x+c)^7/a^3/d+29/128*cot(d*x+c)*csc(d*x+c)/a^3/d+29/192*cot(d*x+c)*csc(d*x+c)^3/a^3/d-23/48*cot(d*x+c)*csc(d*x+c)^5/a^3/d-1/8*cot(d*x+c)*csc(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^2*(a+a*sin(d*x+c))*tan(d*x+c)^2,x,8,-3/2*a*x+2*a*cos(d*x+c)/d-1/3*a*cos(d*x+c)^3/d+a*sec(d*x+c)/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d+a*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c)^2,x,9,-3/2*a*x+a*cos(d*x+c)/d+a*sec(d*x+c)/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d+a*tan(d*x+c)/d,1],
[(a+a*sin(d*x+c))*tan(d*x+c)^2,x,5,-a*x+a*cos(d*x+c)/d+a*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[sec(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c),x,5,-a*x+a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c)),x,6,-a*arctanh(cos(d*x+c))/d+a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c)),x,7,-a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d+a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c)),x,9,-3/2*a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c)),x,9,-3/2*a*arctanh(cos(d*x+c))/d-2*a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+a*sin(d*x+c))^2*tan(d*x+c)^2,x,13,-3*a^2*x+3*a^2*cos(d*x+c)/d-1/3*a^2*cos(d*x+c)^3/d+2*a^2*sec(d*x+c)/d+a^2*cos(d*x+c)*sin(d*x+c)/d+2*a^2*tan(d*x+c)/d,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^2,x,6,-5/2*a^2*x+2*a^2*cos(d*x+c)/d+2*a^2*cos(d*x+c)/d/(1-sin(d*x+c))+1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^2*tan(d*x+c),x,3,-2*a^2*x+2*a^2*cos(d*x+c)/d+sec(d*x+c)*(a+a*sin(d*x+c))^2/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x,9,-a^2*arctanh(cos(d*x+c))/d+2*a^2*sec(d*x+c)/d+2*a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x,10,-2*a^2*arctanh(cos(d*x+c))/d-a^2*cot(d*x+c)/d+2*a^2*sec(d*x+c)/d+2*a^2*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x,13,-5/2*a^2*arctanh(cos(d*x+c))/d-2*a^2*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d+2*a^2*sec(d*x+c)/d+2*a^2*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+a*sin(d*x+c))^3*tan(d*x+c)^2,x,11,-51/8*a^3*x+7*a^3*cos(d*x+c)/d-a^3*cos(d*x+c)^3/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c))+19/8*a^3*cos(d*x+c)*sin(d*x+c)/d+1/4*a^3*cos(d*x+c)*sin(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^2,x,8,-11/2*a^3*x+5*a^3*cos(d*x+c)/d-1/3*a^3*cos(d*x+c)^3/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c))+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^3*tan(d*x+c),x,2,-9/2*a^3*x+6*a^3*cos(d*x+c)/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d+sec(d*x+c)*(a+a*sin(d*x+c))^3/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,-a^3*x-a^3*arctanh(cos(d*x+c))/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x,6,-3*a^3*arctanh(cos(d*x+c))/d-a^3*cot(d*x+c)/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x,8,-9/2*a^3*arctanh(cos(d*x+c))/d-3*a^3*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x,10,-11/2*a^3*arctanh(cos(d*x+c))/d-5*a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^3*cot(d*x+c)*csc(d*x+c)/d+4*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c)),x,7,x/a+cos(d*x+c)/a/d+2*sec(d*x+c)/a/d-1/3*sec(d*x+c)^3/a/d-tan(d*x+c)/a/d+1/3*tan(d*x+c)^3/a/d,1],
[sin(d*x+c)*tan(d*x+c)^2/(a+a*sin(d*x+c)),x,6,-x/a-sec(d*x+c)/a/d+1/3*sec(d*x+c)^3/a/d+tan(d*x+c)/a/d-1/3*tan(d*x+c)^3/a/d,1],
[tan(d*x+c)^2/(a+a*sin(d*x+c)),x,5,sec(d*x+c)/a/d-1/3*sec(d*x+c)^3/a/d+1/3*tan(d*x+c)^3/a/d,1],
[sec(d*x+c)*tan(d*x+c)/(a+a*sin(d*x+c)),x,5,1/3*sec(d*x+c)^3/a/d-1/3*tan(d*x+c)^3/a/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x,7,-arctanh(cos(d*x+c))/a/d+sec(d*x+c)/a/d+1/3*sec(d*x+c)^3/a/d-tan(d*x+c)/a/d-1/3*tan(d*x+c)^3/a/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x,8,arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d-sec(d*x+c)/a/d-1/3*sec(d*x+c)^3/a/d+2*tan(d*x+c)/a/d+1/3*tan(d*x+c)^3/a/d,1],
[sin(d*x+c)^4*tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,15,-9/2*x/a^2-2*cos(d*x+c)/a^2/d-6*sec(d*x+c)/a^2/d+2*sec(d*x+c)^3/a^2/d-2/5*sec(d*x+c)^5/a^2/d+1/2*cos(d*x+c)*sin(d*x+c)/a^2/d+4*tan(d*x+c)/a^2/d-tan(d*x+c)^3/a^2/d+2/5*tan(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^3*tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,13,2*x/a^2+cos(d*x+c)/a^2/d+4*sec(d*x+c)/a^2/d-5/3*sec(d*x+c)^3/a^2/d+2/5*sec(d*x+c)^5/a^2/d-2*tan(d*x+c)/a^2/d+2/3*tan(d*x+c)^3/a^2/d-2/5*tan(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,12,-x/a^2-2*sec(d*x+c)/a^2/d+4/3*sec(d*x+c)^3/a^2/d-2/5*sec(d*x+c)^5/a^2/d+tan(d*x+c)/a^2/d-1/3*tan(d*x+c)^3/a^2/d+2/5*tan(d*x+c)^5/a^2/d,1],
[sin(d*x+c)*tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,11,sec(d*x+c)/a^2/d-sec(d*x+c)^3/a^2/d+2/5*sec(d*x+c)^5/a^2/d-2/5*tan(d*x+c)^5/a^2/d,1],
[tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,10,2/3*sec(d*x+c)^3/a^2/d-2/5*sec(d*x+c)^5/a^2/d+1/3*tan(d*x+c)^3/a^2/d+2/5*tan(d*x+c)^5/a^2/d,1],
[sec(d*x+c)*tan(d*x+c)/(a+a*sin(d*x+c))^2,x,4,1/5*sec(d*x+c)/d/(a+a*sin(d*x+c))^2-2/15*sec(d*x+c)/d/(a^2+a^2*sin(d*x+c))+4/15*tan(d*x+c)/a^2/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x,11,-arctanh(cos(d*x+c))/a^2/d+sec(d*x+c)/a^2/d+1/3*sec(d*x+c)^3/a^2/d+2/5*sec(d*x+c)^5/a^2/d-2*tan(d*x+c)/a^2/d-4/3*tan(d*x+c)^3/a^2/d-2/5*tan(d*x+c)^5/a^2/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x,12,2*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a^2/d-2*sec(d*x+c)/a^2/d-2/3*sec(d*x+c)^3/a^2/d-2/5*sec(d*x+c)^5/a^2/d+4*tan(d*x+c)/a^2/d+5/3*tan(d*x+c)^3/a^2/d+2/5*tan(d*x+c)^5/a^2/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x,15,-9/2*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+4*sec(d*x+c)/a^2/d+sec(d*x+c)^3/a^2/d+2/5*sec(d*x+c)^5/a^2/d-6*tan(d*x+c)/a^2/d-2*tan(d*x+c)^3/a^2/d-2/5*tan(d*x+c)^5/a^2/d,1],
[sin(d*x+c)^4*tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,16,3*x/a^3+cos(d*x+c)/a^3/d+7*sec(d*x+c)/a^3/d-5*sec(d*x+c)^3/a^3/d+13/5*sec(d*x+c)^5/a^3/d-4/7*sec(d*x+c)^7/a^3/d-3*tan(d*x+c)/a^3/d+tan(d*x+c)^3/a^3/d-3/5*tan(d*x+c)^5/a^3/d+4/7*tan(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^3*tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,16,-x/a^3-3*sec(d*x+c)/a^3/d+10/3*sec(d*x+c)^3/a^3/d-11/5*sec(d*x+c)^5/a^3/d+4/7*sec(d*x+c)^7/a^3/d+tan(d*x+c)/a^3/d-1/3*tan(d*x+c)^3/a^3/d+1/5*tan(d*x+c)^5/a^3/d-4/7*tan(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,14,sec(d*x+c)/a^3/d-2*sec(d*x+c)^3/a^3/d+9/5*sec(d*x+c)^5/a^3/d-4/7*sec(d*x+c)^7/a^3/d+1/5*tan(d*x+c)^5/a^3/d+4/7*tan(d*x+c)^7/a^3/d,1],
[sin(d*x+c)*tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,14,sec(d*x+c)^3/a^3/d-7/5*sec(d*x+c)^5/a^3/d+4/7*sec(d*x+c)^7/a^3/d-3/5*tan(d*x+c)^5/a^3/d-4/7*tan(d*x+c)^7/a^3/d,1],
[tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,14,-1/3*sec(d*x+c)^3/a^3/d+sec(d*x+c)^5/a^3/d-4/7*sec(d*x+c)^7/a^3/d+1/3*tan(d*x+c)^3/a^3/d+tan(d*x+c)^5/a^3/d+4/7*tan(d*x+c)^7/a^3/d,1],
[sec(d*x+c)*tan(d*x+c)/(a+a*sin(d*x+c))^3,x,5,1/7*sec(d*x+c)/d/(a+a*sin(d*x+c))^3-3/35*sec(d*x+c)/a/d/(a+a*sin(d*x+c))^2-3/35*sec(d*x+c)/d/(a^3+a^3*sin(d*x+c))+6/35*tan(d*x+c)/a^3/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x,14,-arctanh(cos(d*x+c))/a^3/d+sec(d*x+c)/a^3/d+1/3*sec(d*x+c)^3/a^3/d+1/5*sec(d*x+c)^5/a^3/d+4/7*sec(d*x+c)^7/a^3/d-3*tan(d*x+c)/a^3/d-10/3*tan(d*x+c)^3/a^3/d-11/5*tan(d*x+c)^5/a^3/d-4/7*tan(d*x+c)^7/a^3/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x,14,3*arctanh(cos(d*x+c))/a^3/d-cot(d*x+c)/a^3/d-3*sec(d*x+c)/a^3/d-sec(d*x+c)^3/a^3/d-3/5*sec(d*x+c)^5/a^3/d-4/7*sec(d*x+c)^7/a^3/d+7*tan(d*x+c)/a^3/d+5*tan(d*x+c)^3/a^3/d+13/5*tan(d*x+c)^5/a^3/d+4/7*tan(d*x+c)^7/a^3/d,1],
[sin(d*x+c)^2*(a+a*sin(d*x+c))*tan(d*x+c)^4,x,9,5/2*a*x-3*a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d-3*a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d-2*a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[sin(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c)^4,x,9,5/2*a*x-a*cos(d*x+c)/d-2*a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d-2*a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))*tan(d*x+c)^4,x,8,a*x-a*cos(d*x+c)/d-2*a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d-a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c)^3,x,6,a*x-a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d-a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))*tan(d*x+c)^2,x,5,-a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d+1/3*a*tan(d*x+c)^3/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))*tan(d*x+c),x,5,1/3*a*sec(d*x+c)^3/d+1/3*a*tan(d*x+c)^3/d,1],
[csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c)),x,7,-a*arctanh(cos(d*x+c))/d+a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d+a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c)),x,8,-a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d+a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d+2*a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c)),x,9,-5/2*a*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+2*a*sec(d*x+c)/d+1/3*a*sec(d*x+c)^3/d+2*a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[(a+a*sin(d*x+c))^2*tan(d*x+c)^4,x,4,7/2*a^2*x-2*a^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)/d/(1-sin(d*x+c))^2-11/3*a^2*cos(d*x+c)/d/(1-sin(d*x+c))-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^2*tan(d*x+c)^3,x,7,2*a^2*x-4/3*a^2*cos(d*x+c)/d-2*a^2*cos(d*x+c)/d/(1-sin(d*x+c))+1/3*a^4*cos(d*x+c)*sin(d*x+c)^2/d/(a-a*sin(d*x+c))^2,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^2*tan(d*x+c)^2,x,4,a^2*x-5/3*a^2*cos(d*x+c)/d/(1-sin(d*x+c))+1/3*a^4*cos(d*x+c)/d/(a-a*sin(d*x+c))^2,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^2*tan(d*x+c),x,4,-2/3*a^2*sec(d*x+c)/d+1/3*sec(d*x+c)^3*(a+a*sin(d*x+c))^2/d-2/3*a^2*tan(d*x+c)/d,1],
[csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x,5,-a^2*arctanh(cos(d*x+c))/d+4/3*a^2*cos(d*x+c)/d/(1-sin(d*x+c))+1/3*a^4*cos(d*x+c)/d/(a-a*sin(d*x+c))^2,1],
[csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x,7,-2*a^2*arctanh(cos(d*x+c))/d-10/3*a^2*cot(d*x+c)/d+2*a^2*cot(d*x+c)/d/(1-sin(d*x+c))+1/3*a^4*cot(d*x+c)/d/(a-a*sin(d*x+c))^2,1],
[csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x,8,-7/2*a^2*arctanh(cos(d*x+c))/d-16/3*a^2*cot(d*x+c)/d-7/2*a^2*cot(d*x+c)*csc(d*x+c)/d+8/3*a^2*cot(d*x+c)*csc(d*x+c)/d/(1-sin(d*x+c))+1/3*a^4*cot(d*x+c)*csc(d*x+c)/d/(a-a*sin(d*x+c))^2,1],
[(a+a*sin(d*x+c))^3*tan(d*x+c)^4,x,10,17/2*a^3*x-6*a^3*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2-25/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^3*tan(d*x+c)^3,x,8,11/2*a^3*x-3*a^3*cos(d*x+c)/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2-19/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))-1/2*a^3*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^3*tan(d*x+c)^2,x,5,3*a^3*x-3*a^3*cos(d*x+c)/d-2*a^5*cos(d*x+c)^3/d/(a-a*sin(d*x+c))^2+1/3*sec(d*x+c)^3*(a+a*sin(d*x+c))^3/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^3*tan(d*x+c),x,4,a^3*x+1/3*sec(d*x+c)^3*(a+a*sin(d*x+c))^3/d-2*a^5*cos(d*x+c)/d/(a^2-a^2*sin(d*x+c)),1],
[csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x,6,-a^3*arctanh(cos(d*x+c))/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2+5/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x,8,-3*a^3*arctanh(cos(d*x+c))/d-a^3*cot(d*x+c)/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2+11/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x,10,-11/2*a^3*arctanh(cos(d*x+c))/d-3*a^3*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2+17/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[csc(d*x+c)^4*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x,12,-17/2*a^3*arctanh(cos(d*x+c))/d-6*a^3*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^3*cot(d*x+c)*csc(d*x+c)/d+2/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c))^2+23/3*a^3*cos(d*x+c)/d/(1-sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4*tan(d*x+c)^4,x,13,163/8*a^4*x-16*a^4*cos(d*x+c)/d+4/3*a^4*cos(d*x+c)^3/d+4/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))^2-56/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))-35/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/4*a^4*cos(d*x+c)*sin(d*x+c)^3/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^4*tan(d*x+c)^2,x,8,17/2*a^4*x-4*a^4*cos(d*x+c)/d+4/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))^2-32/3*a^4*cos(d*x+c)/d/(1-sin(d*x+c))-1/2*a^4*cos(d*x+c)*sin(d*x+c)/d,1],
[sin(d*x+c)^2*tan(d*x+c)^4/(a+a*sin(d*x+c)),x,8,-x/a-cos(d*x+c)/a/d-3*sec(d*x+c)/a/d+sec(d*x+c)^3/a/d-1/5*sec(d*x+c)^5/a/d+tan(d*x+c)/a/d-1/3*tan(d*x+c)^3/a/d+1/5*tan(d*x+c)^5/a/d,1],
[sin(d*x+c)*tan(d*x+c)^4/(a+a*sin(d*x+c)),x,8,x/a+sec(d*x+c)/a/d-2/3*sec(d*x+c)^3/a/d+1/5*sec(d*x+c)^5/a/d-tan(d*x+c)/a/d+1/3*tan(d*x+c)^3/a/d-1/5*tan(d*x+c)^5/a/d,1],
[tan(d*x+c)^4/(a+a*sin(d*x+c)),x,6,-sec(d*x+c)/a/d+2/3*sec(d*x+c)^3/a/d-1/5*sec(d*x+c)^5/a/d+1/5*tan(d*x+c)^5/a/d,1],
[sec(d*x+c)*tan(d*x+c)^3/(a+a*sin(d*x+c)),x,6,-1/3*sec(d*x+c)^3/a/d+1/5*sec(d*x+c)^5/a/d-1/5*tan(d*x+c)^5/a/d,1],
[sec(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c)),x,7,1/3*sec(d*x+c)^3/a/d-1/5*sec(d*x+c)^5/a/d+1/3*tan(d*x+c)^3/a/d+1/5*tan(d*x+c)^5/a/d,1],
[sec(d*x+c)^3*tan(d*x+c)/(a+a*sin(d*x+c)),x,6,1/5*sec(d*x+c)^5/a/d-1/3*tan(d*x+c)^3/a/d-1/5*tan(d*x+c)^5/a/d,1],
[csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c)),x,7,-arctanh(cos(d*x+c))/a/d+sec(d*x+c)/a/d+1/3*sec(d*x+c)^3/a/d+1/5*sec(d*x+c)^5/a/d-tan(d*x+c)/a/d-2/3*tan(d*x+c)^3/a/d-1/5*tan(d*x+c)^5/a/d,1],
[csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c)),x,8,arctanh(cos(d*x+c))/a/d-cot(d*x+c)/a/d-sec(d*x+c)/a/d-1/3*sec(d*x+c)^3/a/d-1/5*sec(d*x+c)^5/a/d+3*tan(d*x+c)/a/d+tan(d*x+c)^3/a/d+1/5*tan(d*x+c)^5/a/d,1],
[sin(d*x+c)^3*tan(d*x+c)^4/(a+a*sin(d*x+c))^2,x,14,-2*x/a^2-cos(d*x+c)/a^2/d-5*sec(d*x+c)/a^2/d+3*sec(d*x+c)^3/a^2/d-7/5*sec(d*x+c)^5/a^2/d+2/7*sec(d*x+c)^7/a^2/d+2*tan(d*x+c)/a^2/d-2/3*tan(d*x+c)^3/a^2/d+2/5*tan(d*x+c)^5/a^2/d-2/7*tan(d*x+c)^7/a^2/d,1],
[sin(d*x+c)^2*tan(d*x+c)^4/(a+a*sin(d*x+c))^2,x,13,x/a^2+2*sec(d*x+c)/a^2/d-2*sec(d*x+c)^3/a^2/d+6/5*sec(d*x+c)^5/a^2/d-2/7*sec(d*x+c)^7/a^2/d-tan(d*x+c)/a^2/d+1/3*tan(d*x+c)^3/a^2/d-1/5*tan(d*x+c)^5/a^2/d+2/7*tan(d*x+c)^7/a^2/d,1],
[sin(d*x+c)*tan(d*x+c)^4/(a+a*sin(d*x+c))^2,x,11,-sec(d*x+c)/a^2/d+4/3*sec(d*x+c)^3/a^2/d-sec(d*x+c)^5/a^2/d+2/7*sec(d*x+c)^7/a^2/d-2/7*tan(d*x+c)^7/a^2/d,1],
[tan(d*x+c)^4/(a+a*sin(d*x+c))^2,x,10,-2/3*sec(d*x+c)^3/a^2/d+4/5*sec(d*x+c)^5/a^2/d-2/7*sec(d*x+c)^7/a^2/d+1/5*tan(d*x+c)^5/a^2/d+2/7*tan(d*x+c)^7/a^2/d,1],
[sec(d*x+c)*tan(d*x+c)^3/(a+a*sin(d*x+c))^2,x,12,1/3*sec(d*x+c)^3/a^2/d-3/5*sec(d*x+c)^5/a^2/d+2/7*sec(d*x+c)^7/a^2/d-2/5*tan(d*x+c)^5/a^2/d-2/7*tan(d*x+c)^7/a^2/d,1],
[sec(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c))^2,x,12,2/5*sec(d*x+c)^5/a^2/d-2/7*sec(d*x+c)^7/a^2/d+1/3*tan(d*x+c)^3/a^2/d+3/5*tan(d*x+c)^5/a^2/d+2/7*tan(d*x+c)^7/a^2/d,1],
[sec(d*x+c)^3*tan(d*x+c)/(a+a*sin(d*x+c))^2,x,4,1/7*sec(d*x+c)^3/d/(a+a*sin(d*x+c))^2-2/35*sec(d*x+c)^3/d/(a^2+a^2*sin(d*x+c))+8/35*tan(d*x+c)/a^2/d+8/105*tan(d*x+c)^3/a^2/d,1],
[csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x,11,-arctanh(cos(d*x+c))/a^2/d+sec(d*x+c)/a^2/d+1/3*sec(d*x+c)^3/a^2/d+1/5*sec(d*x+c)^5/a^2/d+2/7*sec(d*x+c)^7/a^2/d-2*tan(d*x+c)/a^2/d-2*tan(d*x+c)^3/a^2/d-6/5*tan(d*x+c)^5/a^2/d-2/7*tan(d*x+c)^7/a^2/d,1],
[csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x,12,2*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a^2/d-2*sec(d*x+c)/a^2/d-2/3*sec(d*x+c)^3/a^2/d-2/5*sec(d*x+c)^5/a^2/d-2/7*sec(d*x+c)^7/a^2/d+5*tan(d*x+c)/a^2/d+3*tan(d*x+c)^3/a^2/d+7/5*tan(d*x+c)^5/a^2/d+2/7*tan(d*x+c)^7/a^2/d,1],
[csc(d*x+c)^3*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x,15,-11/2*arctanh(cos(d*x+c))/a^2/d+2*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+5*sec(d*x+c)/a^2/d+4/3*sec(d*x+c)^3/a^2/d+3/5*sec(d*x+c)^5/a^2/d+2/7*sec(d*x+c)^7/a^2/d-8*tan(d*x+c)/a^2/d-4*tan(d*x+c)^3/a^2/d-8/5*tan(d*x+c)^5/a^2/d-2/7*tan(d*x+c)^7/a^2/d,1],
[sin(d*x+c)^3*tan(d*x+c)^4/(a+a*sin(d*x+c))^3,x,17,x/a^3+3*sec(d*x+c)/a^3/d-13/3*sec(d*x+c)^3/a^3/d+21/5*sec(d*x+c)^5/a^3/d-15/7*sec(d*x+c)^7/a^3/d+4/9*sec(d*x+c)^9/a^3/d-tan(d*x+c)/a^3/d+1/3*tan(d*x+c)^3/a^3/d-1/5*tan(d*x+c)^5/a^3/d+1/7*tan(d*x+c)^7/a^3/d-4/9*tan(d*x+c)^9/a^3/d,1],
[sin(d*x+c)^2*tan(d*x+c)^4/(a+a*sin(d*x+c))^3,x,14,-sec(d*x+c)/a^3/d+7/3*sec(d*x+c)^3/a^3/d-3*sec(d*x+c)^5/a^3/d+13/7*sec(d*x+c)^7/a^3/d-4/9*sec(d*x+c)^9/a^3/d+1/7*tan(d*x+c)^7/a^3/d+4/9*tan(d*x+c)^9/a^3/d,1],
[sin(d*x+c)*tan(d*x+c)^4/(a+a*sin(d*x+c))^3,x,14,-sec(d*x+c)^3/a^3/d+2*sec(d*x+c)^5/a^3/d-11/7*sec(d*x+c)^7/a^3/d+4/9*sec(d*x+c)^9/a^3/d-3/7*tan(d*x+c)^7/a^3/d-4/9*tan(d*x+c)^9/a^3/d,1],
[tan(d*x+c)^4/(a+a*sin(d*x+c))^3,x,14,1/3*sec(d*x+c)^3/a^3/d-6/5*sec(d*x+c)^5/a^3/d+9/7*sec(d*x+c)^7/a^3/d-4/9*sec(d*x+c)^9/a^3/d+1/5*tan(d*x+c)^5/a^3/d+5/7*tan(d*x+c)^7/a^3/d+4/9*tan(d*x+c)^9/a^3/d,1],
[sec(d*x+c)*tan(d*x+c)^3/(a+a*sin(d*x+c))^3,x,15,3/5*sec(d*x+c)^5/a^3/d-sec(d*x+c)^7/a^3/d+4/9*sec(d*x+c)^9/a^3/d-3/5*tan(d*x+c)^5/a^3/d-tan(d*x+c)^7/a^3/d-4/9*tan(d*x+c)^9/a^3/d,1],
[sec(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c))^3,x,15,-1/5*sec(d*x+c)^5/a^3/d+5/7*sec(d*x+c)^7/a^3/d-4/9*sec(d*x+c)^9/a^3/d+1/3*tan(d*x+c)^3/a^3/d+6/5*tan(d*x+c)^5/a^3/d+9/7*tan(d*x+c)^7/a^3/d+4/9*tan(d*x+c)^9/a^3/d,1],
[sec(d*x+c)^3*tan(d*x+c)/(a+a*sin(d*x+c))^3,x,5,1/9*sec(d*x+c)^3/d/(a+a*sin(d*x+c))^3-1/21*sec(d*x+c)^3/a/d/(a+a*sin(d*x+c))^2-1/21*sec(d*x+c)^3/d/(a^3+a^3*sin(d*x+c))+4/21*tan(d*x+c)/a^3/d+4/63*tan(d*x+c)^3/a^3/d,1],
[csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x,14,-arctanh(cos(d*x+c))/a^3/d+sec(d*x+c)/a^3/d+1/3*sec(d*x+c)^3/a^3/d+1/5*sec(d*x+c)^5/a^3/d+1/7*sec(d*x+c)^7/a^3/d+4/9*sec(d*x+c)^9/a^3/d-3*tan(d*x+c)/a^3/d-13/3*tan(d*x+c)^3/a^3/d-21/5*tan(d*x+c)^5/a^3/d-15/7*tan(d*x+c)^7/a^3/d-4/9*tan(d*x+c)^9/a^3/d,1],
[csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x,14,3*arctanh(cos(d*x+c))/a^3/d-cot(d*x+c)/a^3/d-3*sec(d*x+c)/a^3/d-sec(d*x+c)^3/a^3/d-3/5*sec(d*x+c)^5/a^3/d-3/7*sec(d*x+c)^7/a^3/d-4/9*sec(d*x+c)^9/a^3/d+8*tan(d*x+c)/a^3/d+22/3*tan(d*x+c)^3/a^3/d+28/5*tan(d*x+c)^5/a^3/d+17/7*tan(d*x+c)^7/a^3/d+4/9*tan(d*x+c)^9/a^3/d,1],
[tan(d*x+c)^4/(a+a*sin(d*x+c))^4,x,17,4/5*sec(d*x+c)^5/a^4/d-16/7*sec(d*x+c)^7/a^4/d+20/9*sec(d*x+c)^9/a^4/d-8/11*sec(d*x+c)^11/a^4/d+1/5*tan(d*x+c)^5/a^4/d+9/7*tan(d*x+c)^7/a^4/d+16/9*tan(d*x+c)^9/a^4/d+8/11*tan(d*x+c)^11/a^4/d,1],
[sec(d*x+c)*tan(d*x+c)^3/(a+a*sin(d*x+c))^4,x,18,-1/5*sec(d*x+c)^5/a^4/d+9/7*sec(d*x+c)^7/a^4/d-16/9*sec(d*x+c)^9/a^4/d+8/11*sec(d*x+c)^11/a^4/d-4/5*tan(d*x+c)^5/a^4/d-16/7*tan(d*x+c)^7/a^4/d-20/9*tan(d*x+c)^9/a^4/d-8/11*tan(d*x+c)^11/a^4/d,1],
[sec(d*x+c)^2*tan(d*x+c)^2/(a+a*sin(d*x+c))^4,x,8,-4/7*sec(d*x+c)^7/a^4/d+4/3*sec(d*x+c)^9/a^4/d-8/11*sec(d*x+c)^11/a^4/d+1/3*tan(d*x+c)^3/a^4/d+2*tan(d*x+c)^5/a^4/d+25/7*tan(d*x+c)^7/a^4/d+8/3*tan(d*x+c)^9/a^4/d+8/11*tan(d*x+c)^11/a^4/d,1],
[sin(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c)^5,x,4,-39/16*a*ln(1-sin(d*x+c))/d-9/16*a*ln(1+sin(d*x+c))/d-a*sin(d*x+c)/d-1/2*a*sin(d*x+c)^2/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2-5/4*a^5/d/(a^4-a^4*sin(d*x+c))-1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))*tan(d*x+c)^5,x,3,-23/16*a*ln(1-sin(d*x+c))/d+7/16*a*ln(1+sin(d*x+c))/d-a*sin(d*x+c)/d+1/8*a^3/d/(a-a*sin(d*x+c))^2-a^2/d/(a-a*sin(d*x+c))+1/8*a^2/d/(a+a*sin(d*x+c)),1],
[sec(d*x+c)*(a+a*sin(d*x+c))*tan(d*x+c)^4,x,4,-11/16*a*ln(1-sin(d*x+c))/d-5/16*a*ln(1+sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2-3/4*a^5/d/(a^4-a^4*sin(d*x+c))-1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))*tan(d*x+c)^3,x,5,3/8*a*arctanh(sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2-1/2*a^5/d/(a^4-a^4*sin(d*x+c))+1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))*tan(d*x+c)^2,x,5,-1/8*a*arctanh(sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2-1/4*a^5/d/(a^4-a^4*sin(d*x+c))-1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))*tan(d*x+c),x,5,-1/8*a*arctanh(sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2+1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c)),x,4,-11/16*a*ln(1-sin(d*x+c))/d+a*ln(sin(d*x+c))/d-5/16*a*ln(1+sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2+1/2*a^5/d/(a^4-a^4*sin(d*x+c))+1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d-23/16*a*ln(1-sin(d*x+c))/d+a*ln(sin(d*x+c))/d+7/16*a*ln(1+sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2+3/4*a^5/d/(a^4-a^4*sin(d*x+c))-1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c)),x,4,-a*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-39/16*a*ln(1-sin(d*x+c))/d+3*a*ln(sin(d*x+c))/d-9/16*a*ln(1+sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2+a^5/d/(a^4-a^4*sin(d*x+c))+1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
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[(a+a*sin(d*x+c))^2*tan(d*x+c)^5,x,3,-31/8*a^2*ln(1-sin(d*x+c))/d-1/8*a^2*ln(1+sin(d*x+c))/d-2*a^2*sin(d*x+c)/d-1/2*a^2*sin(d*x+c)^2/d+1/4*a^4/d/(a-a*sin(d*x+c))^2-9/4*a^3/d/(a-a*sin(d*x+c)),1],
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[sec(d*x+c)^3*tan(d*x+c)^6/(a+a*sin(d*x+c)),x,11,-3/256*arctanh(sin(d*x+c))/a/d-3/256*sec(d*x+c)*tan(d*x+c)/a/d-1/128*sec(d*x+c)^3*tan(d*x+c)/a/d+1/32*sec(d*x+c)^5*tan(d*x+c)/a/d-1/16*sec(d*x+c)^5*tan(d*x+c)^3/a/d+1/10*sec(d*x+c)^5*tan(d*x+c)^5/a/d-1/8*tan(d*x+c)^8/a/d-1/10*tan(d*x+c)^10/a/d,1],
[sec(d*x+c)^4*tan(d*x+c)^5/(a+a*sin(d*x+c)),x,11,3/256*arctanh(sin(d*x+c))/a/d+1/6*sec(d*x+c)^6/a/d-1/4*sec(d*x+c)^8/a/d+1/10*sec(d*x+c)^10/a/d+3/256*sec(d*x+c)*tan(d*x+c)/a/d+1/128*sec(d*x+c)^3*tan(d*x+c)/a/d-1/32*sec(d*x+c)^5*tan(d*x+c)/a/d+1/16*sec(d*x+c)^5*tan(d*x+c)^3/a/d-1/10*sec(d*x+c)^5*tan(d*x+c)^5/a/d,1],
[sec(d*x+c)^5*tan(d*x+c)^4/(a+a*sin(d*x+c)),x,11,3/256*arctanh(sin(d*x+c))/a/d-1/6*sec(d*x+c)^6/a/d+1/4*sec(d*x+c)^8/a/d-1/10*sec(d*x+c)^10/a/d+3/256*sec(d*x+c)*tan(d*x+c)/a/d+1/128*sec(d*x+c)^3*tan(d*x+c)/a/d+1/160*sec(d*x+c)^5*tan(d*x+c)/a/d-3/80*sec(d*x+c)^7*tan(d*x+c)/a/d+1/10*sec(d*x+c)^7*tan(d*x+c)^3/a/d,1],
[sec(d*x+c)^6*tan(d*x+c)^3/(a+a*sin(d*x+c)),x,11,-3/256*arctanh(sin(d*x+c))/a/d-1/8*sec(d*x+c)^8/a/d+1/10*sec(d*x+c)^10/a/d-3/256*sec(d*x+c)*tan(d*x+c)/a/d-1/128*sec(d*x+c)^3*tan(d*x+c)/a/d-1/160*sec(d*x+c)^5*tan(d*x+c)/a/d+3/80*sec(d*x+c)^7*tan(d*x+c)/a/d-1/10*sec(d*x+c)^7*tan(d*x+c)^3/a/d,1],
[sec(d*x+c)^7*tan(d*x+c)^2/(a+a*sin(d*x+c)),x,11,-7/256*arctanh(sin(d*x+c))/a/d+1/8*sec(d*x+c)^8/a/d-1/10*sec(d*x+c)^10/a/d-7/256*sec(d*x+c)*tan(d*x+c)/a/d-7/384*sec(d*x+c)^3*tan(d*x+c)/a/d-7/480*sec(d*x+c)^5*tan(d*x+c)/a/d-1/80*sec(d*x+c)^7*tan(d*x+c)/a/d+1/10*sec(d*x+c)^9*tan(d*x+c)/a/d,1],
[sec(d*x+c)^8*tan(d*x+c)/(a+a*sin(d*x+c)),x,9,7/256*arctanh(sin(d*x+c))/a/d+1/10*sec(d*x+c)^10/a/d+7/256*sec(d*x+c)*tan(d*x+c)/a/d+7/384*sec(d*x+c)^3*tan(d*x+c)/a/d+7/480*sec(d*x+c)^5*tan(d*x+c)/a/d+1/80*sec(d*x+c)^7*tan(d*x+c)/a/d-1/10*sec(d*x+c)^9*tan(d*x+c)/a/d,1],
[sec(d*x+c)^9/(a+a*sin(d*x+c)),x,4,63/256*arctanh(sin(d*x+c))/a/d+1/256*a^3/d/(a-a*sin(d*x+c))^4+1/64*a^2/d/(a-a*sin(d*x+c))^3+7/64/d/(a-a*sin(d*x+c))-5/256*a^3/d/(a+a*sin(d*x+c))^4-5/128*a^2/d/(a+a*sin(d*x+c))^3-35/256/d/(a+a*sin(d*x+c))-1/160*a^9/d/(a^2+a^2*sin(d*x+c))^5+21/512*a^9/d/(a^5-a^5*sin(d*x+c))^2-35/512*a^9/d/(a^5+a^5*sin(d*x+c))^2,1],
[csc(d*x+c)*sec(d*x+c)^9/(a+a*sin(d*x+c)),x,4,-193/512*ln(1-sin(d*x+c))/a/d+ln(sin(d*x+c))/a/d-319/512*ln(1+sin(d*x+c))/a/d+1/256*a^3/d/(a-a*sin(d*x+c))^4+1/48*a^2/d/(a-a*sin(d*x+c))^3+65/256/d/(a-a*sin(d*x+c))+7/256*a^3/d/(a+a*sin(d*x+c))^4+29/384*a^2/d/(a+a*sin(d*x+c))^3+1/2/d/(a+a*sin(d*x+c))+1/160*a^9/d/(a^2+a^2*sin(d*x+c))^5+37/512*a^9/d/(a^5-a^5*sin(d*x+c))^2+93/512*a^9/d/(a^5+a^5*sin(d*x+c))^2,1],
[csc(d*x+c)^2*sec(d*x+c)^9/(a+a*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-437/512*ln(1-sin(d*x+c))/a/d-ln(sin(d*x+c))/a/d+949/512*ln(1+sin(d*x+c))/a/d+1/256*a^3/d/(a-a*sin(d*x+c))^4+5/192*a^2/d/(a-a*sin(d*x+c))^3+61/128/d/(a-a*sin(d*x+c))-9/256*a^3/d/(a+a*sin(d*x+c))^4-47/384*a^2/d/(a+a*sin(d*x+c))^3-315/256/d/(a+a*sin(d*x+c))-1/160*a^9/d/(a^2+a^2*sin(d*x+c))^5+57/512*a^9/d/(a^5-a^5*sin(d*x+c))^2-187/512*a^9/d/(a^5+a^5*sin(d*x+c))^2,1],
[(g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x,5,AppellF1(1+n,1/2*p+1/2,1/2-m+1/2*p,2+n,sin(f*x+e),-sin(f*x+e))*sec(f*x+e)*(g*sec(f*x+e))^p*(1-sin(f*x+e))^(1/2*p+1/2)*(d*sin(f*x+e))^(1+n)*(1+sin(f*x+e))^(1/2-m+1/2*p)*(a+a*sin(f*x+e))^m/d/f/(1+n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,3,hypergeom([1+m, -n],[2+m],-d*(1+sin(f*x+e))/(c-d))*(a+a*sin(f*x+e))^(1+m)*(c+d*sin(f*x+e))^n/a/f/(1+m)/(((c+d*sin(f*x+e))/(c-d))^n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x,3,a^4*(c-d)^4*(c+d*sin(f*x+e))^(1+n)/d^5/f/(1+n)-4*a^4*(c-d)^3*(c+d*sin(f*x+e))^(2+n)/d^5/f/(2+n)+6*a^4*(c-d)^2*(c+d*sin(f*x+e))^(3+n)/d^5/f/(3+n)-4*a^4*(c-d)*(c+d*sin(f*x+e))^(4+n)/d^5/f/(4+n)+a^4*(c+d*sin(f*x+e))^(5+n)/d^5/f/(5+n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x,3,-a^3*(c-d)^3*(c+d*sin(f*x+e))^(1+n)/d^4/f/(1+n)+3*a^3*(c-d)^2*(c+d*sin(f*x+e))^(2+n)/d^4/f/(2+n)-3*a^3*(c-d)*(c+d*sin(f*x+e))^(3+n)/d^4/f/(3+n)+a^3*(c+d*sin(f*x+e))^(4+n)/d^4/f/(4+n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x,3,a^2*(c-d)^2*(c+d*sin(f*x+e))^(1+n)/d^3/f/(1+n)-2*a^2*(c-d)*(c+d*sin(f*x+e))^(2+n)/d^3/f/(2+n)+a^2*(c+d*sin(f*x+e))^(3+n)/d^3/f/(3+n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x,3,-a*(c-d)*(c+d*sin(f*x+e))^(1+n)/d^2/f/(1+n)+a*(c+d*sin(f*x+e))^(2+n)/d^2/f/(2+n),1],
[cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x,2,-hypergeom([1, 1+n],[2+n],(c+d*sin(f*x+e))/(c-d))*(c+d*sin(f*x+e))^(1+n)/a/(c-d)/f/(1+n),1],
[cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x,2,d*hypergeom([2, 1+n],[2+n],(c+d*sin(f*x+e))/(c-d))*(c+d*sin(f*x+e))^(1+n)/a^2/(c-d)^2/f/(1+n),1],
[cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x,2,-d^2*hypergeom([3, 1+n],[2+n],(c+d*sin(f*x+e))/(c-d))*(c+d*sin(f*x+e))^(1+n)/a^3/(c-d)^3/f/(1+n),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x,3,(c-d)^4*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m)+4*(c-d)^3*d*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m)+6*(c-d)^2*d^2*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m)+4*(c-d)*d^3*(a+a*sin(f*x+e))^(4+m)/a^4/f/(4+m)+d^4*(a+a*sin(f*x+e))^(5+m)/a^5/f/(5+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x,3,(c-d)^3*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m)+3*(c-d)^2*d*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m)+3*(c-d)*d^2*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m)+d^3*(a+a*sin(f*x+e))^(4+m)/a^4/f/(4+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x,3,(c-d)^2*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m)+2*(c-d)*d*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m)+d^2*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x,3,(c-d)*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m)+d*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x,2,hypergeom([1, 1+m],[2+m],-d*(1+sin(f*x+e))/(c-d))*(a+a*sin(f*x+e))^(1+m)/a/(c-d)/f/(1+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x,2,hypergeom([2, 1+m],[2+m],-d*(1+sin(f*x+e))/(c-d))*(a+a*sin(f*x+e))^(1+m)/a/(c-d)^2/f/(1+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x,2,hypergeom([3, 1+m],[2+m],-d*(1+sin(f*x+e))/(c-d))*(a+a*sin(f*x+e))^(1+m)/a/(c-d)^3/f/(1+m),1],
[cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x,3,-hypergeom([1, 2+m+n],[2+m],1+sin(d*x+c))*sin(d*x+c)^(1+n)*(a+a*sin(d*x+c))^(1+m)/a/d/(1+m),1],
[cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x,4,(a+a*sin(d*x+c))^(1+m)/a/d/(1+m)-4*(a+a*sin(d*x+c))^(2+m)/a^2/d/(2+m)+6*(a+a*sin(d*x+c))^(3+m)/a^3/d/(3+m)-4*(a+a*sin(d*x+c))^(4+m)/a^4/d/(4+m)+(a+a*sin(d*x+c))^(5+m)/a^5/d/(5+m),1],
[cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x,4,-(a+a*sin(d*x+c))^(1+m)/a/d/(1+m)+3*(a+a*sin(d*x+c))^(2+m)/a^2/d/(2+m)-3*(a+a*sin(d*x+c))^(3+m)/a^3/d/(3+m)+(a+a*sin(d*x+c))^(4+m)/a^4/d/(4+m),1],
[cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x,4,(a+a*sin(d*x+c))^(1+m)/a/d/(1+m)-2*(a+a*sin(d*x+c))^(2+m)/a^2/d/(2+m)+(a+a*sin(d*x+c))^(3+m)/a^3/d/(3+m),1],
[cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x,4,-(a+a*sin(d*x+c))^(1+m)/a/d/(1+m)+(a+a*sin(d*x+c))^(2+m)/a^2/d/(2+m),1],
[cot(d*x+c)*(a+a*sin(d*x+c))^m,x,2,-hypergeom([1, 1+m],[2+m],1+sin(d*x+c))*(a+a*sin(d*x+c))^(1+m)/a/d/(1+m),1],
[cot(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x,3,hypergeom([2, 1+m],[2+m],1+sin(d*x+c))*(a+a*sin(d*x+c))^(1+m)/a/d/(1+m),1],
[cot(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x,3,-hypergeom([3, 1+m],[2+m],1+sin(d*x+c))*(a+a*sin(d*x+c))^(1+m)/a/d/(1+m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x,4,1/8*a*(4*c+d)*x-1/3*a*(c+d)*cos(f*x+e)^3/f+1/8*a*(4*c+d)*cos(f*x+e)*sin(f*x+e)/f-1/4*a*d*cos(f*x+e)^3*sin(f*x+e)/f,1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x,6,-2*sqrt(2)*arctanh(sqrt(a)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e)))/a^(3/2)/(c-d)/f+2*sqrt(c+d)*arctanh(sqrt(a)*sqrt(d)*cos(f*x+e)/sqrt(c+d)/sqrt(a+a*sin(f*x+e)))/a^(3/2)/(c-d)/sqrt(d)/f,1],
[cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/sqrt(c+d*sin(f*x+e)),x,6,2*arctan(sqrt(a)*sqrt(d)*cos(f*x+e)/sqrt(a+a*sin(f*x+e))/sqrt(c+d*sin(f*x+e)))/a^(3/2)/sqrt(d)/f-2*sqrt(2)*arctanh(sqrt(a)*sqrt(c-d)*cos(f*x+e)/sqrt(2)/sqrt(a+a*sin(f*x+e))/sqrt(c+d*sin(f*x+e)))/a^(3/2)/sqrt(c-d)/f,1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,3,-1/3*2^(3/2+m)*AppellF1(3/2,-1/2-m,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(1+sin(f*x+e))^(-1/2-m)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n/f/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x,4,-16/3*sqrt(2)*a^3*AppellF1(3/2,-7/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x,4,-8/3*sqrt(2)*a^2*AppellF1(3/2,-5/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x,4,-4/3*sqrt(2)*a*AppellF1(3/2,-3/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x,5,2*sqrt(2)*AppellF1(1/2,-1/2,-n,3/2,1/2+1/2*sin(f*x+e),-d*(1+sin(f*x+e))/(c-d))*cos(f*x+e)*(c+d*sin(f*x+e))^n/a/f/sqrt(1-sin(f*x+e))/(((c+d*sin(f*x+e))/(c-d))^n),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x,4,-1/3*AppellF1(3/2,3/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/sqrt(2)/a^2/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x,4,-1/6*AppellF1(3/2,5/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/sqrt(2)/a^3/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,3,-1/5*2^(5/2+m)*AppellF1(5/2,-3/2-m,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))^2*(1+sin(f*x+e))^(-1/2-m)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n/f/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x,4,-16/5*sqrt(2)*a^2*AppellF1(5/2,-7/2,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))^2*(c+d*sin(f*x+e))^n/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x,4,-8/5*sqrt(2)*a*AppellF1(5/2,-5/2,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)^3*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/f/(1+sin(f*x+e))^(3/2)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x,5,4/3*sqrt(2)*AppellF1(3/2,-3/2,-n,5/2,1/2+1/2*sin(f*x+e),-d*(1+sin(f*x+e))/(c-d))*cos(f*x+e)*(1+sin(f*x+e))*(c+d*sin(f*x+e))^n/a/f/sqrt(1-sin(f*x+e))/(((c+d*sin(f*x+e))/(c-d))^n),1],
[cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x,5,4*sqrt(2)*AppellF1(1/2,-3/2,-n,3/2,1/2+1/2*sin(f*x+e),-d*(1+sin(f*x+e))/(c-d))*cos(f*x+e)*(c+d*sin(f*x+e))^n/a^2/f/sqrt(1-sin(f*x+e))/(((c+d*sin(f*x+e))/(c-d))^n),1],
[cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x,4,-1/5*AppellF1(5/2,3/2,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))^2*(c+d*sin(f*x+e))^n/sqrt(2)/a^3/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x,4,-1/10*AppellF1(5/2,5/2,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))^2*(c+d*sin(f*x+e))^n/sqrt(2)/a^4/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x,4,-1/20*AppellF1(5/2,7/2,-n,7/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))^2*(c+d*sin(f*x+e))^n/sqrt(2)/a^5/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,8/5*(A-B)*(a+a*sin(d*x+c))^5/a^4/d-2/3*(3*A-5*B)*(a+a*sin(d*x+c))^6/a^5/d+6/7*(A-3*B)*(a+a*sin(d*x+c))^7/a^6/d-1/8*(A-7*B)*(a+a*sin(d*x+c))^8/a^7/d-1/9*B*(a+a*sin(d*x+c))^9/a^8/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,(A-B)*(a+a*sin(d*x+c))^4/a^3/d-4/5*(A-2*B)*(a+a*sin(d*x+c))^5/a^4/d+1/6*(A-5*B)*(a+a*sin(d*x+c))^6/a^5/d+1/7*B*(a+a*sin(d*x+c))^7/a^6/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,2/3*(A-B)*(a+a*sin(d*x+c))^3/a^2/d-1/4*(A-3*B)*(a+a*sin(d*x+c))^4/a^3/d-1/5*B*(a+a*sin(d*x+c))^5/a^4/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,a*A*sin(d*x+c)/d+1/2*a*(A+B)*sin(d*x+c)^2/d+1/3*a*B*sin(d*x+c)^3/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,-a*(A+B)*ln(1-sin(d*x+c))/d-a*B*sin(d*x+c)/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/2*a*(A-B)*arctanh(sin(d*x+c))/d+1/2*a^3*(A+B)/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/8*a*(3*A-B)*arctanh(sin(d*x+c))/d+1/8*a^5*(A+B)/d/(a^2-a^2*sin(d*x+c))^2+1/4*a^5*A/d/(a^4-a^4*sin(d*x+c))-1/8*a^5*(A-B)/d/(a^4+a^4*sin(d*x+c)),1],
[sec(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/16*a*(5*A-B)*arctanh(sin(d*x+c))/d+1/24*a^7*(A+B)/d/(a^2-a^2*sin(d*x+c))^3+1/32*a^7*(3*A+B)/d/(a^3-a^3*sin(d*x+c))^2-1/32*a^7*(A-B)/d/(a^3+a^3*sin(d*x+c))^2+3/16*a^7*A/d/(a^6-a^6*sin(d*x+c))-1/16*a^7*(2*A-B)/d/(a^6+a^6*sin(d*x+c)),1],
[cos(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,6,5/128*a*(8*A+B)*x-1/56*a*(8*A+B)*cos(d*x+c)^7/d+5/128*a*(8*A+B)*cos(d*x+c)*sin(d*x+c)/d+5/192*a*(8*A+B)*cos(d*x+c)^3*sin(d*x+c)/d+1/48*a*(8*A+B)*cos(d*x+c)^5*sin(d*x+c)/d-1/8*B*cos(d*x+c)^7*(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,5,1/16*a*(6*A+B)*x-1/30*a*(6*A+B)*cos(d*x+c)^5/d+1/16*a*(6*A+B)*cos(d*x+c)*sin(d*x+c)/d+1/24*a*(6*A+B)*cos(d*x+c)^3*sin(d*x+c)/d-1/6*B*cos(d*x+c)^5*(a+a*sin(d*x+c))/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/8*a*(4*A+B)*x-1/12*a*(4*A+B)*cos(d*x+c)^3/d+1/8*a*(4*A+B)*cos(d*x+c)*sin(d*x+c)/d-1/4*B*cos(d*x+c)^3*(a+a*sin(d*x+c))/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,2,-a*B*x+(A+B)*sec(d*x+c)*(a+a*sin(d*x+c))/d,1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,1/3*(A+B)*sec(d*x+c)^3*(a+a*sin(d*x+c))/d+1/3*a*(2*A-B)*tan(d*x+c)/d,1],
[sec(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,1/5*(A+B)*sec(d*x+c)^5*(a+a*sin(d*x+c))/d+1/5*a*(4*A-B)*tan(d*x+c)/d+1/15*a*(4*A-B)*tan(d*x+c)^3/d,1],
[sec(d*x+c)^8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,1/7*(A+B)*sec(d*x+c)^7*(a+a*sin(d*x+c))/d+1/7*a*(6*A-B)*tan(d*x+c)/d+2/21*a*(6*A-B)*tan(d*x+c)^3/d+1/35*a*(6*A-B)*tan(d*x+c)^5/d,1],
[sec(d*x+c)^10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,1/9*(A+B)*sec(d*x+c)^9*(a+a*sin(d*x+c))/d+1/9*a*(8*A-B)*tan(d*x+c)/d+1/9*a*(8*A-B)*tan(d*x+c)^3/d+1/15*a*(8*A-B)*tan(d*x+c)^5/d+1/63*a*(8*A-B)*tan(d*x+c)^7/d,1],
[cos(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,4/3*(A-B)*(a+a*sin(d*x+c))^6/a^4/d-4/7*(3*A-5*B)*(a+a*sin(d*x+c))^7/a^5/d+3/4*(A-3*B)*(a+a*sin(d*x+c))^8/a^6/d-1/9*(A-7*B)*(a+a*sin(d*x+c))^9/a^7/d-1/10*B*(a+a*sin(d*x+c))^10/a^8/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,4/5*(A-B)*(a+a*sin(d*x+c))^5/a^3/d-2/3*(A-2*B)*(a+a*sin(d*x+c))^6/a^4/d+1/7*(A-5*B)*(a+a*sin(d*x+c))^7/a^5/d+1/8*B*(a+a*sin(d*x+c))^8/a^6/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,1/2*(A-B)*(a+a*sin(d*x+c))^4/a^2/d-1/5*(A-3*B)*(a+a*sin(d*x+c))^5/a^3/d-1/6*B*(a+a*sin(d*x+c))^6/a^4/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,1/3*(A-B)*(a+a*sin(d*x+c))^3/a/d+1/4*B*(a+a*sin(d*x+c))^4/a^2/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,-2*a^2*(A+B)*ln(1-sin(d*x+c))/d-a^2*(A+B)*sin(d*x+c)/d-1/2*B*(a+a*sin(d*x+c))^2/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,a^2*B*ln(1-sin(d*x+c))/d+a^3*(A+B)/d/(a-a*sin(d*x+c)),1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/4*a^2*(A-B)*arctanh(sin(d*x+c))/d+1/4*a^4*(A+B)/d/(a-a*sin(d*x+c))^2+1/4*a^5*(A-B)/d/(a^3-a^3*sin(d*x+c)),1],
[sec(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/8*a^2*(2*A-B)*arctanh(sin(d*x+c))/d+1/12*a^5*(A+B)/d/(a-a*sin(d*x+c))^3+1/8*a^4*A/d/(a-a*sin(d*x+c))^2+1/16*a^7*(3*A-B)/d/(a^5-a^5*sin(d*x+c))-1/16*a^7*(A-B)/d/(a^5+a^5*sin(d*x+c)),1],
[cos(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,7,5/128*a^2*(9*A+2*B)*x-1/56*a^2*(9*A+2*B)*cos(d*x+c)^7/d+5/128*a^2*(9*A+2*B)*cos(d*x+c)*sin(d*x+c)/d+5/192*a^2*(9*A+2*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/48*a^2*(9*A+2*B)*cos(d*x+c)^5*sin(d*x+c)/d-1/9*B*cos(d*x+c)^7*(a+a*sin(d*x+c))^2/d-1/72*(9*A+2*B)*cos(d*x+c)^7*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,6,1/16*a^2*(7*A+2*B)*x-1/30*a^2*(7*A+2*B)*cos(d*x+c)^5/d+1/16*a^2*(7*A+2*B)*cos(d*x+c)*sin(d*x+c)/d+1/24*a^2*(7*A+2*B)*cos(d*x+c)^3*sin(d*x+c)/d-1/7*B*cos(d*x+c)^5*(a+a*sin(d*x+c))^2/d-1/42*(7*A+2*B)*cos(d*x+c)^5*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,5,1/8*a^2*(5*A+2*B)*x-1/12*a^2*(5*A+2*B)*cos(d*x+c)^3/d+1/8*a^2*(5*A+2*B)*cos(d*x+c)*sin(d*x+c)/d-1/5*B*cos(d*x+c)^3*(a+a*sin(d*x+c))^2/d-1/20*(5*A+2*B)*cos(d*x+c)^3*(a^2+a^2*sin(d*x+c))/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,-a^2*(A+2*B)*x+a^2*(A+2*B)*cos(d*x+c)/d+(A+B)*sec(d*x+c)*(a+a*sin(d*x+c))^2/d,1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/3*a^2*(A-2*B)*sec(d*x+c)/d+1/3*(A+B)*sec(d*x+c)^3*(a+a*sin(d*x+c))^2/d+1/3*a^2*(A-2*B)*tan(d*x+c)/d,1],
[sec(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/15*a^2*(3*A-2*B)*sec(d*x+c)^3/d+1/5*(A+B)*sec(d*x+c)^5*(a+a*sin(d*x+c))^2/d+1/5*a^2*(3*A-2*B)*tan(d*x+c)/d+1/15*a^2*(3*A-2*B)*tan(d*x+c)^3/d,1],
[sec(d*x+c)^8*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/35*a^2*(5*A-2*B)*sec(d*x+c)^5/d+1/7*(A+B)*sec(d*x+c)^7*(a+a*sin(d*x+c))^2/d+1/7*a^2*(5*A-2*B)*tan(d*x+c)/d+2/21*a^2*(5*A-2*B)*tan(d*x+c)^3/d+1/35*a^2*(5*A-2*B)*tan(d*x+c)^5/d,1],
[sec(d*x+c)^10*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/63*a^2*(7*A-2*B)*sec(d*x+c)^7/d+1/9*(A+B)*sec(d*x+c)^9*(a+a*sin(d*x+c))^2/d+1/9*a^2*(7*A-2*B)*tan(d*x+c)/d+1/9*a^2*(7*A-2*B)*tan(d*x+c)^3/d+1/15*a^2*(7*A-2*B)*tan(d*x+c)^5/d+1/63*a^2*(7*A-2*B)*tan(d*x+c)^7/d,1],
[sec(d*x+c)^12*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/99*a^2*(9*A-2*B)*sec(d*x+c)^9/d+1/11*(A+B)*sec(d*x+c)^11*(a+a*sin(d*x+c))^2/d+1/11*a^2*(9*A-2*B)*tan(d*x+c)/d+4/33*a^2*(9*A-2*B)*tan(d*x+c)^3/d+6/55*a^2*(9*A-2*B)*tan(d*x+c)^5/d+4/77*a^2*(9*A-2*B)*tan(d*x+c)^7/d+1/99*a^2*(9*A-2*B)*tan(d*x+c)^9/d,1],
[cos(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,8/7*(A-B)*(a+a*sin(d*x+c))^7/a^4/d-1/2*(3*A-5*B)*(a+a*sin(d*x+c))^8/a^5/d+2/3*(A-3*B)*(a+a*sin(d*x+c))^9/a^6/d-1/10*(A-7*B)*(a+a*sin(d*x+c))^10/a^7/d-1/11*B*(a+a*sin(d*x+c))^11/a^8/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,2/3*(A-B)*(a+a*sin(d*x+c))^6/a^3/d-4/7*(A-2*B)*(a+a*sin(d*x+c))^7/a^4/d+1/8*(A-5*B)*(a+a*sin(d*x+c))^8/a^5/d+1/9*B*(a+a*sin(d*x+c))^9/a^6/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,2/5*(A-B)*(a+a*sin(d*x+c))^5/a^2/d-1/6*(A-3*B)*(a+a*sin(d*x+c))^6/a^3/d-1/7*B*(a+a*sin(d*x+c))^7/a^4/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,1/4*(A-B)*(a+a*sin(d*x+c))^4/a/d+1/5*B*(a+a*sin(d*x+c))^5/a^2/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,-4*a^3*(A+B)*ln(1-sin(d*x+c))/d-3*a^3*(A+B)*sin(d*x+c)/d-1/2*a^3*(A+B)*sin(d*x+c)^2/d-1/3*B*(a+a*sin(d*x+c))^3/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,3,a^3*(A+3*B)*ln(1-sin(d*x+c))/d+2*a^3*(A+B)/d/(1-sin(d*x+c))+a^3*B*sin(d*x+c)/d,1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,2,1/2*a^5*(a*A+a*B*sin(d*x+c))^2/(A+B)/d/(a^2-a^2*sin(d*x+c))^2,1],
[sec(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,1/8*a^3*(A-B)*arctanh(sin(d*x+c))/d+1/6*a^6*(A+B)/d/(a-a*sin(d*x+c))^3+1/8*a^7*(A-B)/d/(a^2-a^2*sin(d*x+c))^2+1/8*a^7*(A-B)/d/(a^4-a^4*sin(d*x+c)),1],
[sec(d*x+c)^9*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,1/32*a^3*(5*A-3*B)*arctanh(sin(d*x+c))/d+1/16*a^7*(A+B)/d/(a-a*sin(d*x+c))^4+1/12*a^9*A/d/(a^2-a^2*sin(d*x+c))^3+1/32*a^9*(3*A-B)/d/(a^3-a^3*sin(d*x+c))^2+1/16*a^9*(2*A-B)/d/(a^6-a^6*sin(d*x+c))-1/32*a^9*(A-B)/d/(a^6+a^6*sin(d*x+c)),1],
[cos(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,8,11/256*a^3*(10*A+3*B)*x-11/560*a^3*(10*A+3*B)*cos(d*x+c)^7/d+11/256*a^3*(10*A+3*B)*cos(d*x+c)*sin(d*x+c)/d+11/384*a^3*(10*A+3*B)*cos(d*x+c)^3*sin(d*x+c)/d+11/480*a^3*(10*A+3*B)*cos(d*x+c)^5*sin(d*x+c)/d-1/90*a*(10*A+3*B)*cos(d*x+c)^7*(a+a*sin(d*x+c))^2/d-1/10*B*cos(d*x+c)^7*(a+a*sin(d*x+c))^3/d-11/720*(10*A+3*B)*cos(d*x+c)^7*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,7,9/128*a^3*(8*A+3*B)*x-3/80*a^3*(8*A+3*B)*cos(d*x+c)^5/d+9/128*a^3*(8*A+3*B)*cos(d*x+c)*sin(d*x+c)/d+3/64*a^3*(8*A+3*B)*cos(d*x+c)^3*sin(d*x+c)/d-1/56*a*(8*A+3*B)*cos(d*x+c)^5*(a+a*sin(d*x+c))^2/d-1/8*B*cos(d*x+c)^5*(a+a*sin(d*x+c))^3/d-3/112*(8*A+3*B)*cos(d*x+c)^5*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,6,7/16*a^3*(2*A+B)*x-7/24*a^3*(2*A+B)*cos(d*x+c)^3/d+7/16*a^3*(2*A+B)*cos(d*x+c)*sin(d*x+c)/d-1/10*a*(2*A+B)*cos(d*x+c)^3*(a+a*sin(d*x+c))^2/d-1/6*B*cos(d*x+c)^3*(a+a*sin(d*x+c))^3/d-7/40*(2*A+B)*cos(d*x+c)^3*(a^3+a^3*sin(d*x+c))/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,2,-3/2*a^3*(2*A+3*B)*x+2*a^3*(2*A+3*B)*cos(d*x+c)/d+1/2*a^3*(2*A+3*B)*cos(d*x+c)*sin(d*x+c)/d+(A+B)*sec(d*x+c)*(a+a*sin(d*x+c))^3/d,1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,a^3*B*x+1/3*(A+B)*sec(d*x+c)^3*(a+a*sin(d*x+c))^3/d-2*a^5*B*cos(d*x+c)/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,1/15*a^5*(2*A-3*B)*cos(d*x+c)/d/(a-a*sin(d*x+c))^2+1/5*(A+B)*sec(d*x+c)^5*(a+a*sin(d*x+c))^3/d+1/15*a^5*(2*A-3*B)*cos(d*x+c)/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^8*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,1/7*(A+B)*sec(d*x+c)^7*(a+a*sin(d*x+c))^3/d+2/35*(4*A-3*B)*sec(d*x+c)^5*(a^3+a^3*sin(d*x+c))/d+3/35*a^3*(4*A-3*B)*tan(d*x+c)/d+1/35*a^3*(4*A-3*B)*tan(d*x+c)^3/d,1],
[sec(d*x+c)^10*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x,4,1/9*(A+B)*sec(d*x+c)^9*(a+a*sin(d*x+c))^3/d+2/21*(2*A-B)*sec(d*x+c)^7*(a^3+a^3*sin(d*x+c))/d+5/21*a^3*(2*A-B)*tan(d*x+c)/d+10/63*a^3*(2*A-B)*tan(d*x+c)^3/d+1/21*a^3*(2*A-B)*tan(d*x+c)^5/d,1],
[cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,3,-(A+B)*(a-a*sin(d*x+c))^4/a^5/d+4/5*(A+2*B)*(a-a*sin(d*x+c))^5/a^6/d-1/6*(A+5*B)*(a-a*sin(d*x+c))^6/a^7/d+1/7*B*(a-a*sin(d*x+c))^7/a^8/d,1],
[cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,3,-2/3*(A+B)*(a-a*sin(d*x+c))^3/a^4/d+1/4*(A+3*B)*(a-a*sin(d*x+c))^4/a^5/d-1/5*B*(a-a*sin(d*x+c))^5/a^6/d,1],
[cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,3,A*sin(d*x+c)/a/d-1/2*(A-B)*sin(d*x+c)^2/a/d-1/3*B*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,3,(A-B)*ln(1+sin(d*x+c))/a/d+B*sin(d*x+c)/a/d,1],
[sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,4,1/2*(A+B)*arctanh(sin(d*x+c))/a/d-1/2*(A-B)/d/(a+a*sin(d*x+c)),1],
[sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,4,1/8*(3*A+B)*arctanh(sin(d*x+c))/a/d+1/8*(A+B)/d/(a-a*sin(d*x+c))-1/4*A/d/(a+a*sin(d*x+c))-1/8*a^3*(A-B)/d/(a^2+a^2*sin(d*x+c))^2,1],
[sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,4,1/16*(5*A+B)*arctanh(sin(d*x+c))/a/d+1/16*(2*A+B)/d/(a-a*sin(d*x+c))-3/16*A/d/(a+a*sin(d*x+c))-1/24*a^5*(A-B)/d/(a^2+a^2*sin(d*x+c))^3+1/32*a^5*(A+B)/d/(a^3-a^3*sin(d*x+c))^2-1/32*a^5*(3*A-B)/d/(a^3+a^3*sin(d*x+c))^2,1],
[sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x,4,5/128*(7*A+B)*arctanh(sin(d*x+c))/a/d+1/96*a^2*(A+B)/d/(a-a*sin(d*x+c))^3+5/128*(3*A+B)/d/(a-a*sin(d*x+c))-1/48*a^2*(2*A-B)/d/(a+a*sin(d*x+c))^3-5/32*A/d/(a+a*sin(d*x+c))-1/64*a^7*(A-B)/d/(a^2+a^2*sin(d*x+c))^4+1/128*a^7*(5*A+3*B)/d/(a^4-a^4*sin(d*x+c))^2-1/64*a^7*(5*A-B)/d/(a^4+a^4*sin(d*x+c))^2,1],
[cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,3,-1/2*(A+B)*(a-a*sin(d*x+c))^4/a^6/d+1/5*(A+3*B)*(a-a*sin(d*x+c))^5/a^7/d-1/6*B*(a-a*sin(d*x+c))^6/a^8/d,1],
[cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,3,-1/3*(A+B)*(a-a*sin(d*x+c))^3/a^5/d+1/4*B*(a-a*sin(d*x+c))^4/a^6/d,1],
[cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,3,2*(A-B)*ln(1+sin(d*x+c))/a^2/d-(A-B)*sin(d*x+c)/a^2/d-1/2*B*(a-a*sin(d*x+c))^2/a^4/d,1],
[cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,3,B*ln(1+sin(d*x+c))/a^2/d-(A-B)/d/(a^2+a^2*sin(d*x+c)),1],
[sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,4,1/4*(A+B)*arctanh(sin(d*x+c))/a^2/d-1/4*(A-B)/d/(a+a*sin(d*x+c))^2-1/4*(A+B)/d/(a^2+a^2*sin(d*x+c)),1],
[sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,4,1/8*(2*A+B)*arctanh(sin(d*x+c))/a^2/d-1/12*a*(A-B)/d/(a+a*sin(d*x+c))^3-1/8*A/d/(a+a*sin(d*x+c))^2+1/16*(A+B)/d/(a^2-a^2*sin(d*x+c))-1/16*(3*A+B)/d/(a^2+a^2*sin(d*x+c)),1],
[sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x,4,5/64*(3*A+B)*arctanh(sin(d*x+c))/a^2/d+1/64*(A+B)/d/(a-a*sin(d*x+c))^2-1/32*a^2*(A-B)/d/(a+a*sin(d*x+c))^4-1/48*a*(3*A-B)/d/(a+a*sin(d*x+c))^3-3/32*A/d/(a+a*sin(d*x+c))^2+1/64*(5*A+3*B)/d/(a^2-a^2*sin(d*x+c))-1/32*(5*A+B)/d/(a^2+a^2*sin(d*x+c)),1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-B*(g*cos(f*x+e))^(p+1)*(a+a*sin(f*x+e))^m/f/g/(1+m+p)-2^(1/2+m+1/2*p)*(B*m+A*(1+m+p))*(g*cos(f*x+e))^(p+1)*hypergeom([1/2-m-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-1/2-m-1/2*p)*(a+a*sin(f*x+e))^m/f/g/(p+1)/(1+m+p),1],
[cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,8*(A-B)*(a+a*sin(f*x+e))^(4+m)/a^4/f/(4+m)-4*(3*A-5*B)*(a+a*sin(f*x+e))^(5+m)/a^5/f/(5+m)+6*(A-3*B)*(a+a*sin(f*x+e))^(6+m)/a^6/f/(6+m)-(A-7*B)*(a+a*sin(f*x+e))^(7+m)/a^7/f/(7+m)-B*(a+a*sin(f*x+e))^(8+m)/a^8/f/(8+m),1],
[cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,4*(A-B)*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m)-4*(A-2*B)*(a+a*sin(f*x+e))^(4+m)/a^4/f/(4+m)+(A-5*B)*(a+a*sin(f*x+e))^(5+m)/a^5/f/(5+m)+B*(a+a*sin(f*x+e))^(6+m)/a^6/f/(6+m),1],
[cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,2*(A-B)*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m)-(A-3*B)*(a+a*sin(f*x+e))^(3+m)/a^3/f/(3+m)-B*(a+a*sin(f*x+e))^(4+m)/a^4/f/(4+m),1],
[cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,(A-B)*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m)+B*(a+a*sin(f*x+e))^(2+m)/a^2/f/(2+m),1],
[sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,1/2*(A-B)*(a+a*sin(f*x+e))^m/f/m+1/4*(A+B)*hypergeom([1, 1+m],[2+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(1+m)/a/f/(1+m),1],
[sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-1/4*a*(A*(2-m)-B*m)*hypergeom([1, -1+m],[m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(-1+m)/f/(1-m)+1/2*a^3*(A+B)*(a+a*sin(f*x+e))^(-1+m)/f/(a^2-a^2*sin(f*x+e)),1],
[sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-1/16*a^2*(A*(4-m)-B*m)*hypergeom([2, -2+m],[-1+m],1/2+1/2*sin(f*x+e))*(a+a*sin(f*x+e))^(-2+m)/f/(2-m)+1/4*a^4*(A+B)*(a+a*sin(f*x+e))^(-2+m)/f/(a-a*sin(f*x+e))^2,1],
[cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-B*cos(f*x+e)^7*(a+a*sin(f*x+e))^m/f/(7+m)-1/7*2^(7/2+m)*(B*m+A*(7+m))*cos(f*x+e)^7*hypergeom([7/2, -5/2-m],[9/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-7/2-m)*(a+a*sin(f*x+e))^m/f/(7+m),1],
[cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-B*cos(f*x+e)^5*(a+a*sin(f*x+e))^m/f/(5+m)-1/5*2^(5/2+m)*(B*m+A*(5+m))*cos(f*x+e)^5*hypergeom([5/2, -3/2-m],[7/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-5/2-m)*(a+a*sin(f*x+e))^m/f/(5+m),1],
[cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,-B*cos(f*x+e)^3*(a+a*sin(f*x+e))^m/f/(3+m)-1/3*2^(3/2+m)*(B*m+A*(3+m))*cos(f*x+e)^3*hypergeom([3/2, -1/2-m],[5/2],1/2-1/2*sin(f*x+e))*(1+sin(f*x+e))^(-3/2-m)*(a+a*sin(f*x+e))^m/f/(3+m),1],
[sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,B*sec(f*x+e)*(a+a*sin(f*x+e))^m/f/(1-m)+2^(-1/2+m)*(A*(1-m)-B*m)*hypergeom([-1/2, 3/2-m],[1/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)*(1+sin(f*x+e))^(1/2-m)*(a+a*sin(f*x+e))^m/f/(1-m),1],
[sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,B*sec(f*x+e)^3*(a+a*sin(f*x+e))^m/f/(3-m)+1/3*2^(-3/2+m)*(A*(3-m)-B*m)*hypergeom([-3/2, 5/2-m],[-1/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)^3*(1+sin(f*x+e))^(3/2-m)*(a+a*sin(f*x+e))^m/f/(3-m),1],
[sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,3,B*sec(f*x+e)^5*(a+a*sin(f*x+e))^m/f/(5-m)+1/5*2^(-5/2+m)*(A*(5-m)-B*m)*hypergeom([-5/2, 7/2-m],[-3/2],1/2-1/2*sin(f*x+e))*sec(f*x+e)^5*(1+sin(f*x+e))^(5/2-m)*(a+a*sin(f*x+e))^m/f/(5-m),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x,4,(A+B)*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-4-p)/f/g/(7+p)+(3*A-B*(4+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-3-p)/c/f/g/(5+p)/(7+p)+2*(3*A-B*(4+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-2-p)/c^2/f/g/(3+p)/(5+p)/(7+p)+2*(3*A-B*(4+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-1-p)/c^3/f/g/(p+1)/(3+p)/(5+p)/(7+p),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x,3,(A+B)*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-3-p)/f/g/(5+p)+(2*A-B*(3+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-2-p)/c/f/g/(3+p)/(5+p)+(2*A-B*(3+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-1-p)/c^2/f/g/(p+1)/(3+p)/(5+p),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x,2,(A+B)*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-2-p)/f/g/(3+p)+(A-B*(2+p))*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-1-p)/c/f/g/(p+1)/(3+p),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x,3,(A+B)*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(-1-p)/f/g/(p+1)-2^(1/2-1/2*p)*B*(g*cos(f*x+e))^(p+1)*hypergeom([1/2*p+1/2, 1/2*p+1/2],[3/2+1/2*p],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1/2+1/2*p)/c/f/g/(p+1)/((c-c*sin(f*x+e))^p),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x,3,-B*(g*cos(f*x+e))^(p+1)/f/g/((c-c*sin(f*x+e))^p)+2^(1/2-1/2*p)*(B*p+A)*(g*cos(f*x+e))^(p+1)*hypergeom([1/2*p+1/2, 1/2*p+1/2],[3/2+1/2*p],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-1/2+1/2*p)/f/g/(p+1)/((c-c*sin(f*x+e))^p),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x,3,-1/2*B*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(1-p)/f/g+2^(1/2-1/2*p)*(2*A-B*(1-p))*(g*cos(f*x+e))^(p+1)*hypergeom([-1/2+1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-3/2+1/2*p)*(c-c*sin(f*x+e))^(1-p)/f/g/(p+1),1],
[(g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x,3,-1/3*B*(g*cos(f*x+e))^(p+1)*(c-c*sin(f*x+e))^(2-p)/f/g+1/3*2^(5/2-1/2*p)*(3*A-B*(2-p))*(g*cos(f*x+e))^(p+1)*hypergeom([-3/2+1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2+1/2*sin(f*x+e))*(1-sin(f*x+e))^(-5/2+1/2*p)*(c-c*sin(f*x+e))^(2-p)/f/g/(p+1),1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A*m-A*(1+m+p)*sin(f*x+e)),x,1,A*(g*cos(f*x+e))^(p+1)*(a+a*sin(f*x+e))^m/f/g,1],
[(g*cos(f*x+e))^p*(a-a*sin(f*x+e))^m*(A*m+A*(1+m+p)*sin(f*x+e)),x,1,-A*(g*cos(f*x+e))^(p+1)*(a-a*sin(f*x+e))^m/f/g,1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,3,-2^(1/2+m+1/2*p)*g*AppellF1(1/2*p+1/2,1/2-m-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(-1+p)*(1-sin(f*x+e))*(1+sin(f*x+e))^(1/2-m-1/2*p)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n/f/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x,4,-2^(5/2+1/2*p)*a^2*AppellF1(1/2*p+1/2,-3/2-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(p+1)*(1+sin(f*x+e))^(-1/2-1/2*p)*(c+d*sin(f*x+e))^n/f/g/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x,4,-2^(3/2+1/2*p)*a*AppellF1(1/2*p+1/2,-1/2-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(p+1)*(1+sin(f*x+e))^(-1/2-1/2*p)*(c+d*sin(f*x+e))^n/f/g/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x,4,-2^(1/2*p+1/2)*g*AppellF1(-1/2+1/2*p,1/2-1/2*p,-n,1/2*p+1/2,1/2+1/2*sin(f*x+e),-d*(1+sin(f*x+e))/(c-d))*(g*cos(f*x+e))^(-1+p)*(1-sin(f*x+e))^(1/2-1/2*p)*(c+d*sin(f*x+e))^n/a/f/(1-p)/(((c+d*sin(f*x+e))/(c-d))^n),1],
[(g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x,4,-2^(-3/2+1/2*p)*AppellF1(1/2*p+1/2,5/2-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(p+1)*(1+sin(f*x+e))^(-1/2-1/2*p)*(c+d*sin(f*x+e))^n/a^2/f/g/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x,4,-2^(-5/2+1/2*p)*AppellF1(1/2*p+1/2,7/2-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(p+1)*(1+sin(f*x+e))^(-1/2-1/2*p)*(c+d*sin(f*x+e))^n/a^3/f/g/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x,4,-2^(-7/2+1/2*p)*AppellF1(1/2*p+1/2,9/2-1/2*p,-n,3/2+1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*(g*cos(f*x+e))^(p+1)*(1+sin(f*x+e))^(-1/2-1/2*p)*(c+d*sin(f*x+e))^n/a^4/f/g/(p+1)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[(g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,4,-2^(1/2+m-1/2*p)*AppellF1(1/2-1/2*p,1/2-m+1/2*p,-n,3/2-1/2*p,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*sec(f*x+e)*(g*sec(f*x+e))^p*(1-sin(f*x+e))*(1+sin(f*x+e))^(1/2-m+1/2*p)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n/f/(1-p)/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x,8,1/16*b*x-1/3*a*cos(d*x+c)^3/d+1/5*a*cos(d*x+c)^5/d+1/16*b*cos(d*x+c)*sin(d*x+c)/d-1/8*b*cos(d*x+c)^3*sin(d*x+c)/d-1/6*b*cos(d*x+c)^3*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x,7,1/8*a*x-1/3*b*cos(d*x+c)^3/d+1/5*b*cos(d*x+c)^5/d+1/8*a*cos(d*x+c)*sin(d*x+c)/d-1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x,6,1/8*b*x-1/3*a*cos(d*x+c)^3/d+1/8*b*cos(d*x+c)*sin(d*x+c)/d-1/4*b*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+b*sin(d*x+c)),x,6,1/2*b*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/2*b*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c)),x,7,-a*x-b*arctanh(cos(d*x+c))/d+b*cos(d*x+c)/d-a*cot(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c)),x,5,-b*x+1/2*a*arctanh(cos(d*x+c))/d-b*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c)),x,5,1/2*b*arctanh(cos(d*x+c))/d-1/3*a*cot(d*x+c)^3/d-1/2*b*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c)),x,6,1/8*a*arctanh(cos(d*x+c))/d-1/3*b*cot(d*x+c)^3/d+1/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c)),x,7,1/8*b*arctanh(cos(d*x+c))/d-1/3*a*cot(d*x+c)^3/d-1/5*a*cot(d*x+c)^5/d+1/8*b*cot(d*x+c)*csc(d*x+c)/d-1/4*b*cot(d*x+c)*csc(d*x+c)^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x,10,1/8*a*b*x-1/35*(7*a^2+4*b^2)*cos(d*x+c)/d+1/105*(7*a^2+4*b^2)*cos(d*x+c)^3/d-1/8*a*b*cos(d*x+c)*sin(d*x+c)/d-1/12*a*b*cos(d*x+c)*sin(d*x+c)^3/d+1/35*(2*a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/d+1/21*a*b*cos(d*x+c)*sin(d*x+c)^5/d+1/7*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x,9,1/16*(2*a^2+b^2)*x-2/5*a*b*cos(d*x+c)/d+2/15*a*b*cos(d*x+c)^3/d-1/16*(2*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d+1/24*(2*a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/d+1/15*a*b*cos(d*x+c)*sin(d*x+c)^4/d+1/6*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x,5,1/4*a*b*x-1/30*(a^2+4*b^2)*cos(d*x+c)^3/d+1/4*a*b*cos(d*x+c)*sin(d*x+c)/d-1/10*a*cos(d*x+c)^3*(a+b*sin(d*x+c))/d-1/5*cos(d*x+c)^3*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+b*sin(d*x+c))^2,x,6,a*b*x-a^2*arctanh(cos(d*x+c))/d+1/3*(2*a^2-b^2)*cos(d*x+c)/d+1/3*a*b*cos(d*x+c)*sin(d*x+c)/d+1/3*cos(d*x+c)*(a+b*sin(d*x+c))^2/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x,9,-a^2*x+1/2*b^2*x-2*a*b*arctanh(cos(d*x+c))/d+2*a*b*cos(d*x+c)/d-a^2*cot(d*x+c)/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^2,x,6,-2*a*b*x+1/2*(a^2-2*b^2)*arctanh(cos(d*x+c))/d+3/2*b^2*cos(d*x+c)/d-a*b*cot(d*x+c)/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^2/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x,6,-b^2*x+a*b*arctanh(cos(d*x+c))/d+1/3*(a^2-2*b^2)*cot(d*x+c)/d-1/3*a*b*cot(d*x+c)*csc(d*x+c)/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^2/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x,8,1/8*(a^2+4*b^2)*arctanh(cos(d*x+c))/d+2/3*a*b*cot(d*x+c)/d+1/8*(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/d-1/6*a*b*cot(d*x+c)*csc(d*x+c)^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^2/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x,9,1/4*a*b*arctanh(cos(d*x+c))/d+1/15*(2*a^2+5*b^2)*cot(d*x+c)/d+1/4*a*b*cot(d*x+c)*csc(d*x+c)/d+1/15*(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)^2/d-1/10*a*b*cot(d*x+c)*csc(d*x+c)^3/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^2/d,1],
[cot(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x,9,1/16*(a^2+2*b^2)*arctanh(cos(d*x+c))/d+2/5*a*b*cot(d*x+c)/d+2/15*a*b*cot(d*x+c)^3/d+1/16*(a^2+2*b^2)*cot(d*x+c)*csc(d*x+c)/d+1/24*(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)^3/d-1/15*a*b*cot(d*x+c)*csc(d*x+c)^4/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x,10,1/16*a*(2*a^2+3*b^2)*x-1/35*b*(21*a^2+4*b^2)*cos(d*x+c)/d+1/105*b*(21*a^2+4*b^2)*cos(d*x+c)^3/d-1/16*a*(2*a^2+3*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/56*a*(2*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)^3/d+1/35*b*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/d+1/14*a*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^2/d+1/7*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x,6,1/16*b*(6*a^2+b^2)*x-1/120*a*(2*a^2+33*b^2)*cos(d*x+c)^3/d+1/16*b*(6*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d-1/40*(2*a^2+5*b^2)*cos(d*x+c)^3*(a+b*sin(d*x+c))/d-1/10*a*cos(d*x+c)^3*(a+b*sin(d*x+c))^2/d-1/6*cos(d*x+c)^3*(a+b*sin(d*x+c))^3/d,1],
[cos(d*x+c)*cot(d*x+c)*(a+b*sin(d*x+c))^3,x,7,1/8*b*(12*a^2+b^2)*x-a^3*arctanh(cos(d*x+c))/d+1/2*a*(a^2-2*b^2)*cos(d*x+c)/d+1/8*b*(2*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)*(a+b*sin(d*x+c))^2/d+1/4*cos(d*x+c)*(a+b*sin(d*x+c))^3/d,1],
[cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x,11,-a^3*x+3/2*a*b^2*x-3*a^2*b*arctanh(cos(d*x+c))/d+3*a^2*b*cos(d*x+c)/d-1/3*b^3*cos(d*x+c)^3/d-a^3*cot(d*x+c)/d+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^3,x,7,-1/2*b*(6*a^2-b^2)*x+1/2*a*(a^2-6*b^2)*arctanh(cos(d*x+c))/d+15/2*a*b^2*cos(d*x+c)/d+5/2*b^3*cos(d*x+c)*sin(d*x+c)/d-3/2*b*cot(d*x+c)*(a+b*sin(d*x+c))^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x,7,-3*a*b^2*x+1/2*b*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/d+11/6*b^3*cos(d*x+c)/d+1/3*a*(a^2-3*b^2)*cot(d*x+c)/d-1/2*b*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x,7,-b^3*x+1/8*a*(a^2+12*b^2)*arctanh(cos(d*x+c))/d+1/2*b*(2*a^2-b^2)*cot(d*x+c)/d+1/8*a*(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/d-1/4*b*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x,9,1/8*b*(3*a^2+4*b^2)*arctanh(cos(d*x+c))/d+1/15*a*(2*a^2+15*b^2)*cot(d*x+c)/d+3/40*b*(5*a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/d+1/30*a*(2*a^2-3*b^2)*cot(d*x+c)*csc(d*x+c)^2/d-3/20*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^3/d,1],
[cot(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x,10,1/16*a*(a^2+6*b^2)*arctanh(cos(d*x+c))/d+1/15*b*(6*a^2+5*b^2)*cot(d*x+c)/d+1/16*a*(a^2+6*b^2)*cot(d*x+c)*csc(d*x+c)/d+1/15*b*(3*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^2/d+1/120*a*(5*a^2-6*b^2)*cot(d*x+c)*csc(d*x+c)^3/d-1/10*b*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x,9,a*(4*a^2-b^2)*x/b^5-2*a^2*(4*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/sqrt(a^2-b^2)/d+1/3*(12*a^2-b^2)*cos(d*x+c)/b^4/d-2*a*cos(d*x+c)*sin(d*x+c)/b^3/d+4/3*cos(d*x+c)*sin(d*x+c)^2/b^2/d-cos(d*x+c)*sin(d*x+c)^3/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x,8,-1/2*(6*a^2-b^2)*x/b^4+2*a*(3*a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/sqrt(a^2-b^2)/d-3*a*cos(d*x+c)/b^3/d+3/2*cos(d*x+c)*sin(d*x+c)/b^2/d-cos(d*x+c)*sin(d*x+c)^2/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x,5,2*a*x/b^3-2*(2*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^3/sqrt(a^2-b^2)/d+cos(d*x+c)*(2*a+b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c))^2,x,8,-2*b*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/sqrt(a^2-b^2)/d-arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x,8,-2*(a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/sqrt(a^2-b^2)/d+2*b*arctanh(cos(d*x+c))/a^3/d-2*cot(d*x+c)/a^2/d+cot(d*x+c)/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^2,x,9,2*b*(2*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/sqrt(a^2-b^2)/d+1/2*(a^2-6*b^2)*arctanh(cos(d*x+c))/a^4/d+3*b*cot(d*x+c)/a^3/d-3/2*cot(d*x+c)*csc(d*x+c)/a^2/d+cot(d*x+c)*csc(d*x+c)/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x,10,-2*b^2*(3*a^2-4*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/sqrt(a^2-b^2)/d-b*(a^2-4*b^2)*arctanh(cos(d*x+c))/a^5/d+1/3*(a^2-12*b^2)*cot(d*x+c)/a^4/d+2*b*cot(d*x+c)*csc(d*x+c)/a^3/d-4/3*cot(d*x+c)*csc(d*x+c)^2/a^2/d+cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x,9,-1/2*(12*a^2-b^2)*x/b^5+a*(12*a^4-19*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/(a^2-b^2)^(3/2)/d-1/2*a*(12*a^2-11*b^2)*cos(d*x+c)/b^4/(a^2-b^2)/d+1/2*(6*a^2-5*b^2)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)/d-1/2*cos(d*x+c)*sin(d*x+c)^3/b/d/(a+b*sin(d*x+c))^2-1/2*(4*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^2/b^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x,8,3*a*x/b^4-(6*a^4-9*a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/(a^2-b^2)^(3/2)/d+3/2*cos(d*x+c)/b^3/d-1/2*cos(d*x+c)*sin(d*x+c)^2/b/d/(a+b*sin(d*x+c))^2+1/2*a*(3*a^2-2*b^2)*cos(d*x+c)/b^3/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x,6,-x/b^3+a*(2*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^3/(a^2-b^2)^(3/2)/d-1/2*a*cos(d*x+c)^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^2-1/2*cos(d*x+c)*(2*a^2-2*b^2+a*b*sin(d*x+c))/b^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c))^3,x,8,-b*(3*a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(3/2)/d-arctanh(cos(d*x+c))/a^3/d+1/2*cos(d*x+c)/a/d/(a+b*sin(d*x+c))^2+1/2*(a^2-2*b^2)*cos(d*x+c)/a^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x,9,-(2*a^4-9*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/(a^2-b^2)^(3/2)/d+3*b*arctanh(cos(d*x+c))/a^4/d-1/2*(5*a^2-6*b^2)*cot(d*x+c)/a^3/(a^2-b^2)/d+1/2*cot(d*x+c)/a/d/(a+b*sin(d*x+c))^2+1/2*(2*a^2-3*b^2)*cot(d*x+c)/a^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^3,x,10,b*(6*a^4-19*a^2*b^2+12*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/(a^2-b^2)^(3/2)/d+1/2*(a^2-12*b^2)*arctanh(cos(d*x+c))/a^5/d+1/2*b*(11*a^2-12*b^2)*cot(d*x+c)/a^4/(a^2-b^2)/d-1/2*(5*a^2-6*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/(a^2-b^2)/d+1/2*cot(d*x+c)*csc(d*x+c)/a/d/(a+b*sin(d*x+c))^2+1/2*(3*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[cos(f*x+e)^2/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e))^(5/2),x,5,2/3*cos(f*x+e)*sqrt(d*sin(f*x+e))/a/d/f/(a+b*sin(f*x+e))^(3/2)+4/3*b*cos(f*x+e)/a/(a^2-b^2)/f/sqrt(d*sin(f*x+e))/sqrt(a+b*sin(f*x+e))-4/3*b*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*EllipticE(sin(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e)))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^3/sqrt(a+b)/sqrt(d)/f-4/3*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^2/sqrt(a+b)/sqrt(d)/f,1],
[cos(d*x+c)^4*sin(d*x+c)^4*(a+b*sin(d*x+c)),x,9,3/128*a*x-1/5*b*cos(d*x+c)^5/d+2/7*b*cos(d*x+c)^7/d-1/9*b*cos(d*x+c)^9/d+3/128*a*cos(d*x+c)*sin(d*x+c)/d+1/64*a*cos(d*x+c)^3*sin(d*x+c)/d-1/16*a*cos(d*x+c)^5*sin(d*x+c)/d-1/8*a*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c)),x,9,3/128*b*x-1/5*a*cos(d*x+c)^5/d+1/7*a*cos(d*x+c)^7/d+3/128*b*cos(d*x+c)*sin(d*x+c)/d+1/64*b*cos(d*x+c)^3*sin(d*x+c)/d-1/16*b*cos(d*x+c)^5*sin(d*x+c)/d-1/8*b*cos(d*x+c)^5*sin(d*x+c)^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c)),x,8,1/16*a*x-1/5*b*cos(d*x+c)^5/d+1/7*b*cos(d*x+c)^7/d+1/16*a*cos(d*x+c)*sin(d*x+c)/d+1/24*a*cos(d*x+c)^3*sin(d*x+c)/d-1/6*a*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c)),x,7,1/16*b*x-1/5*a*cos(d*x+c)^5/d+1/16*b*cos(d*x+c)*sin(d*x+c)/d+1/24*b*cos(d*x+c)^3*sin(d*x+c)/d-1/6*b*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c)),x,8,3/8*b*x-a*arctanh(cos(d*x+c))/d+a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d+3/8*b*cos(d*x+c)*sin(d*x+c)/d+1/4*b*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c)),x,10,-3/2*a*x-b*arctanh(cos(d*x+c))/d+b*cos(d*x+c)/d+1/3*b*cos(d*x+c)^3/d-a*cot(d*x+c)/d-1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c)),x,11,-3/2*b*x+3/2*a*arctanh(cos(d*x+c))/d-a*cos(d*x+c)/d-b*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d-1/2*b*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c)),x,10,a*x+3/2*b*arctanh(cos(d*x+c))/d-b*cos(d*x+c)/d+a*cot(d*x+c)/d-1/3*a*cot(d*x+c)^3/d-1/2*b*cot(d*x+c)*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c)),x,7,b*x-3/8*a*arctanh(cos(d*x+c))/d+b*cot(d*x+c)/d-1/3*b*cot(d*x+c)^3/d+3/8*a*cot(d*x+c)*csc(d*x+c)/d-1/4*a*cot(d*x+c)^3*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c)),x,6,-3/8*b*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d+3/8*b*cot(d*x+c)*csc(d*x+c)/d-1/4*b*cot(d*x+c)^3*csc(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c)),x,7,-1/16*a*arctanh(cos(d*x+c))/d-1/5*b*cot(d*x+c)^5/d-1/16*a*cot(d*x+c)*csc(d*x+c)/d+1/8*a*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c)),x,8,-1/16*b*arctanh(cos(d*x+c))/d-1/5*a*cot(d*x+c)^5/d-1/7*a*cot(d*x+c)^7/d-1/16*b*cot(d*x+c)*csc(d*x+c)/d+1/8*b*cot(d*x+c)*csc(d*x+c)^3/d-1/6*b*cot(d*x+c)^3*csc(d*x+c)^3/d,1],
[cot(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c)),x,9,-3/128*a*arctanh(cos(d*x+c))/d-1/5*b*cot(d*x+c)^5/d-1/7*b*cot(d*x+c)^7/d-3/128*a*cot(d*x+c)*csc(d*x+c)/d-1/64*a*cot(d*x+c)*csc(d*x+c)^3/d+1/16*a*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a*cot(d*x+c)^3*csc(d*x+c)^5/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x,10,3/64*a*b*x-1/105*(9*a^2+4*b^2)*cos(d*x+c)/d+1/315*(9*a^2+4*b^2)*cos(d*x+c)^3/d-3/64*a*b*cos(d*x+c)*sin(d*x+c)/d-1/32*a*b*cos(d*x+c)*sin(d*x+c)^3/d-1/630*(15*a^4-44*a^2*b^2+6*b^4)*cos(d*x+c)*sin(d*x+c)^4/b^2/d-1/504*a*(10*a^2-29*b^2)*cos(d*x+c)*sin(d*x+c)^5/b/d-5/252*(3*a^2-8*b^2)*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^2/b^2/d+1/12*a*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^3/b^2/d-1/9*cos(d*x+c)*sin(d*x+c)^5*(a+b*sin(d*x+c))^3/b/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x,9,1/128*(8*a^2+3*b^2)*x-6/35*a*b*cos(d*x+c)/d+2/35*a*b*cos(d*x+c)^3/d-1/128*(8*a^2+3*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/1344*(40*a^4-140*a^2*b^2+21*b^4)*cos(d*x+c)*sin(d*x+c)^3/b^2/d-1/840*a*(20*a^2-69*b^2)*cos(d*x+c)*sin(d*x+c)^4/b/d-1/336*(20*a^2-63*b^2)*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^2/b^2/d+5/56*a*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^3/b^2/d-1/8*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^3/b/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^2,x,6,1/8*a*b*x-1/105*(a^2+6*b^2)*cos(d*x+c)^5/d+1/8*a*b*cos(d*x+c)*sin(d*x+c)/d+1/12*a*b*cos(d*x+c)^3*sin(d*x+c)/d-1/21*a*cos(d*x+c)^5*(a+b*sin(d*x+c))/d-1/7*cos(d*x+c)^5*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^2,x,6,3/4*a*b*x-a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)^3/d-1/5*b^2*cos(d*x+c)^5/d+3/4*a*b*cos(d*x+c)*sin(d*x+c)/d+1/2*a*b*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x,6,-3/8*(4*a^2-b^2)*x-2*a*b*arctanh(cos(d*x+c))/d+1/6*a*(a^2+28*b^2)*cos(d*x+c)/b/d+1/24*(2*a^2+39*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(a^2+12*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^2/a/b/d-1/4*cos(d*x+c)*(a+b*sin(d*x+c))^3/b/d-cot(d*x+c)*(a+b*sin(d*x+c))^3/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x,6,-3*a*b*x+1/2*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/d-1/6*(4*a^2-23*b^2)*cos(d*x+c)/d-1/3*b*(a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)/a/d-1/6*(2*a^2-3*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^2/a^2/d-1/2*b*cot(d*x+c)*(a+b*sin(d*x+c))^3/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^3/a/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x,15,a^2*x-3/2*b^2*x+3*a*b*arctanh(cos(d*x+c))/d-2*a*b*cos(d*x+c)/d+a^2*cot(d*x+c)/d-b^2*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a*b*cot(d*x+c)*csc(d*x+c)/d-1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^2,x,6,2*a*b*x-3/8*(a^2-4*b^2)*arctanh(cos(d*x+c))/d-1/24*b^2*(39*a^2+2*b^2)*cos(d*x+c)/a^2/d+17/12*a*b*cot(d*x+c)/d+5/8*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^2/d+1/12*b*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^3/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x,6,b^2*x-3/4*a*b*arctanh(cos(d*x+c))/d-1/15*(3*a^4-14*a^2*b^2+b^4)*cot(d*x+c)/a^2/d+1/60*b*(27*a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/a/d+1/30*(12*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^2/a^2/d+1/10*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^3/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x,8,-1/16*(a^2+6*b^2)*arctanh(cos(d*x+c))/d-2/5*a*b*cot(d*x+c)/d-1/240*(15*a^4-80*a^2*b^2+12*b^4)*cot(d*x+c)*csc(d*x+c)/a^2/d+1/60*b*(13*a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)^2/a/d+1/120*(35*a^2-6*b^2)*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^2/a^2/d+1/10*b*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^3/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x,9,-1/8*a*b*arctanh(cos(d*x+c))/d-1/35*(2*a^2+7*b^2)*cot(d*x+c)/d-1/8*a*b*cot(d*x+c)*csc(d*x+c)/d-1/105*(3*a^4-18*a^2*b^2+4*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^2/d+1/420*b*(53*a^2-12*b^2)*cot(d*x+c)*csc(d*x+c)^3/a/d+2/35*(4*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^2/a^2/d+2/21*b*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^3/a^2/d-1/7*cot(d*x+c)*csc(d*x+c)^6*(a+b*sin(d*x+c))^3/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x,10,1/128*a*(8*a^2+9*b^2)*x-1/105*b*(27*a^2+4*b^2)*cos(d*x+c)/d+1/315*b*(27*a^2+4*b^2)*cos(d*x+c)^3/d-1/128*a*(8*a^2+9*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/4032*a*(40*a^4-188*a^2*b^2+189*b^4)*cos(d*x+c)*sin(d*x+c)^3/b^2/d-1/2520*(20*a^4-93*a^2*b^2+24*b^4)*cos(d*x+c)*sin(d*x+c)^4/b/d-1/1008*a*(20*a^2-87*b^2)*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^2/b^2/d-5/126*(a^2-4*b^2)*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^3/b^2/d+5/72*a*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^4/b^2/d-1/9*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^4/b/d,1],
[cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^3,x,7,3/128*b*(8*a^2+b^2)*x-1/560*a*(2*a^2+61*b^2)*cos(d*x+c)^5/d+3/128*b*(8*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d+1/64*b*(8*a^2+b^2)*cos(d*x+c)^3*sin(d*x+c)/d-1/112*(2*a^2+7*b^2)*cos(d*x+c)^5*(a+b*sin(d*x+c))/d-3/56*a*cos(d*x+c)^5*(a+b*sin(d*x+c))^2/d-1/8*cos(d*x+c)^5*(a+b*sin(d*x+c))^3/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^3,x,7,1/16*b*(18*a^2+b^2)*x-a^3*arctanh(cos(d*x+c))/d-1/60*a*(2*a^4-43*a^2*b^2+36*b^4)*cos(d*x+c)/b^2/d-1/240*(4*a^4-84*a^2*b^2+15*b^4)*cos(d*x+c)*sin(d*x+c)/b/d-1/120*a*(2*a^2-39*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^2/b^2/d-1/120*(2*a^2-35*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^3/b^2/d+1/15*a*cos(d*x+c)*(a+b*sin(d*x+c))^4/b^2/d-1/6*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^4/b/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x,7,-3/8*a*(4*a^2-3*b^2)*x-3*a^2*b*arctanh(cos(d*x+c))/d+1/10*(a^4+56*a^2*b^2-2*b^4)*cos(d*x+c)/b/d+1/40*a*(2*a^2+83*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/20*(a^2+28*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^2/b/d+1/20*(a^2+20*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^3/a/b/d-1/5*cos(d*x+c)*(a+b*sin(d*x+c))^4/b/d-cot(d*x+c)*(a+b*sin(d*x+c))^4/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^3,x,7,-3/8*b*(12*a^2-b^2)*x+3/2*a*(a^2-2*b^2)*arctanh(cos(d*x+c))/d-1/2*a*(a^2-17*b^2)*cos(d*x+c)/d-1/8*b*(2*a^2-21*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/4*(a^2-6*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^2/a/d-1/4*(a^2-4*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^3/a^2/d-b*cot(d*x+c)*(a+b*sin(d*x+c))^4/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^3,x,19,a^3*x-9/2*a*b^2*x+9/2*a^2*b*arctanh(cos(d*x+c))/d-b^3*arctanh(cos(d*x+c))/d-3*a^2*b*cos(d*x+c)/d+b^3*cos(d*x+c)/d+1/3*b^3*cos(d*x+c)^3/d+a^3*cot(d*x+c)/d-3*a*b^2*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^2*b*cot(d*x+c)*csc(d*x+c)/d-3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^3,x,7,3/2*b*(2*a^2-b^2)*x-3/8*a*(a^2-12*b^2)*arctanh(cos(d*x+c))/d-1/8*b^2*(73*a^2-2*b^2)*cos(d*x+c)/a/d-13/4*b^3*cos(d*x+c)*sin(d*x+c)/d+17/8*b*cot(d*x+c)*(a+b*sin(d*x+c))^2/d+5/8*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^3/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x,7,3*a*b^2*x-3/8*b*(3*a^2-4*b^2)*arctanh(cos(d*x+c))/d-1/40*b^3*(83*a^2+2*b^2)*cos(d*x+c)/a^2/d-1/20*a*(4*a^2-29*b^2)*cot(d*x+c)/d+27/40*b*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^2/d+2/5*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^3/d+1/20*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^4/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x,7,b^3*x-1/16*a*(a^2+18*b^2)*arctanh(cos(d*x+c))/d-1/60*b*(36*a^4-43*a^2*b^2+2*b^4)*cot(d*x+c)/a^2/d-1/240*(15*a^4-84*a^2*b^2+4*b^4)*cot(d*x+c)*csc(d*x+c)/a/d+1/120*b*(39*a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^2/a^2/d+1/120*(35*a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^3/a^2/d+1/15*b*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^4/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x,9,-3/16*b*(a^2+2*b^2)*arctanh(cos(d*x+c))/d-1/35*a*(2*a^2+21*b^2)*cot(d*x+c)/d-1/560*b*(105*a^4-116*a^2*b^2+12*b^4)*cot(d*x+c)*csc(d*x+c)/a^2/d-1/140*(4*a^4-19*a^2*b^2+2*b^4)*cot(d*x+c)*csc(d*x+c)^2/a/d+1/280*b*(53*a^2-6*b^2)*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^2/a^2/d+1/35*(8*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^3/a^2/d+1/14*b*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^4/a^2/d-1/7*cot(d*x+c)*csc(d*x+c)^6*(a+b*sin(d*x+c))^4/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x,10,-3/128*a*(a^2+8*b^2)*arctanh(cos(d*x+c))/d-1/35*b*(6*a^2+7*b^2)*cot(d*x+c)/d-3/128*a*(a^2+8*b^2)*cot(d*x+c)*csc(d*x+c)/d-1/280*b*(24*a^4-25*a^2*b^2+4*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^2/d-1/2240*(35*a^4-148*a^2*b^2+24*b^4)*cot(d*x+c)*csc(d*x+c)^3/a/d+3/560*b*(23*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^2/a^2/d+1/112*(21*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^3/a^2/d+1/14*b*cot(d*x+c)*csc(d*x+c)^6*(a+b*sin(d*x+c))^4/a^2/d-1/8*cot(d*x+c)*csc(d*x+c)^7*(a+b*sin(d*x+c))^4/a/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x,9,-3/4*a*(8*a^4-8*a^2*b^2+b^4)*x/b^7+6*a^2*(2*a^4-3*a^2*b^2+b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/sqrt(a^2-b^2)/d-1/5*(30*a^4-25*a^2*b^2+b^4)*cos(d*x+c)/b^6/d+3/4*a*(4*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)/b^5/d-1/5*(10*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)^2/b^4/d+1/2*(3*a^2-2*b^2)*cos(d*x+c)*sin(d*x+c)^3/a/b^3/d-1/5*cos(d*x+c)*sin(d*x+c)^4/b^2/d-(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/a/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x,8,1/8*(40*a^4-36*a^2*b^2+3*b^4)*x/b^6-2*a*(5*a^4-7*a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/sqrt(a^2-b^2)/d+1/3*a*(15*a^2-11*b^2)*cos(d*x+c)/b^5/d-1/8*(20*a^2-13*b^2)*cos(d*x+c)*sin(d*x+c)/b^4/d+1/3*(5*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^2/a/b^3/d-1/4*cos(d*x+c)*sin(d*x+c)^3/b^2/d-(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/a/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^2,x,6,-a*(4*a^2-3*b^2)*x/b^5+2*(4*a^4-5*a^2*b^2+b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/sqrt(a^2-b^2)/d+1/3*cos(d*x+c)^3*(4*a+b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c))-cos(d*x+c)*(4*a^2-b^2-2*a*b*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^2,x,6,-2*a*x/b^3+2*sqrt(a^2-b^2)*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^3/d-arctanh(cos(d*x+c))/a^2/d-cos(d*x+c)/b^2/d-(a^2-b^2)*cos(d*x+c)/a/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x,6,x/b^2-2*(a^4+a^2*b^2-2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^2/sqrt(a^2-b^2)/d+2*b*arctanh(cos(d*x+c))/a^3/d+(a^2-2*b^2)*cos(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))-cot(d*x+c)/a/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x,7,6*b*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/d+3/2*(a^2-2*b^2)*arctanh(cos(d*x+c))/a^4/d-1/2*cos(d*x+c)/a^2/d/(1-cos(d*x+c)^2)+2*b*cot(d*x+c)/a^3/d-(a^2-b^2)*cos(d*x+c)/a^3/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x,8,2*(a^4-5*a^2*b^2+4*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/sqrt(a^2-b^2)/d-b*(3*a^2-4*b^2)*arctanh(cos(d*x+c))/a^5/d+1/3*(7*a^2-12*b^2)*cot(d*x+c)/a^4/d-(a^2-2*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/b/d+1/3*(3*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^2,x,9,-2*b*(2*a^4-7*a^2*b^2+5*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/sqrt(a^2-b^2)/d-1/8*(3*a^4-36*a^2*b^2+40*b^4)*arctanh(cos(d*x+c))/a^6/d-1/3*b*(11*a^2-15*b^2)*cot(d*x+c)/a^5/d+1/8*(13*a^2-20*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d-1/3*(3*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^3/b/d+1/4*(4*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^2/b/d/(a+b*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x,9,3/8*(40*a^4-24*a^2*b^2+b^4)*x/b^7-3*a*(10*a^4-11*a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/sqrt(a^2-b^2)/d+1/2*a*(30*a^2-13*b^2)*cos(d*x+c)/b^6/d-3/8*(20*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)/b^5/d+1/2*(10*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^2/a/b^4/d-1/4*(15*a^2-4*b^2)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^3/d-1/2*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/a/b^2/d/(a+b*sin(d*x+c))^2+1/2*(7*a^2-2*b^2)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x,8,1/2*a*(9-20*a^2/b^2)*x/b^4+(20*a^4-19*a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/sqrt(a^2-b^2)/d-1/6*(60*a^2-17*b^2)*cos(d*x+c)/b^5/d+(5*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/a/b^4/d-1/6*(20*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^2/a^2/b^3/d-1/2*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/a/b^2/d/(a+b*sin(d*x+c))^2+1/2*(6*a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^3,x,6,3/2*(4*a^2-b^2)*x/b^5-3*a*(4*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/sqrt(a^2-b^2)/d+1/2*cos(d*x+c)^3*(2*a+b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c))^2+3/2*cos(d*x+c)*(4*a^2-b^2+2*a*b*sin(d*x+c))/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^3,x,6,x/b^3-(2*a^4-a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^3/sqrt(a^2-b^2)/d-arctanh(cos(d*x+c))/a^3/d-1/2*(a^2-b^2)*cos(d*x+c)/a/b^2/d/(a+b*sin(d*x+c))^2+1/2*(3*a^2+2*b^2)*cos(d*x+c)/a^2/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x,7,-3*(a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/sqrt(a^2-b^2)/d+3*b*arctanh(cos(d*x+c))/a^4/d+1/2*(a^2-3*b^2)*cos(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^2-cot(d*x+c)/a/d/(a+b*sin(d*x+c))^2-1/2*(a^2+6*b^2)*cos(d*x+c)/a^3/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x,8,3*b*(3*a^2-4*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/sqrt(a^2-b^2)/d+3/2*(a^2-4*b^2)*arctanh(cos(d*x+c))/a^5/d-1/2*(a^2-12*b^2)*cot(d*x+c)/a^4/b/d+1/2*(a^2-2*b^2)*cot(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^2-1/2*cot(d*x+c)*csc(d*x+c)/a/d/(a+b*sin(d*x+c))^2-3*b*cot(d*x+c)/a^3/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x,9,(2*a^4-19*a^2*b^2+20*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/sqrt(a^2-b^2)/d-1/2*b*(9*a^2-20*b^2)*arctanh(cos(d*x+c))/a^6/d+1/6*(17*a^2-60*b^2)*cot(d*x+c)/a^5/d-(a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/b/d+1/6*(3*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^2-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c))^2+1/6*(3*a^2-20*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/b/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^3,x,10,-3*b*(2*a^4-11*a^2*b^2+10*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^7/sqrt(a^2-b^2)/d-3/8*(a^4-24*a^2*b^2+40*b^4)*arctanh(cos(d*x+c))/a^7/d-1/2*b*(13*a^2-30*b^2)*cot(d*x+c)/a^6/d+3/8*(7*a^2-20*b^2)*cot(d*x+c)*csc(d*x+c)/a^5/d-1/2*(3*a^2-10*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^4/b/d+1/4*(2*a^2-3*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^2/b/d/(a+b*sin(d*x+c))^2-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d/(a+b*sin(d*x+c))^2+1/4*(4*a^2-15*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^3/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c)),x,10,16/45045*a*(160*a^4-279*a^2*b^2+27*b^4)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d-8/45045*(480*a^4-937*a^2*b^2+231*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^5/d+8/3003*a*(40*a^2-81*b^2)*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^4/d-10/1287*(16*a^2-33*b^2)*cos(d*x+c)*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2)/b^3/d+20/143*a*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/b^2/d-2/13*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^(3/2)/b/d-8/45045*(320*a^6-798*a^4*b^2+435*a^2*b^4-693*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))+16/45045*a*(160*a^6-439*a^4*b^2+306*a^2*b^4-27*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)*sqrt(a+b*sin(d*x+c)),x,8,-2/11*cos(d*x+c)^5*sqrt(a+b*sin(d*x+c))/d+8/3465*a*(32*a^4-93*a^2*b^2+93*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/3465*(32*a^6-101*a^4*b^2+114*a^2*b^4-45*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))-2/693*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(8*a^2-9*b^2-7*a*b*sin(d*x+c))/b^2/d+4/3465*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(32*a^4-69*a^2*b^2+45*b^4-24*a*b*(a^2-2*b^2)*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)*sqrt(a+b*sin(d*x+c)),x,10,-2/105*(8*a^2-45*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^2/d+8/35*a*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^2/d-2/7*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b/d+2/105*a*(8*a^2-51*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))-2/105*(8*a^4-53*a^2*b^2-60*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^3/d/sqrt(a+b*sin(d*x+c))+2*a*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2*sqrt(a+b*sin(d*x+c)),x,10,1/15*(4*a^2+15*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a/b/d-2/5*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b/d-cot(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a/d-1/15*(4*a^2+57*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/15*a*(4*a^2+11*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))+b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3*sqrt(a+b*sin(d*x+c)),x,10,-1/12*(8*a^2+3*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/4*b*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a/d+1/12*(8*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a/b/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/12*(8*a^2+31*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b/d/sqrt(a+b*sin(d*x+c))-1/4*(12*a^2+b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*sqrt(a+b*sin(d*x+c)),x,10,1/24*(32*a^2-3*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/4*b*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2)/a/d+1/24*(80*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/24*(32*a^2+b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c))-1/8*b*(12*a^2-b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)*sqrt(a+b*sin(d*x+c)),x,11,1/192*b*(68*a^2-15*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+5/32*(4*a^2-b^2)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+5/24*b*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/a/d+1/192*b*(68*a^2-15*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/192*b*(196*a^2+5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c))+1/64*(48*a^4+24*a^2*b^2-5*b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^2*sqrt(a+b*sin(d*x+c)),x,12,-1/1920*(384*a^4+332*a^2*b^2-105*b^4)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^4/d+1/960*b*(108*a^2-35*b^2)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+1/240*(96*a^2-35*b^2)*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a^2/d+7/40*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^(3/2)/a/d-1/1920*(384*a^4+332*a^2*b^2-105*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/1920*(384*a^4+116*a^2*b^2-35*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c))+1/128*b*(48*a^4-24*a^2*b^2+7*b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x,11,8/45045*(64*a^6-174*a^4*b^2+81*a^2*b^4-195*b^6)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d+16/45045*a*(32*a^4-47*a^2*b^2-27*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^5/d-8/45045*(160*a^4-375*a^2*b^2+117*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b^5/d+8/1287*a*(8*a^2-21*b^2)*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b^4/d-2/2145*(80*a^2-221*b^2)*cos(d*x+c)*sin(d*x+c)^2*(a+b*sin(d*x+c))^(5/2)/b^3/d+4/39*a*cos(d*x+c)*sin(d*x+c)^3*(a+b*sin(d*x+c))^(5/2)/b^2/d-2/15*cos(d*x+c)*sin(d*x+c)^4*(a+b*sin(d*x+c))^(5/2)/b/d-16/45045*a*(32*a^6-111*a^4*b^2+102*a^2*b^4-471*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/45045*(64*a^8-238*a^6*b^2+255*a^4*b^4-276*a^2*b^6+195*b^8)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2),x,9,-6/143*a*cos(d*x+c)^5*sqrt(a+b*sin(d*x+c))/d-2/13*cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2)/d+8/15015*(32*a^6-137*a^4*b^2+258*a^2*b^4+231*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/15015*a*(32*a^6-145*a^4*b^2+290*a^2*b^4-177*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))-2/3003*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(4*a*(2*a^2-5*b^2)-7*b*(a^2+11*b^2)*sin(d*x+c))/b^2/d+4/15015*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*(32*a^4-113*a^2*b^2+177*b^4)-3*b*(8*a^4-27*a^2*b^2-77*b^4)*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2),x,11,-2/315*a*(8*a^2-87*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^2/d-2/315*(8*a^2-77*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^2/d+8/63*a*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b^2/d-2/9*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b/d+2/315*(8*a^4-93*a^2*b^2+84*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))-2/315*a*(8*a^4-95*a^2*b^2-228*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^3/d/sqrt(a+b*sin(d*x+c))+2*a^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x,11,1/35*(4*a^2+65*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d+1/35*(4*a^2+35*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a/b/d-2/7*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b/d-cot(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a/d-1/35*a*(4*a^2+167*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/35*(4*a^4+61*a^2*b^2+40*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))+3*a*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x,11,-1/20*(8*a^2-15*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a/d-1/20*(8*a^2-5*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d-1/4*b*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a/d+1/20*(8*a^2-81*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/20*a*(8*a^2+37*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b/d/sqrt(a+b*sin(d*x+c))-3/4*(4*a^2-b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x,11,-1/8*b*(16*a^2+b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/24*(32*a^2+b^2)*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/12*b*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2)/a/d+1/8*(32*a^2-b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/8*(16*a^2+21*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))-1/8*b*(36*a^2+b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2),x,11,1/64*b*(68*a^2-3*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/32*(20*a^2-b^2)*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/8*b*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2)/a/d+1/64*b*(236*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/64*b*(20*a^2+b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c))+3/64*(16*a^4-24*a^2*b^2+b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x,12,-1/640*(128*a^4-116*a^2*b^2+15*b^4)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+3/320*b*(36*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/80*(32*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/8*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^(5/2)/a/d-1/640*(128*a^4-116*a^2*b^2+15*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/640*(128*a^4+692*a^2*b^2+5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c))+3/128*b*(48*a^4+8*a^2*b^2-b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x,13,-1/7680*b*(2064*a^4+512*a^2*b^2-105*b^4)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^4/d-1/3840*(240*a^4-168*a^2*b^2+35*b^4)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+1/960*b*(156*a^2-35*b^2)*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a^2/d+7/96*(4*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/a^2/d+7/60*b*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^(5/2)/a/d-1/7680*b*(2064*a^4+512*a^2*b^2-105*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/7680*b*(2544*a^4+176*a^2*b^2-35*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c))+1/512*(64*a^6+144*a^4*b^2-36*a^2*b^4+7*b^6)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2),x,10,-2/429*(3*a^2+13*b^2)*cos(d*x+c)^5*sqrt(a+b*sin(d*x+c))/d-2/39*a*cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2)/d-2/15*cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2)/d+8/45045*a*(32*a^6-189*a^4*b^2+570*a^2*b^4+1635*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/45045*(32*a^8-197*a^6*b^2+615*a^4*b^4-255*a^2*b^6-195*b^8)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))-2/9009*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(8*a^4-33*a^2*b^2-39*b^4-7*a*b*(a^2+63*b^2)*sin(d*x+c))/b^2/d+4/45045*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(32*a^6-165*a^4*b^2+450*a^2*b^4+195*b^6-24*a*b*(a^4-5*a^2*b^2-60*b^4)*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2),x,12,-2/693*(8*a^4-141*a^2*b^2+36*b^4)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^2/d-2/693*a*(8*a^2-131*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b^2/d-2/693*(8*a^2-117*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/b^2/d+8/99*a*cos(d*x+c)*(a+b*sin(d*x+c))^(7/2)/b^2/d-2/11*cos(d*x+c)*sin(d*x+c)*(a+b*sin(d*x+c))^(7/2)/b/d+2/693*a*(8*a^4-147*a^2*b^2+444*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))-2/693*(8*a^6-149*a^4*b^2-516*a^2*b^4-36*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^3/d/sqrt(a+b*sin(d*x+c))+2*a^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x,12,1/315*a*(20*a^2+759*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d+1/315*(20*a^2+469*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b/d+1/63*(4*a^2+63*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a/b/d-2/9*cos(d*x+c)*(a+b*sin(d*x+c))^(7/2)/b/d-cot(d*x+c)*(a+b*sin(d*x+c))^(7/2)/a/d-1/315*(20*a^4+1689*a^2*b^2-168*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/315*a*(20*a^4+739*a^2*b^2+816*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))+5*a^2*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x,12,-1/28*(8*a^2-73*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/d-1/28*(8*a^2-35*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a/d-1/28*(8*a^2-21*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a^2/d-3/4*b*cot(d*x+c)*(a+b*sin(d*x+c))^(7/2)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(7/2)/a/d+1/28*a*(8*a^2-247*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/28*(8*a^4+3*a^2*b^2-32*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b/d/sqrt(a+b*sin(d*x+c))-3/4*a*(4*a^2-5*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x,12,-1/40*b*(96*a^2-25*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a/d-1/120*b*(208*a^2-25*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/24*(32*a^2-3*b^2)*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a^2/d-1/12*b*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(7/2)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(7/2)/a/d+1/40*(176*a^2-167*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/40*a*(96*a^2+179*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))-5/8*b*(12*a^2-b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2),x,12,-1/64*b^2*(196*a^2+5*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+5/192*b*(68*a^2+b^2)*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/96*(60*a^2+b^2)*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2)/a^2/d+1/24*b*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(7/2)/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(7/2)/a/d+1/64*b*(492*a^2-5*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/64*b*(148*a^2+169*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))+1/64*(48*a^4-360*a^2*b^2-5*b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x,12,-1/640*(128*a^4-580*a^2*b^2+15*b^4)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/64*b*(36*a^2-b^2)*cot(d*x+c)*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/80*(32*a^2-b^2)*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2)/a^2/d+3/40*b*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(7/2)/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^(7/2)/a/d-1/640*(128*a^4-2476*a^2*b^2-15*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/640*(128*a^4+492*a^2*b^2-5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c))+3/128*b*(80*a^4-40*a^2*b^2+b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x,13,-1/1536*b*(720*a^4-176*a^2*b^2+15*b^4)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d-1/256*(16*a^4-56*a^2*b^2+5*b^4)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d+1/192*b*(52*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2)/a^2/d+1/96*(28*a^2-3*b^2)*cot(d*x+c)*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2)/a^2/d+1/12*b*cot(d*x+c)*csc(d*x+c)^4*(a+b*sin(d*x+c))^(7/2)/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5*(a+b*sin(d*x+c))^(7/2)/a/d-1/1536*b*(720*a^4-176*a^2*b^2+15*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/1536*b*(816*a^4+1696*a^2*b^2+5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c))+1/512*(64*a^6+720*a^4*b^2+60*a^2*b^4-5*b^6)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^3/sqrt(a+b*sin(d*x+c)),x,10,64/15015*a*(80*a^4-118*a^2*b^2+17*b^4)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^6/d-8/15015*(480*a^4-683*a^2*b^2+77*b^4)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d+4/3003*a*(160*a^2-223*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/b^4/d-10/429*(8*a^2-11*b^2)*cos(d*x+c)*sin(d*x+c)^3*sqrt(a+b*sin(d*x+c))/b^3/d+24/143*a*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+b*sin(d*x+c))/b^2/d-2/13*cos(d*x+c)*sin(d*x+c)^5*sqrt(a+b*sin(d*x+c))/b/d+8/15015*(1280*a^6-2048*a^4*b^2+453*a^2*b^4+231*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^7/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/15015*a*(1280*a^6-2368*a^4*b^2+875*a^2*b^4+213*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^7/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/sqrt(a+b*sin(d*x+c)),x,9,-8/3465*(160*a^4-247*a^2*b^2+45*b^4)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d+8/3465*a*(120*a^2-179*b^2)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b^4/d-2/693*(80*a^2-117*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/b^3/d+20/99*a*cos(d*x+c)*sin(d*x+c)^3*sqrt(a+b*sin(d*x+c))/b^2/d-2/11*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+b*sin(d*x+c))/b/d-16/3465*a*(160*a^4-267*a^2*b^2+69*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/3465*(320*a^6-614*a^4*b^2+249*a^2*b^4+45*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/sqrt(a+b*sin(d*x+c)),x,7,-2/63*cos(d*x+c)^3*(8*a-7*b*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/b^2/d+8/315*(32*a^4-57*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/315*a*(32*a^4-65*a^2*b^2+33*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))+4/315*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*(32*a^2-33*b^2)-3*b*(8*a^2-7*b^2)*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)/sqrt(a+b*sin(d*x+c)),x,9,8/15*a*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^2/d-2/5*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d+2/15*(8*a^2-21*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))-2/15*a*(8*a^2-23*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^3/d/sqrt(a+b*sin(d*x+c))+2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/sqrt(a+b*sin(d*x+c)),x,9,-2/3*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d-cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a/d-1/3*(4*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/3*(4*a^2-7*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))-b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/sqrt(a+b*sin(d*x+c)),x,9,3/4*b*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a/d+1/4*(8*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/b/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/4*(8*a^2+b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/b/d/sqrt(a+b*sin(d*x+c))-3/4*(4*a^2-b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/sqrt(a+b*sin(d*x+c)),x,10,1/24*(32*a^2-15*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+5/12*b*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a/d+1/24*(32*a^2-15*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/24*(16*a^2+5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c))+1/8*b*(12*a^2-5*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4*csc(d*x+c)/sqrt(a+b*sin(d*x+c)),x,11,-1/192*b*(188*a^2-105*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^4/d+5/96*(12*a^2-7*b^2)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/d+7/24*b*cot(d*x+c)*csc(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3*sqrt(a+b*sin(d*x+c))/a/d-1/192*b*(188*a^2-105*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/192*b*(68*a^2-35*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c))+1/64*(48*a^4-72*a^2*b^2+35*b^4)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x,10,-2*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/a/b^2/d/sqrt(a+b*sin(d*x+c))-8/1155*(640*a^4-592*a^2*b^2+15*b^4)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^6/d+8/1155*a*(480*a^2-419*b^2)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d-20/231*(32*a^2-27*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/b^4/d+2/33*(40*a^2-33*b^2)*cos(d*x+c)*sin(d*x+c)^3*sqrt(a+b*sin(d*x+c))/a/b^3/d-2/11*cos(d*x+c)*sin(d*x+c)^4*sqrt(a+b*sin(d*x+c))/b^2/d-8/1155*a*(1280*a^4-1344*a^2*b^2+123*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^7/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/1155*(1280*a^6-1664*a^4*b^2+369*a^2*b^4+15*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^7/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x,9,-2*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/a/b^2/d/sqrt(a+b*sin(d*x+c))+8/315*a*(160*a^2-139*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d-16/315*(60*a^2-49*b^2)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b^4/d+2/63*(80*a^2-63*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a/b^3/d-2/9*cos(d*x+c)*sin(d*x+c)^3*sqrt(a+b*sin(d*x+c))/b^2/d+8/315*(320*a^4-318*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))-16/315*a*(160*a^4-199*a^2*b^2+39*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(3/2),x,7,-8/35*a*(32*a^2-29*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/35*(32*a^4-37*a^2*b^2+5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))+2/7*cos(d*x+c)^3*(8*a+b*sin(d*x+c))/b^2/d/sqrt(a+b*sin(d*x+c))-4/35*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(32*a^2-5*b^2-24*a*b*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(3/2),x,9,-2*(a^2-b^2)*cos(d*x+c)/a/b^2/d/sqrt(a+b*sin(d*x+c))-2/3*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^2/d-2/3*(8*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+2/3*(8*a^2-5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^3/d/sqrt(a+b*sin(d*x+c))+2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x,9,(2*a^2-3*b^2)*cos(d*x+c)/a^2/b/d/sqrt(a+b*sin(d*x+c))-cot(d*x+c)/a/d/sqrt(a+b*sin(d*x+c))+(4*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-(4*a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/b^2/d/sqrt(a+b*sin(d*x+c))-3*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x,10,1/2*(4*a^2-5*b^2)*cot(d*x+c)/a^2/b/d/sqrt(a+b*sin(d*x+c))-1/2*cot(d*x+c)*csc(d*x+c)/a/d/sqrt(a+b*sin(d*x+c))-1/4*(8*a^2-15*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/b/d-1/4*(8*a^2-15*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/b/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/4*(8*a^2-5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/b/d/sqrt(a+b*sin(d*x+c))-3/4*(4*a^2-5*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x,11,1/3*(6*a^2-7*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/sqrt(a+b*sin(d*x+c))-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/sqrt(a+b*sin(d*x+c))+5/24*(16*a^2-21*b^2)*cot(d*x+c)*sqrt(a+b*sin(d*x+c))/a^4/d-1/12*(24*a^2-35*b^2)*cot(d*x+c)*csc(d*x+c)*sqrt(a+b*sin(d*x+c))/a^3/b/d+5/24*(16*a^2-21*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^4/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/24*(32*a^2-35*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c))+1/8*b*(36*a^2-35*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x,10,-2/3*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^4/a/b^2/d/(a+b*sin(d*x+c))^(3/2)+2/3*(13*a^2-5*b^2)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^2/d/sqrt(a+b*sin(d*x+c))+128/315*a*(40*a^2-19*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^6/d-8/315*(480*a^2-203*b^2)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d+4/63*(160*a^2-63*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a/b^4/d-10/9*(8*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^3*sqrt(a+b*sin(d*x+c))/a^2/b^3/d+8/315*(1280*a^4-768*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^7/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/315*a*(1280*a^4-1088*a^2*b^2+123*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^7/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x,9,-2/3*(a^2-b^2)*cos(d*x+c)*sin(d*x+c)^3/a/b^2/d/(a+b*sin(d*x+c))^(3/2)+2/3*(11*a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^2/d/sqrt(a+b*sin(d*x+c))-8/21*(32*a^2-11*b^2)*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b^5/d+8/21*(24*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)*sqrt(a+b*sin(d*x+c))/a/b^4/d-2/21*(80*a^2-21*b^2)*cos(d*x+c)*sin(d*x+c)^2*sqrt(a+b*sin(d*x+c))/a^2/b^3/d-16/21*a*(32*a^2-15*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/21*(64*a^4-46*a^2*b^2+3*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(5/2),x,7,8/15*(32*a^2-9*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-8/15*a*(32*a^2-17*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^5/d/sqrt(a+b*sin(d*x+c))+2/15*cos(d*x+c)^3*(8*a+3*b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c))^(3/2)+4/15*cos(d*x+c)*(32*a^2-9*b^2+8*a*b*sin(d*x+c))/b^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(5/2),x,9,-2/3*(a^2-b^2)*cos(d*x+c)/a/b^2/d/(a+b*sin(d*x+c))^(3/2)+2/3*(5*a^2+3*b^2)*cos(d*x+c)/a^2/b^2/d/sqrt(a+b*sin(d*x+c))+2/3*(8*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^2/b^3/d/sqrt((a+b*sin(d*x+c))/(a+b))-2/3*(8*a^2+b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a/b^3/d/sqrt(a+b*sin(d*x+c))+2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x,10,1/3*(2*a^2-5*b^2)*cos(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^(3/2)-cot(d*x+c)/a/d/(a+b*sin(d*x+c))^(3/2)-1/3*(4*a^2+15*b^2)*cos(d*x+c)/a^3/b/d/sqrt(a+b*sin(d*x+c))-1/3*(4*a^2+15*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^3/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/3*(4*a^2+5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^2/b^2/d/sqrt(a+b*sin(d*x+c))-5*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x,11,1/6*(4*a^2-7*b^2)*cot(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^(3/2)-1/2*cot(d*x+c)*csc(d*x+c)/a/d/(a+b*sin(d*x+c))^(3/2)-1/12*(8*a^2-105*b^2)*cos(d*x+c)/a^4/d/sqrt(a+b*sin(d*x+c))-1/12*(8*a^2-35*b^2)*cot(d*x+c)/a^3/b/d/sqrt(a+b*sin(d*x+c))-1/12*(8*a^2-105*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^4/b/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/12*(8*a^2-35*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^3/b/d/sqrt(a+b*sin(d*x+c))-1/4*(12*a^2-35*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c)),1],
[cot(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x,12,1/3*(2*a^2-3*b^2)*cot(d*x+c)*csc(d*x+c)/a^2/b/d/(a+b*sin(d*x+c))^(3/2)-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c))^(3/2)+1/8*b*(32*a^2-105*b^2)*cos(d*x+c)/a^5/d/sqrt(a+b*sin(d*x+c))+1/8*(16*a^2-35*b^2)*cot(d*x+c)/a^4/d/sqrt(a+b*sin(d*x+c))-1/12*(8*a^2-21*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/b/d/sqrt(a+b*sin(d*x+c))+1/8*(32*a^2-105*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/a^5/d/sqrt((a+b*sin(d*x+c))/(a+b))-1/8*(16*a^2-35*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^4/d/sqrt(a+b*sin(d*x+c))+15/8*b*(4*a^2-7*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/a^5/d/sqrt(a+b*sin(d*x+c)),1],
[cos(f*x+e)^4/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e))^(9/2),x,8,2/7*cos(f*x+e)^3*sqrt(d*sin(f*x+e))/a/d/f/(a+b*sin(f*x+e))^(7/2)+12/35*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^2/d/f/(a+b*sin(f*x+e))^(5/2)+8/35*(a^2-2*b^2)*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^3/(a^2-b^2)/d/f/(a+b*sin(f*x+e))^(3/2)+32/35*b*(2*a^2-b^2)*cos(f*x+e)/a^3/(a^2-b^2)^2/f/sqrt(d*sin(f*x+e))/sqrt(a+b*sin(f*x+e))-32/35*b*(2*a^2-b^2)*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*EllipticE(sin(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e)))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^5/(a-b)/(a+b)^(3/2)/sqrt(d)/f-8/35*(5*a^2-3*a*b-4*b^2)*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^4/(a-b)/(a+b)^(3/2)/sqrt(d)/f,1],
[cos(d*x+c)^4*sin(d*x+c)^(1/3)/sqrt(a+b*sin(d*x+c)),x,0,Defer(Int)(cos(d*x+c)^4*sin(d*x+c)^(1/3)/sqrt(a+b*sin(d*x+c)),x),0],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x,0,Defer(Int)(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x),0],
[cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x,0,Defer(Int)(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x),0],
[cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x,0,Defer(Int)(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x),0],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x,8,-3*a*(2*a^4*(n^2+5*n+6)+3*b^4*(n^2+12*n+35)-2*a^2*b^2*(n^2+16*n+58))*cos(d*x+c)*sin(d*x+c)^(1+n)/b^2/d/(2+n)/(4+n)/(5+n)/(6+n)/(7+n)+3*a*(3*b^2*(1+n)+a^2*(6+n))*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/(2+n)/(4+n)/(6+n)/sqrt(cos(d*x+c)^2)-3*(2*a^4*(n^2+5*n+6)+b^4*(n^2+10*n+24)-2*a^2*b^2*(n^2+16*n+57))*cos(d*x+c)*sin(d*x+c)^(2+n)/b/d/(3+n)/(4+n)/(5+n)/(6+n)/(7+n)+3*b*(b^2*(2+n)+3*a^2*(7+n))*cos(d*x+c)*hypergeom([1/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/(3+n)/(5+n)/(7+n)/sqrt(cos(d*x+c)^2)-3*a*(a^2*(n^2+5*n+6)-b^2*(n^2+15*n+53))*cos(d*x+c)*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^2/b^2/d/(4+n)/(5+n)/(6+n)/(7+n)-(a^2*(2+n)*(3+n)-b^2*(6+n)*(8+n))*cos(d*x+c)*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^3/b^2/d/(5+n)/(6+n)/(7+n)+a*(3+n)*cos(d*x+c)*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^4/b^2/d/(6+n)/(7+n)-cos(d*x+c)*sin(d*x+c)^(2+n)*(a+b*sin(d*x+c))^4/b/d/(7+n),1],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x,7,-(3*b^4*(5+n)+2*a^4*(n^2+5*n+6)-2*a^2*b^2*(n^2+13*n+40))*cos(d*x+c)*sin(d*x+c)^(1+n)/b^2/d/(2+n)/(4+n)/(5+n)/(6+n)+3*(b^2*(1+n)+a^2*(6+n))*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/(2+n)/(4+n)/(6+n)/sqrt(cos(d*x+c)^2)-2*a*(a^2*(n^2+5*n+6)-b^2*(n^2+13*n+39))*cos(d*x+c)*sin(d*x+c)^(2+n)/b/d/(3+n)/(4+n)/(5+n)/(6+n)+6*a*b*cos(d*x+c)*hypergeom([1/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/(3+n)/(5+n)/sqrt(cos(d*x+c)^2)-(a^2*(2+n)*(3+n)-b^2*(5+n)*(7+n))*cos(d*x+c)*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^2/b^2/d/(4+n)/(5+n)/(6+n)+a*(3+n)*cos(d*x+c)*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^3/b^2/d/(5+n)/(6+n)-cos(d*x+c)*sin(d*x+c)^(2+n)*(a+b*sin(d*x+c))^3/b/d/(6+n),1],
[cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x,3,a*cos(d*x+c)*hypergeom([-3/2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)/sqrt(cos(d*x+c)^2)+b*cos(d*x+c)*hypergeom([-3/2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)/sqrt(cos(d*x+c)^2),1],
[cos(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x,4,1/6*a*sin(d*x+c)^6/d+1/7*b*sin(d*x+c)^7/d-1/4*a*sin(d*x+c)^8/d-2/9*b*sin(d*x+c)^9/d+1/10*a*sin(d*x+c)^10/d+1/11*b*sin(d*x+c)^11/d,1],
[cos(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x,4,1/5*a*sin(d*x+c)^5/d+1/6*b*sin(d*x+c)^6/d-2/7*a*sin(d*x+c)^7/d-1/4*b*sin(d*x+c)^8/d+1/9*a*sin(d*x+c)^9/d+1/10*b*sin(d*x+c)^10/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x,8,-1/6*a*cos(d*x+c)^6/d+1/8*a*cos(d*x+c)^8/d+1/5*b*sin(d*x+c)^5/d-2/7*b*sin(d*x+c)^7/d+1/9*b*sin(d*x+c)^9/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x,8,-1/6*b*cos(d*x+c)^6/d+1/8*b*cos(d*x+c)^8/d+1/3*a*sin(d*x+c)^3/d-2/5*a*sin(d*x+c)^5/d+1/7*a*sin(d*x+c)^7/d,1],
[cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x,6,-1/6*a*cos(d*x+c)^6/d+1/3*b*sin(d*x+c)^3/d-2/5*b*sin(d*x+c)^5/d+1/7*b*sin(d*x+c)^7/d,1],
[cos(d*x+c)^4*cot(d*x+c)*(a+b*sin(d*x+c)),x,4,a*ln(sin(d*x+c))/d+b*sin(d*x+c)/d-a*sin(d*x+c)^2/d-2/3*b*sin(d*x+c)^3/d+1/4*a*sin(d*x+c)^4/d+1/5*b*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2*(a+b*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+b*ln(sin(d*x+c))/d-2*a*sin(d*x+c)/d-b*sin(d*x+c)^2/d+1/3*a*sin(d*x+c)^3/d+1/4*b*sin(d*x+c)^4/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3*(a+b*sin(d*x+c)),x,4,-b*csc(d*x+c)/d-1/2*a*csc(d*x+c)^2/d-2*a*ln(sin(d*x+c))/d-2*b*sin(d*x+c)/d+1/2*a*sin(d*x+c)^2/d+1/3*b*sin(d*x+c)^3/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+b*sin(d*x+c)),x,4,2*a*csc(d*x+c)/d-1/2*b*csc(d*x+c)^2/d-1/3*a*csc(d*x+c)^3/d-2*b*ln(sin(d*x+c))/d+a*sin(d*x+c)/d+1/2*b*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*(a+b*sin(d*x+c)),x,3,2*b*csc(d*x+c)/d+a*csc(d*x+c)^2/d-1/3*b*csc(d*x+c)^3/d-1/4*a*csc(d*x+c)^4/d+a*ln(sin(d*x+c))/d+b*sin(d*x+c)/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c)),x,4,-a*csc(d*x+c)/d+b*csc(d*x+c)^2/d+2/3*a*csc(d*x+c)^3/d-1/4*b*csc(d*x+c)^4/d-1/5*a*csc(d*x+c)^5/d+b*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c)),x,6,-1/6*a*cot(d*x+c)^6/d-b*csc(d*x+c)/d+2/3*b*csc(d*x+c)^3/d-1/5*b*csc(d*x+c)^5/d,1],
[cot(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c)),x,6,-1/6*b*cot(d*x+c)^6/d-1/3*a*csc(d*x+c)^3/d+2/5*a*csc(d*x+c)^5/d-1/7*a*csc(d*x+c)^7/d,1],
[cot(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c)),x,8,-1/6*a*cot(d*x+c)^6/d-1/8*a*cot(d*x+c)^8/d-1/3*b*csc(d*x+c)^3/d+2/5*b*csc(d*x+c)^5/d-1/7*b*csc(d*x+c)^7/d,1],
[cot(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c)),x,8,-1/6*b*cot(d*x+c)^6/d-1/8*b*cot(d*x+c)^8/d-1/5*a*csc(d*x+c)^5/d+2/7*a*csc(d*x+c)^7/d-1/9*a*csc(d*x+c)^9/d,1],
[cot(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c)),x,4,-1/5*b*csc(d*x+c)^5/d-1/6*a*csc(d*x+c)^6/d+2/7*b*csc(d*x+c)^7/d+1/4*a*csc(d*x+c)^8/d-1/9*b*csc(d*x+c)^9/d-1/10*a*csc(d*x+c)^10/d,1],
[cot(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c)),x,4,-1/6*b*csc(d*x+c)^6/d-1/7*a*csc(d*x+c)^7/d+1/4*b*csc(d*x+c)^8/d+2/9*a*csc(d*x+c)^9/d-1/10*b*csc(d*x+c)^10/d-1/11*a*csc(d*x+c)^11/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x,4,1/3*a^2*sin(d*x+c)^3/d+1/2*a*b*sin(d*x+c)^4/d-1/5*(2*a^2-b^2)*sin(d*x+c)^5/d-2/3*a*b*sin(d*x+c)^6/d+1/7*(a^2-2*b^2)*sin(d*x+c)^7/d+1/4*a*b*sin(d*x+c)^8/d+1/9*b^2*sin(d*x+c)^9/d,1],
[cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x,6,-1/24*(4*a^2+b^2)*cos(d*x+c)^6/d-1/8*b^2*cos(d*x+c)^6*sin(d*x+c)^2/d+2/3*a*b*sin(d*x+c)^3/d-4/5*a*b*sin(d*x+c)^5/d+2/7*a*b*sin(d*x+c)^7/d,1],
[cos(d*x+c)^4*cot(d*x+c)*(a+b*sin(d*x+c))^2,x,4,a^2*ln(sin(d*x+c))/d+2*a*b*sin(d*x+c)/d-1/2*(2*a^2-b^2)*sin(d*x+c)^2/d-4/3*a*b*sin(d*x+c)^3/d+1/4*(a^2-2*b^2)*sin(d*x+c)^4/d+2/5*a*b*sin(d*x+c)^5/d+1/6*b^2*sin(d*x+c)^6/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x,4,-a^2*csc(d*x+c)/d+2*a*b*ln(sin(d*x+c))/d-(2*a^2-b^2)*sin(d*x+c)/d-2*a*b*sin(d*x+c)^2/d+1/3*(a^2-2*b^2)*sin(d*x+c)^3/d+1/2*a*b*sin(d*x+c)^4/d+1/5*b^2*sin(d*x+c)^5/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x,4,-2*a*b*csc(d*x+c)/d-1/2*a^2*csc(d*x+c)^2/d-(2*a^2-b^2)*ln(sin(d*x+c))/d-4*a*b*sin(d*x+c)/d+1/2*(a^2-2*b^2)*sin(d*x+c)^2/d+2/3*a*b*sin(d*x+c)^3/d+1/4*b^2*sin(d*x+c)^4/d,1],
[cos(d*x+c)*cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x,4,(2*a^2-b^2)*csc(d*x+c)/d-a*b*csc(d*x+c)^2/d-1/3*a^2*csc(d*x+c)^3/d-4*a*b*ln(sin(d*x+c))/d+(a^2-2*b^2)*sin(d*x+c)/d+a*b*sin(d*x+c)^2/d+1/3*b^2*sin(d*x+c)^3/d,1],
[cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x,3,4*a*b*csc(d*x+c)/d+1/2*(2*a^2-b^2)*csc(d*x+c)^2/d-2/3*a*b*csc(d*x+c)^3/d-1/4*a^2*csc(d*x+c)^4/d+(a^2-2*b^2)*ln(sin(d*x+c))/d+2*a*b*sin(d*x+c)/d+1/2*b^2*sin(d*x+c)^2/d,1],
[cot(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c))^2,x,4,-(a^2-2*b^2)*csc(d*x+c)/d+2*a*b*csc(d*x+c)^2/d+1/3*(2*a^2-b^2)*csc(d*x+c)^3/d-1/2*a*b*csc(d*x+c)^4/d-1/5*a^2*csc(d*x+c)^5/d+2*a*b*ln(sin(d*x+c))/d+b^2*sin(d*x+c)/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x,4,-2*a*b*csc(d*x+c)/d-1/2*(a^2-2*b^2)*csc(d*x+c)^2/d+4/3*a*b*csc(d*x+c)^3/d+1/4*(2*a^2-b^2)*csc(d*x+c)^4/d-2/5*a*b*csc(d*x+c)^5/d-1/6*a^2*csc(d*x+c)^6/d+b^2*ln(sin(d*x+c))/d,1],
[cot(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x,4,-b^2*csc(d*x+c)/d-a*b*csc(d*x+c)^2/d-1/3*(a^2-2*b^2)*csc(d*x+c)^3/d+a*b*csc(d*x+c)^4/d+1/5*(2*a^2-b^2)*csc(d*x+c)^5/d-1/3*a*b*csc(d*x+c)^6/d-1/7*a^2*csc(d*x+c)^7/d,1],
[cot(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x,4,-1/2*b^2*csc(d*x+c)^2/d-2/3*a*b*csc(d*x+c)^3/d-1/4*(a^2-2*b^2)*csc(d*x+c)^4/d+4/5*a*b*csc(d*x+c)^5/d+1/6*(2*a^2-b^2)*csc(d*x+c)^6/d-2/7*a*b*csc(d*x+c)^7/d-1/8*a^2*csc(d*x+c)^8/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x,4,a^2*(7*a^4-10*a^2*b^2+3*b^4)*ln(a+b*sin(d*x+c))/b^8/d-2*a*(3*a^4-4*a^2*b^2+b^4)*sin(d*x+c)/b^7/d+1/2*(5*a^4-6*a^2*b^2+b^4)*sin(d*x+c)^2/b^6/d-4/3*a*(a^2-b^2)*sin(d*x+c)^3/b^5/d+1/4*(3*a^2-2*b^2)*sin(d*x+c)^4/b^4/d-2/5*a*sin(d*x+c)^5/b^3/d+1/6*sin(d*x+c)^6/b^2/d+a^3*(a^2-b^2)^2/b^8/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x,4,-2*a*(3*a^4-4*a^2*b^2+b^4)*ln(a+b*sin(d*x+c))/b^7/d+(5*a^4-6*a^2*b^2+b^4)*sin(d*x+c)/b^6/d-2*a*(a^2-b^2)*sin(d*x+c)^2/b^5/d+1/3*(3*a^2-2*b^2)*sin(d*x+c)^3/b^4/d-1/2*a*sin(d*x+c)^4/b^3/d+1/5*sin(d*x+c)^5/b^2/d-a^2*(a^2-b^2)^2/b^7/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c))^2,x,4,(5*a^4-6*a^2*b^2+b^4)*ln(a+b*sin(d*x+c))/b^6/d-4*a*(a^2-b^2)*sin(d*x+c)/b^5/d+1/2*(3*a^2-2*b^2)*sin(d*x+c)^2/b^4/d-2/3*a*sin(d*x+c)^3/b^3/d+1/4*sin(d*x+c)^4/b^2/d+a*(a^2-b^2)^2/b^6/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*cot(d*x+c)/(a+b*sin(d*x+c))^2,x,4,ln(sin(d*x+c))/a^2/d+(a^2-b^2)*(3*a^2+b^2)*ln(a+b*sin(d*x+c))/a^2/b^4/d-2*a*sin(d*x+c)/b^3/d+1/2*sin(d*x+c)^2/b^2/d+(a^2-b^2)^2/a/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x,4,-csc(d*x+c)/a^2/d-2*b*ln(sin(d*x+c))/a^3/d-2*(a^4-b^4)*ln(a+b*sin(d*x+c))/a^3/b^3/d+sin(d*x+c)/b^2/d-(a^2-b^2)^2/a^2/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x,4,2*b*csc(d*x+c)/a^3/d-1/2*csc(d*x+c)^2/a^2/d-(2*a^2-3*b^2)*ln(sin(d*x+c))/a^4/d+(a^4+2*a^2*b^2-3*b^4)*ln(a+b*sin(d*x+c))/a^4/b^2/d+(a^2-b^2)^2/a^3/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x,4,(2*a^2-3*b^2)*csc(d*x+c)/a^4/d+b*csc(d*x+c)^2/a^3/d-1/3*csc(d*x+c)^3/a^2/d+4*b*(a^2-b^2)*ln(sin(d*x+c))/a^5/d-4*b*(a^2-b^2)*ln(a+b*sin(d*x+c))/a^5/d-(a^2-b^2)^2/a^4/b/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x,3,-4*b*(a^2-b^2)*csc(d*x+c)/a^5/d+1/2*(2*a^2-3*b^2)*csc(d*x+c)^2/a^4/d+2/3*b*csc(d*x+c)^3/a^3/d-1/4*csc(d*x+c)^4/a^2/d+(a^4-6*a^2*b^2+5*b^4)*ln(sin(d*x+c))/a^6/d-(a^4-6*a^2*b^2+5*b^4)*ln(a+b*sin(d*x+c))/a^6/d+(a^2-b^2)^2/a^5/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c))^2,x,4,-(a^4-6*a^2*b^2+5*b^4)*csc(d*x+c)/a^6/d-2*b*(a^2-b^2)*csc(d*x+c)^2/a^5/d+1/3*(2*a^2-3*b^2)*csc(d*x+c)^3/a^4/d+1/2*b*csc(d*x+c)^4/a^3/d-1/5*csc(d*x+c)^5/a^2/d-2*b*(a^4-4*a^2*b^2+3*b^4)*ln(sin(d*x+c))/a^7/d+2*b*(a^4-4*a^2*b^2+3*b^4)*ln(a+b*sin(d*x+c))/a^7/d-b*(a^2-b^2)^2/a^6/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x,3,a^2*sin(d*x+c)^(1+n)/d/(1+n)+2*a*b*sin(d*x+c)^(2+n)/d/(2+n)-(2*a^2-b^2)*sin(d*x+c)^(3+n)/d/(3+n)-4*a*b*sin(d*x+c)^(4+n)/d/(4+n)+(a^2-2*b^2)*sin(d*x+c)^(5+n)/d/(5+n)+2*a*b*sin(d*x+c)^(6+n)/d/(6+n)+b^2*sin(d*x+c)^(7+n)/d/(7+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x,3,a*sin(d*x+c)^(1+n)/d/(1+n)+b*sin(d*x+c)^(2+n)/d/(2+n)-2*a*sin(d*x+c)^(3+n)/d/(3+n)-2*b*sin(d*x+c)^(4+n)/d/(4+n)+a*sin(d*x+c)^(5+n)/d/(5+n)+b*sin(d*x+c)^(6+n)/d/(6+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x,4,-a*(a^2-2*b^2)*sin(d*x+c)^(1+n)/b^4/d/(1+n)+(a^2-b^2)^2*hypergeom([1, 1+n],[2+n],-b*sin(d*x+c)/a)*sin(d*x+c)^(1+n)/a/b^4/d/(1+n)+(a^2-2*b^2)*sin(d*x+c)^(2+n)/b^3/d/(2+n)-a*sin(d*x+c)^(3+n)/b^2/d/(3+n)+sin(d*x+c)^(4+n)/b/d/(4+n),1],
[cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x,5,(3*a^2-2*b^2)*sin(d*x+c)^(1+n)/b^4/d/(1+n)+(a^2-b^2)*(b^2*n-a^2*(4+n))*hypergeom([1, 1+n],[2+n],-b*sin(d*x+c)/a)*sin(d*x+c)^(1+n)/a^2/b^4/d/(1+n)-2*a*sin(d*x+c)^(2+n)/b^3/d/(2+n)+sin(d*x+c)^(3+n)/b^2/d/(3+n)+(a^2-b^2)^2*sin(d*x+c)^(1+n)/a/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x,12,5/512*a*b*x-1/7*(a^2+b^2)*cos(d*x+c)^7/d+1/9*(2*a^2+3*b^2)*cos(d*x+c)^9/d-1/11*(a^2+3*b^2)*cos(d*x+c)^11/d+1/13*b^2*cos(d*x+c)^13/d+5/512*a*b*cos(d*x+c)*sin(d*x+c)/d+5/768*a*b*cos(d*x+c)^3*sin(d*x+c)/d+1/192*a*b*cos(d*x+c)^5*sin(d*x+c)/d-1/32*a*b*cos(d*x+c)^7*sin(d*x+c)/d-1/12*a*b*cos(d*x+c)^7*sin(d*x+c)^3/d-1/6*a*b*cos(d*x+c)^7*sin(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x,12,1/1024*(12*a^2+5*b^2)*x-2/7*a*b*cos(d*x+c)^7/d+4/9*a*b*cos(d*x+c)^9/d-2/11*a*b*cos(d*x+c)^11/d+1/1024*(12*a^2+5*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/1536*(12*a^2+5*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/1920*(12*a^2+5*b^2)*cos(d*x+c)^5*sin(d*x+c)/d-1/320*(44*a^2+45*b^2)*cos(d*x+c)^7*sin(d*x+c)/d+1/120*(12*a^2+25*b^2)*cos(d*x+c)^9*sin(d*x+c)/d-1/12*b^2*cos(d*x+c)^11*sin(d*x+c)/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x,11,3/128*a*b*x-1/7*(a^2+b^2)*cos(d*x+c)^7/d+1/9*(a^2+2*b^2)*cos(d*x+c)^9/d-1/11*b^2*cos(d*x+c)^11/d+3/128*a*b*cos(d*x+c)*sin(d*x+c)/d+1/64*a*b*cos(d*x+c)^3*sin(d*x+c)/d+1/80*a*b*cos(d*x+c)^5*sin(d*x+c)/d-3/40*a*b*cos(d*x+c)^7*sin(d*x+c)/d-1/5*a*b*cos(d*x+c)^7*sin(d*x+c)^3/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x,11,1/256*(10*a^2+3*b^2)*x-2/7*a*b*cos(d*x+c)^7/d+2/9*a*b*cos(d*x+c)^9/d+1/256*(10*a^2+3*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/384*(10*a^2+3*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/480*(10*a^2+3*b^2)*cos(d*x+c)^5*sin(d*x+c)/d-1/80*(10*a^2+11*b^2)*cos(d*x+c)^7*sin(d*x+c)/d+1/10*b^2*cos(d*x+c)^9*sin(d*x+c)/d,1],
[cos(d*x+c)^6*sin(d*x+c)*(a+b*sin(d*x+c))^2,x,7,5/64*a*b*x-1/252*(a^2+8*b^2)*cos(d*x+c)^7/d+5/64*a*b*cos(d*x+c)*sin(d*x+c)/d+5/96*a*b*cos(d*x+c)^3*sin(d*x+c)/d+1/24*a*b*cos(d*x+c)^5*sin(d*x+c)/d-1/36*a*cos(d*x+c)^7*(a+b*sin(d*x+c))/d-1/9*cos(d*x+c)^7*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^5*cot(d*x+c)*(a+b*sin(d*x+c))^2,x,9,5/8*a*b*x-a^2*arctanh(cos(d*x+c))/d+a^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)^3/d+1/5*a^2*cos(d*x+c)^5/d-1/7*b^2*cos(d*x+c)^7/d+5/8*a*b*cos(d*x+c)*sin(d*x+c)/d+5/12*a*b*cos(d*x+c)^3*sin(d*x+c)/d+1/3*a*b*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x,12,-5/16*(6*a^2-b^2)*x-2*a*b*arctanh(cos(d*x+c))/d+2*a*b*cos(d*x+c)/d+2/3*a*b*cos(d*x+c)^3/d+2/5*a*b*cos(d*x+c)^5/d-a^2*cot(d*x+c)/d-1/16*(14*a^2-5*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/24*(6*a^2-5*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*b^2*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x,12,-15/4*a*b*x+1/2*(5*a^2-2*b^2)*arctanh(cos(d*x+c))/d-(2*a^2-b^2)*cos(d*x+c)/d-1/3*(a^2-b^2)*cos(d*x+c)^3/d+1/5*b^2*cos(d*x+c)^5/d-2*a*b*cot(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d-9/4*a*b*cos(d*x+c)*sin(d*x+c)/d+1/2*a*b*cos(d*x+c)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x,12,5/8*(4*a^2-3*b^2)*x+5*a*b*arctanh(cos(d*x+c))/d-4*a*b*cos(d*x+c)/d-2/3*a*b*cos(d*x+c)^3/d+(2*a^2-b^2)*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a*b*cot(d*x+c)*csc(d*x+c)/d+1/8*(4*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/4*b^2*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)*cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x,12,5*a*b*x-5/8*(3*a^2-4*b^2)*arctanh(cos(d*x+c))/d+(a^2-2*b^2)*cos(d*x+c)/d-1/3*b^2*cos(d*x+c)^3/d+4*a*b*cot(d*x+c)/d-2/3*a*b*cot(d*x+c)^3/d+1/8*(9*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/d-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d+a*b*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*(a+b*sin(d*x+c))^2,x,17,-a^2*x+5/2*b^2*x-15/4*a*b*arctanh(cos(d*x+c))/d+2*a*b*cos(d*x+c)/d-a^2*cot(d*x+c)/d+2*b^2*cot(d*x+c)/d+1/3*a^2*cot(d*x+c)^3/d-1/3*b^2*cot(d*x+c)^3/d-1/5*a^2*cot(d*x+c)^5/d+9/4*a*b*cot(d*x+c)*csc(d*x+c)/d-1/2*a*b*cot(d*x+c)*csc(d*x+c)^3/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)*(a+b*sin(d*x+c))^2,x,12,-2*a*b*x+5/16*(a^2-6*b^2)*arctanh(cos(d*x+c))/d+b^2*cos(d*x+c)/d-2*a*b*cot(d*x+c)/d+2/3*a*b*cot(d*x+c)^3/d-2/5*a*b*cot(d*x+c)^5/d-1/16*(11*a^2-18*b^2)*cot(d*x+c)*csc(d*x+c)/d+1/24*(13*a^2-6*b^2)*cot(d*x+c)*csc(d*x+c)^3/d-1/6*a^2*cot(d*x+c)*csc(d*x+c)^5/d,1],
[cot(d*x+c)^6*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x,12,-b^2*x+5/8*a*b*arctanh(cos(d*x+c))/d-b^2*cot(d*x+c)/d+1/3*b^2*cot(d*x+c)^3/d-1/5*b^2*cot(d*x+c)^5/d-1/7*a^2*cot(d*x+c)^7/d-5/8*a*b*cot(d*x+c)*csc(d*x+c)/d+5/12*a*b*cot(d*x+c)^3*csc(d*x+c)/d-1/3*a*b*cot(d*x+c)^5*csc(d*x+c)/d,1],
[cot(d*x+c)^6*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x,9,5/128*(a^2+8*b^2)*arctanh(cos(d*x+c))/d-2/7*a*b*cot(d*x+c)^7/d+1/128*(5*a^2-88*b^2)*cot(d*x+c)*csc(d*x+c)/d-1/192*(59*a^2-104*b^2)*cot(d*x+c)*csc(d*x+c)^3/d+1/48*(17*a^2-8*b^2)*cot(d*x+c)*csc(d*x+c)^5/d-1/8*a^2*cot(d*x+c)*csc(d*x+c)^7/d,1],
[cot(d*x+c)^6*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x,9,5/64*a*b*arctanh(cos(d*x+c))/d-1/7*(a^2+b^2)*cot(d*x+c)^7/d-1/9*a^2*cot(d*x+c)^9/d+5/64*a*b*cot(d*x+c)*csc(d*x+c)/d-5/32*a*b*cot(d*x+c)*csc(d*x+c)^3/d+5/24*a*b*cot(d*x+c)^3*csc(d*x+c)^3/d-1/4*a*b*cot(d*x+c)^5*csc(d*x+c)^3/d,1],
[cot(d*x+c)^6*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x,11,1/256*(3*a^2+10*b^2)*arctanh(cos(d*x+c))/d-2/7*a*b*cot(d*x+c)^7/d-2/9*a*b*cot(d*x+c)^9/d+1/256*(3*a^2+10*b^2)*cot(d*x+c)*csc(d*x+c)/d+1/384*(3*a^2-118*b^2)*cot(d*x+c)*csc(d*x+c)^3/d-1/480*(93*a^2-170*b^2)*cot(d*x+c)*csc(d*x+c)^5/d+1/80*(21*a^2-10*b^2)*cot(d*x+c)*csc(d*x+c)^7/d-1/10*a^2*cot(d*x+c)*csc(d*x+c)^9/d,1],
[cot(d*x+c)^6*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x,10,3/128*a*b*arctanh(cos(d*x+c))/d-1/7*(a^2+b^2)*cot(d*x+c)^7/d-1/9*(2*a^2+b^2)*cot(d*x+c)^9/d-1/11*a^2*cot(d*x+c)^11/d+3/128*a*b*cot(d*x+c)*csc(d*x+c)/d+1/64*a*b*cot(d*x+c)*csc(d*x+c)^3/d-1/16*a*b*cot(d*x+c)*csc(d*x+c)^5/d+1/8*a*b*cot(d*x+c)^3*csc(d*x+c)^5/d-1/5*a*b*cot(d*x+c)^5*csc(d*x+c)^5/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x,11,1/8*a*(64*a^6-120*a^4*b^2+60*a^2*b^4-5*b^6)*x/b^9-2*a^2*(8*a^2-3*b^2)*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^9/d+1/105*(840*a^6-1435*a^4*b^2+588*a^2*b^4-15*b^6)*cos(d*x+c)/b^8/d-1/8*a*(32*a^4-52*a^2*b^2+19*b^4)*cos(d*x+c)*sin(d*x+c)/b^7/d+1/105*(280*a^4-441*a^2*b^2+150*b^4)*cos(d*x+c)*sin(d*x+c)^2/b^6/d-1/12*(24*a^4-37*a^2*b^2+12*b^4)*cos(d*x+c)*sin(d*x+c)^3/a/b^5/d+1/140*(224*a^4-340*a^2*b^2+105*b^4)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^4/d+1/4*cos(d*x+c)*sin(d*x+c)^4/a/d/(a+b*sin(d*x+c))-3/20*b*cos(d*x+c)*sin(d*x+c)^5/a^2/d/(a+b*sin(d*x+c))-1/15*(20*a^4-30*a^2*b^2+9*b^4)*cos(d*x+c)*sin(d*x+c)^5/a^2/b^3/d/(a+b*sin(d*x+c))-4/21*a*cos(d*x+c)*sin(d*x+c)^6/b^2/d/(a+b*sin(d*x+c))+1/7*cos(d*x+c)*sin(d*x+c)^7/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x,10,-1/16*(112*a^6-200*a^4*b^2+90*a^2*b^4-5*b^6)*x/b^8+2*a*(7*a^2-2*b^2)*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^8/d-1/15*a*(105*a^4-170*a^2*b^2+61*b^4)*cos(d*x+c)/b^7/d+1/16*(56*a^4-86*a^2*b^2+27*b^4)*cos(d*x+c)*sin(d*x+c)/b^6/d-1/15*(35*a^4-52*a^2*b^2+15*b^4)*cos(d*x+c)*sin(d*x+c)^2/a/b^5/d+1/24*(42*a^4-61*a^2*b^2+16*b^4)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^4/d+1/3*cos(d*x+c)*sin(d*x+c)^3/a/d/(a+b*sin(d*x+c))-1/6*b*cos(d*x+c)*sin(d*x+c)^4/a^2/d/(a+b*sin(d*x+c))-1/10*(14*a^4-20*a^2*b^2+5*b^4)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^3/d/(a+b*sin(d*x+c))-7/30*a*cos(d*x+c)*sin(d*x+c)^5/b^2/d/(a+b*sin(d*x+c))+1/6*cos(d*x+c)*sin(d*x+c)^6/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^2,x,7,1/4*a*(24*a^4-40*a^2*b^2+15*b^4)*x/b^7-2*(a^2-b^2)^(3/2)*(6*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/d+1/5*cos(d*x+c)^5*(6*a+b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c))-1/6*cos(d*x+c)^3*(12*a^2-2*b^2-9*a*b*sin(d*x+c))/b^4/d+1/4*cos(d*x+c)*(24*a^4-28*a^2*b^2+4*b^4-a*b*(12*a^2-11*b^2)*sin(d*x+c))/b^6/d,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+b*sin(d*x+c))^2,x,16,a*x/b^3+2*a*(2*a^2-3*b^2)*x/b^5+2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/d-2*(a^2-b^2)^(3/2)*(5*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^5/d-arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/b^2/d+3*(a^2-b^2)*cos(d*x+c)/b^4/d-1/3*cos(d*x+c)^3/b^2/d-a*cos(d*x+c)*sin(d*x+c)/b^3/d+(a^2-b^2)^2*cos(d*x+c)/a/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x,16,-1/2*x/b^2-3*(a^2-b^2)*x/b^4-2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b^4/d+4*(2*a^6-3*a^4*b^2+b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^4/sqrt(a^2-b^2)/d+2*b*arctanh(cos(d*x+c))/a^3/d-2*a*cos(d*x+c)/b^3/d-cot(d*x+c)/a^2/d+1/2*cos(d*x+c)*sin(d*x+c)/b^2/d-(a^2-b^2)^2*cos(d*x+c)/a^2/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x,16,2*a*x/b^3+2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^3/d-6*(a^2-b^2)^(3/2)*(a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/b^3/d-1/2*arctanh(cos(d*x+c))/a^2/d+3*(a^2-b^2)*arctanh(cos(d*x+c))/a^4/d+cos(d*x+c)/b^2/d+2*b*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+(a^2-b^2)^2*cos(d*x+c)/a^3/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x,17,-x/b^2-2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^2/d+4*(a^6-3*a^2*b^4+2*b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/b^2/sqrt(a^2-b^2)/d+b*arctanh(cos(d*x+c))/a^3/d-2*b*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/a^5/d-cot(d*x+c)/a^2/d+3*(a^2-b^2)*cot(d*x+c)/a^4/d-1/3*cot(d*x+c)^3/a^2/d+b*cot(d*x+c)*csc(d*x+c)/a^3/d-(a^2-b^2)^2*cos(d*x+c)/a^4/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x,9,-10*b*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d-5/8*(3*a^4-12*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^6/d+1/3*(3*a^4-20*a^2*b^2+15*b^4)*cot(d*x+c)/a^5/b/d+5/8*(5*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d-cot(d*x+c)/b/d/(a+b*sin(d*x+c))-1/3*(6*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/d/(a+b*sin(d*x+c))+5/12*b*cot(d*x+c)*csc(d*x+c)^2/a^2/d/(a+b*sin(d*x+c))-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6/(a+b*sin(d*x+c))^2,x,10,-2*(a^2-6*b^2)*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^7/d+1/4*b*(15*a^4-40*a^2*b^2+24*b^4)*arctanh(cos(d*x+c))/a^7/d-1/15*(38*a^4-135*a^2*b^2+90*b^4)*cot(d*x+c)/a^6/d+1/4*(4*a^4-17*a^2*b^2+12*b^4)*cot(d*x+c)*csc(d*x+c)/a^5/b/d-1/30*(15*a^4-82*a^2*b^2+60*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^4/b^2/d-1/2*cot(d*x+c)*csc(d*x+c)/b/d/(a+b*sin(d*x+c))+1/6*a*cot(d*x+c)*csc(d*x+c)^2/b^2/d/(a+b*sin(d*x+c))+1/6*(2*a^4-12*a^2*b^2+9*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^3/b^2/d/(a+b*sin(d*x+c))+3/10*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d/(a+b*sin(d*x+c))-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^2,x,11,2*b*(2*a^2-7*b^2)*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^8/d+1/16*(5*a^6-90*a^4*b^2+200*a^2*b^4-112*b^6)*arctanh(cos(d*x+c))/a^8/d+1/15*b*(61*a^4-170*a^2*b^2+105*b^4)*cot(d*x+c)/a^7/d-1/16*(27*a^4-86*a^2*b^2+56*b^4)*cot(d*x+c)*csc(d*x+c)/a^6/d+1/15*(15*a^4-52*a^2*b^2+35*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^5/b/d-1/24*(16*a^4-61*a^2*b^2+42*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^4/b^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2/b/d/(a+b*sin(d*x+c))+1/6*a*cot(d*x+c)*csc(d*x+c)^3/b^2/d/(a+b*sin(d*x+c))+1/10*(5*a^4-20*a^2*b^2+14*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^3/b^2/d/(a+b*sin(d*x+c))+7/30*b*cot(d*x+c)*csc(d*x+c)^4/a^2/d/(a+b*sin(d*x+c))-1/6*cot(d*x+c)*csc(d*x+c)^5/a/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x,11,-1/16*(448*a^6-600*a^4*b^2+180*a^2*b^4-5*b^6)*x/b^9+a*sqrt(a^2-b^2)*(56*a^4-47*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^9/d-1/30*a*(840*a^4-985*a^2*b^2+213*b^4)*cos(d*x+c)/b^8/d+1/16*(224*a^4-244*a^2*b^2+43*b^4)*cos(d*x+c)*sin(d*x+c)/b^7/d-1/30*(280*a^4-291*a^2*b^2+45*b^4)*cos(d*x+c)*sin(d*x+c)^2/a/b^6/d+1/24*(168*a^4-169*a^2*b^2+24*b^4)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^5/d+1/4*cos(d*x+c)*sin(d*x+c)^4/a/d/(a+b*sin(d*x+c))^2-1/10*b*cos(d*x+c)*sin(d*x+c)^5/a^2/d/(a+b*sin(d*x+c))^2-1/60*(56*a^4-60*a^2*b^2+9*b^4)*cos(d*x+c)*sin(d*x+c)^5/a^2/b^3/d/(a+b*sin(d*x+c))^2-4/15*a*cos(d*x+c)*sin(d*x+c)^6/b^2/d/(a+b*sin(d*x+c))^2+1/6*cos(d*x+c)*sin(d*x+c)^7/b/d/(a+b*sin(d*x+c))^2-1/20*(112*a^4-110*a^2*b^2+15*b^4)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x,10,1/8*a*(168*a^4-200*a^2*b^2+45*b^4)*x/b^8-sqrt(a^2-b^2)*(42*a^4-29*a^2*b^2+2*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^8/d+1/30*(630*a^4-645*a^2*b^2+91*b^4)*cos(d*x+c)/b^7/d-1/8*(84*a^4-79*a^2*b^2+8*b^4)*cos(d*x+c)*sin(d*x+c)/a/b^6/d+1/30*(210*a^4-187*a^2*b^2+15*b^4)*cos(d*x+c)*sin(d*x+c)^2/a^2/b^5/d+1/3*cos(d*x+c)*sin(d*x+c)^3/a/d/(a+b*sin(d*x+c))^2-1/12*b*cos(d*x+c)*sin(d*x+c)^4/a^2/d/(a+b*sin(d*x+c))^2-1/60*(63*a^4-60*a^2*b^2+5*b^4)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^3/d/(a+b*sin(d*x+c))^2-7/20*a*cos(d*x+c)*sin(d*x+c)^5/b^2/d/(a+b*sin(d*x+c))^2+1/5*cos(d*x+c)*sin(d*x+c)^6/b/d/(a+b*sin(d*x+c))^2-1/12*(63*a^4-54*a^2*b^2+4*b^4)*cos(d*x+c)*sin(d*x+c)^3/a^2/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^3,x,7,-15/8*(8*a^4-8*a^2*b^2+b^4)*x/b^7+15*a*(2*a^4-3*a^2*b^2+b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/sqrt(a^2-b^2)/d+1/4*cos(d*x+c)^5*(3*a+b*sin(d*x+c))/b^2/d/(a+b*sin(d*x+c))^2+5/4*cos(d*x+c)^3*(4*a^2-b^2+a*b*sin(d*x+c))/b^4/d/(a+b*sin(d*x+c))-15/8*cos(d*x+c)*(4*a*(2*a^2-b^2)-b*(4*a^2-b^2)*sin(d*x+c))/b^6/d,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+b*sin(d*x+c))^3,x,20,-1/2*x/b^3-3*(2*a^2-b^2)*x/b^5+sqrt(a^2-b^2)*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b^5/d-2*sqrt(a^2-b^2)*(5*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b^5/d+2*(10*a^6-9*a^4*b^2-b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^5/sqrt(a^2-b^2)/d-arctanh(cos(d*x+c))/a^3/d-3*a*cos(d*x+c)/b^4/d+1/2*cos(d*x+c)*sin(d*x+c)/b^3/d+1/2*(a^2-b^2)^2*cos(d*x+c)/a/b^4/d/(a+b*sin(d*x+c))^2+3/2*(a^2-b^2)*cos(d*x+c)/b^4/d/(a+b*sin(d*x+c))-(a^2-b^2)*(5*a^2+b^2)*cos(d*x+c)/a^2/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x,20,3*a*x/b^4+3*sqrt(a^2-b^2)*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^4/d-6*(2*a^6-a^4*b^2-b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/b^4/sqrt(a^2-b^2)/d+3*b*arctanh(cos(d*x+c))/a^4/d+cos(d*x+c)/b^3/d-cot(d*x+c)/a^3/d-1/2*(a^2-b^2)^2*cos(d*x+c)/a^2/b^3/d/(a+b*sin(d*x+c))^2-3/2*(a^2-b^2)*cos(d*x+c)/a/b^3/d/(a+b*sin(d*x+c))+2*(a^2-b^2)*(2*a^2+b^2)*cos(d*x+c)/a^3/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x,21,-x/b^3-6*sqrt(a^2-b^2)*(a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^3/d+sqrt(a^2-b^2)*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^3/d+6*(a^6+a^2*b^4-2*b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/b^3/sqrt(a^2-b^2)/d-1/2*arctanh(cos(d*x+c))/a^3/d+3*(a^2-2*b^2)*arctanh(cos(d*x+c))/a^5/d+3*b*cot(d*x+c)/a^4/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d+1/2*(a^2-b^2)^2*cos(d*x+c)/a^3/b^2/d/(a+b*sin(d*x+c))^2+3/2*(a^2-b^2)*cos(d*x+c)/a^2/b^2/d/(a+b*sin(d*x+c))-3*(a^4-b^4)*cos(d*x+c)/a^4/b^2/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x,9,5*(a^2-4*b^2)*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d-5/2*b*(3*a^2-4*b^2)*arctanh(cos(d*x+c))/a^6/d+1/6*(3*a^4+35*a^2*b^2-60*b^4)*cot(d*x+c)/a^5/b^2/d-cos(d*x+c)/b/d/(a+b*sin(d*x+c))^2-1/2*a*cot(d*x+c)/b^2/d/(a+b*sin(d*x+c))^2-1/3*(3*a^2-5*b^2)*cot(d*x+c)/a^3/d/(a+b*sin(d*x+c))^2+5/6*b*cot(d*x+c)*csc(d*x+c)/a^2/d/(a+b*sin(d*x+c))^2-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d/(a+b*sin(d*x+c))^2-5/2*(a^2-2*b^2)*cot(d*x+c)/a^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*cot(d*x+c)^5/(a+b*sin(d*x+c))^3,x,10,-15*b*(a^2-2*b^2)*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^7/d-15/8*(a^4-8*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^7/d+1/2*(a^4-25*a^2*b^2+30*b^4)*cot(d*x+c)/a^6/b/d+15/8*(3*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^5/d-1/2*cot(d*x+c)/b/d/(a+b*sin(d*x+c))^2-1/4*(4*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/d/(a+b*sin(d*x+c))^2+1/2*b*cot(d*x+c)*csc(d*x+c)^2/a^2/d/(a+b*sin(d*x+c))^2-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d/(a+b*sin(d*x+c))^2-1/2*(7*a^2-10*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6/(a+b*sin(d*x+c))^3,x,11,-sqrt(a^2-b^2)*(2*a^4-29*a^2*b^2+42*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^8/d+1/8*b*(45*a^4-200*a^2*b^2+168*b^4)*arctanh(cos(d*x+c))/a^8/d-1/30*(91*a^4-645*a^2*b^2+630*b^4)*cot(d*x+c)/a^7/d+1/8*(8*a^4-79*a^2*b^2+84*b^4)*cot(d*x+c)*csc(d*x+c)/a^6/b/d-1/30*(15*a^4-187*a^2*b^2+210*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^5/b^2/d-1/3*cot(d*x+c)*csc(d*x+c)/b/d/(a+b*sin(d*x+c))^2+1/12*a*cot(d*x+c)*csc(d*x+c)^2/b^2/d/(a+b*sin(d*x+c))^2+1/60*(5*a^4-60*a^2*b^2+63*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^3/b^2/d/(a+b*sin(d*x+c))^2+7/20*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d/(a+b*sin(d*x+c))^2-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d/(a+b*sin(d*x+c))^2+1/12*(4*a^4-54*a^2*b^2+63*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^4/b^2/d/(a+b*sin(d*x+c)),1],
[cot(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x,13,-3*b^2*sqrt(a^2-b^2)*(4*a^4-23*a^2*b^2+24*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^10/d-3/16*b*(5*a^6-100*a^4*b^2+280*a^2*b^4-192*b^6)*arctanh(cos(d*x+c))/a^10/d+1/70*(10*a^6-889*a^4*b^2+3255*a^2*b^4-2520*b^6)*cot(d*x+c)/a^9/d+3/16*b*(27*a^4-116*a^2*b^2+96*b^4)*cot(d*x+c)*csc(d*x+c)/a^8/d-1/70*(205*a^4-973*a^2*b^2+840*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^7/d+1/8*(16*a^4-81*a^2*b^2+72*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^6/b/d-3/70*(35*a^4-185*a^2*b^2+168*b^4)*cot(d*x+c)*csc(d*x+c)^4/a^5/b^2/d-1/5*cot(d*x+c)*csc(d*x+c)^3/b/d/(a+b*sin(d*x+c))^2+1/10*a*cot(d*x+c)*csc(d*x+c)^4/b^2/d/(a+b*sin(d*x+c))^2+1/35*(7*a^4-35*a^2*b^2+30*b^4)*cot(d*x+c)*csc(d*x+c)^4/a^3/b^2/d/(a+b*sin(d*x+c))^2+3/14*b*cot(d*x+c)*csc(d*x+c)^5/a^2/d/(a+b*sin(d*x+c))^2-1/7*cot(d*x+c)*csc(d*x+c)^6/a/d/(a+b*sin(d*x+c))^2+1/10*(12*a^4-65*a^2*b^2+60*b^4)*cot(d*x+c)*csc(d*x+c)^4/a^4/b^2/d/(a+b*sin(d*x+c)),1],
[cos(f*x+e)^6/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e))^(13/2),x,8,2/11*cos(f*x+e)^5*sqrt(d*sin(f*x+e))/a/d/f/(a+b*sin(f*x+e))^(11/2)-20/99*(a^2-b^2)*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^2/b^2/d/f/(a+b*sin(f*x+e))^(9/2)+80/693*(3*a^2+2*b^2)*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^3/b^2/d/f/(a+b*sin(f*x+e))^(7/2)-4/231*(5*a^4-17*a^2*b^2+16*b^4)*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^4/b^2/(a^2-b^2)/d/f/(a+b*sin(f*x+e))^(5/2)-8/693*(5*a^6-22*a^4*b^2+65*a^2*b^4-32*b^6)*cos(f*x+e)*sqrt(d*sin(f*x+e))/a^5/b^2/(a^2-b^2)^2/d/f/(a+b*sin(f*x+e))^(3/2)+16/693*b*(93*a^4-93*a^2*b^2+32*b^4)*cos(f*x+e)/a^5/(a^2-b^2)^3/f/sqrt(d*sin(f*x+e))/sqrt(a+b*sin(f*x+e))-16/693*b*(93*a^4-93*a^2*b^2+32*b^4)*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*EllipticE(sin(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e)))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^7/(a-b)^2/(a+b)^(5/2)/sqrt(d)/f-16/693*(45*a^4-48*a^3*b-69*a^2*b^2+24*a*b^3+32*b^4)*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/a^6/(a-b)^2/(a+b)^(5/2)/sqrt(d)/f,1],
[(a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(5/2)/sqrt(d*sin(f*x+e)),x,8,2/3*(a^2+b^2)*sqrt(d*sin(f*x+e))/d/f/g/(g*cos(f*x+e))^(3/2)+4/3*a*b*(d*sin(f*x+e))^(3/2)/d^2/f/g/(g*cos(f*x+e))^(3/2)+1/3*(2*a^2-b^2)*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/f/g^2/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(7/2)/sqrt(d*sin(f*x+e)),x,6,8/5*a^2*sqrt(d*sin(f*x+e))/d/f/g^3/sqrt(g*cos(f*x+e))+8/5*a*b*(d*sin(f*x+e))^(3/2)/d^2/f/g^3/sqrt(g*cos(f*x+e))+2/5*sqrt(d*sin(f*x+e))*(a+b*sin(f*x+e))^2/d/f/g/(g*cos(f*x+e))^(5/2)-8/5*a*b*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/d/f/g^4/sqrt(sin(2*f*x+2*e)),1],
[cos(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,4,-a^3*ln(a+b*sin(d*x+c))/b^4/d+a^2*sin(d*x+c)/b^3/d-1/2*a*sin(d*x+c)^2/b^2/d+1/3*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,4,a^2*ln(a+b*sin(d*x+c))/b^3/d-a*sin(d*x+c)/b^2/d+1/2*sin(d*x+c)^2/b/d,1],
[cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x,4,-a*ln(a+b*sin(d*x+c))/b^2/d+sin(d*x+c)/b/d,1],
[cot(d*x+c)/(a+b*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-ln(a+b*sin(d*x+c))/a/d,1],
[cot(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-b*ln(sin(d*x+c))/a^2/d+b*ln(a+b*sin(d*x+c))/a^2/d,1],
[cot(d*x+c)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x,4,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d+b^2*ln(sin(d*x+c))/a^3/d-b^2*ln(a+b*sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x,10,1/8*a*(8*a^4-4*a^2*b^2-b^4)*x/b^6-2*a^4*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/d+1/15*(15*a^4-5*a^2*b^2-2*b^4)*cos(d*x+c)/b^5/d-1/8*a*(4*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/b^4/d+1/15*(5*a^2-b^2)*cos(d*x+c)*sin(d*x+c)^2/b^3/d-1/4*a*cos(d*x+c)*sin(d*x+c)^3/b^2/d+1/5*cos(d*x+c)*sin(d*x+c)^4/b/d,1],
[cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,9,-1/8*(8*a^4-4*a^2*b^2-b^4)*x/b^5+2*a^3*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/d-1/3*a*(3*a^2-b^2)*cos(d*x+c)/b^4/d+1/8*(4*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/b^3/d-1/3*a*cos(d*x+c)*sin(d*x+c)^2/b^2/d+1/4*cos(d*x+c)*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,8,1/2*a*(2*a^2-b^2)*x/b^4-2*a^2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/d+1/3*(3*a^2-b^2)*cos(d*x+c)/b^3/d-1/2*a*cos(d*x+c)*sin(d*x+c)/b^2/d+1/3*cos(d*x+c)*sin(d*x+c)^2/b/d,1],
[cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x,5,-1/2*(2*a^2-b^2)*x/b^3+2*a*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^3/d-1/2*cos(d*x+c)*(2*a-b*sin(d*x+c))/b^2/d,1],
[cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x,6,-x/b+2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b/d-arctanh(cos(d*x+c))/a/d,1],
[cot(d*x+c)^2/(a+b*sin(d*x+c)),x,7,-2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/d+b*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x,8,2*b*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/d+1/2*(a^2-2*b^2)*arctanh(cos(d*x+c))/a^3/d+b*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x,9,-2*b^2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/d-1/2*b*(a^2-2*b^2)*arctanh(cos(d*x+c))/a^4/d+1/3*(a^2-3*b^2)*cot(d*x+c)/a^3/d+1/2*b*cot(d*x+c)*csc(d*x+c)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c)),x,10,2*b^3*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/d+1/8*(a^4+4*a^2*b^2-8*b^4)*arctanh(cos(d*x+c))/a^5/d-1/3*b*(a^2-3*b^2)*cot(d*x+c)/a^4/d+1/8*(a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/d+1/3*b*cot(d*x+c)*csc(d*x+c)^2/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c)),x,11,-2*b^4*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d-1/8*b*(a^4+4*a^2*b^2-8*b^4)*arctanh(cos(d*x+c))/a^6/d+1/15*(2*a^4+5*a^2*b^2-15*b^4)*cot(d*x+c)/a^5/d-1/8*b*(a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d+1/15*(a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^3/d+1/4*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d,1],
[cos(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,4,a^3*(a^2-b^2)*ln(a+b*sin(d*x+c))/b^6/d-a^2*(a^2-b^2)*sin(d*x+c)/b^5/d+1/2*a*(a^2-b^2)*sin(d*x+c)^2/b^4/d-1/3*(a^2-b^2)*sin(d*x+c)^3/b^3/d+1/4*a*sin(d*x+c)^4/b^2/d-1/5*sin(d*x+c)^5/b/d,1],
[cos(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,4,-a^2*(a^2-b^2)*ln(a+b*sin(d*x+c))/b^5/d+a*(a^2-b^2)*sin(d*x+c)/b^4/d-1/2*(a^2-b^2)*sin(d*x+c)^2/b^3/d+1/3*a*sin(d*x+c)^3/b^2/d-1/4*sin(d*x+c)^4/b/d,1],
[cos(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x,4,a*(a^2-b^2)*ln(a+b*sin(d*x+c))/b^4/d-(a^2-b^2)*sin(d*x+c)/b^3/d+1/2*a*sin(d*x+c)^2/b^2/d-1/3*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d+(a^2-b^2)*ln(a+b*sin(d*x+c))/a/b^2/d-sin(d*x+c)/b/d,1],
[cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-b*ln(sin(d*x+c))/a^2/d-(1-b^2/a^2)*ln(a+b*sin(d*x+c))/b/d,1],
[cot(d*x+c)^3/(a+b*sin(d*x+c)),x,3,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-(a^2-b^2)*ln(sin(d*x+c))/a^3/d+(a^2-b^2)*ln(a+b*sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,9,1/16*(16*a^6-24*a^4*b^2+6*a^2*b^4+b^6)*x/b^7-2*a^3*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/d+1/15*a*(15*a^4-20*a^2*b^2+3*b^4)*cos(d*x+c)/b^6/d-1/16*(8*a^4-10*a^2*b^2+b^4)*cos(d*x+c)*sin(d*x+c)/b^5/d+1/15*a*(5*a^2-6*b^2)*cos(d*x+c)*sin(d*x+c)^2/b^4/d-1/24*(6*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)^3/b^3/d+1/5*a*cos(d*x+c)*sin(d*x+c)^4/b^2/d-1/6*cos(d*x+c)*sin(d*x+c)^5/b/d,1],
[cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,8,-1/8*a*(8*a^4-12*a^2*b^2+3*b^4)*x/b^6+2*a^2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/d-1/15*(15*a^4-20*a^2*b^2+3*b^4)*cos(d*x+c)/b^5/d+1/8*a*(4*a^2-5*b^2)*cos(d*x+c)*sin(d*x+c)/b^4/d-1/15*(5*a^2-6*b^2)*cos(d*x+c)*sin(d*x+c)^2/b^3/d+1/4*a*cos(d*x+c)*sin(d*x+c)^3/b^2/d-1/5*cos(d*x+c)*sin(d*x+c)^4/b/d,1],
[cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x,6,1/8*(8*a^4-12*a^2*b^2+3*b^4)*x/b^5-2*a*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^5/d-1/12*cos(d*x+c)^3*(4*a-3*b*sin(d*x+c))/b^2/d+1/8*cos(d*x+c)*(8*a*(a^2-b^2)-b*(4*a^2-3*b^2)*sin(d*x+c))/b^4/d,1],
[cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x,6,1/2*(2*a^2-3*b^2)*x/b^3-2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b^3/d-arctanh(cos(d*x+c))/a/d+a*cos(d*x+c)/b^2/d-1/2*cos(d*x+c)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x,6,-a*x/b^2+2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^2/d+b*arctanh(cos(d*x+c))/a^2/d-cos(d*x+c)/b/d-cot(d*x+c)/a/d,1],
[cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c)),x,6,x/b-2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b/d+1/2*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/a^3/d+b*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[cot(d*x+c)^4/(a+b*sin(d*x+c)),x,7,2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/d-1/2*b*(3*a^2-2*b^2)*arctanh(cos(d*x+c))/a^4/d+1/3*(4*a^2-3*b^2)*cot(d*x+c)/a^3/d+1/2*b*cot(d*x+c)*csc(d*x+c)/a^2/d-1/3*cot(d*x+c)*csc(d*x+c)^2/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c)),x,8,-2*b*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/d-1/8*(3*a^4-12*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^5/d-1/3*b*(4*a^2-3*b^2)*cot(d*x+c)/a^4/d+1/8*(5*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/d+1/3*b*cot(d*x+c)*csc(d*x+c)^2/a^2/d-1/4*cot(d*x+c)*csc(d*x+c)^3/a/d,1],
[cot(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c)),x,9,2*b^2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d+1/8*b*(3*a^4-12*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^6/d-1/15*(3*a^4-20*a^2*b^2+15*b^4)*cot(d*x+c)/a^5/d-1/8*b*(5*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d+1/15*(6*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^3/d+1/4*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d,1],
[cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,4,-a^3*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/b^8/d+a^2*(a^2-b^2)^2*sin(d*x+c)/b^7/d-1/2*a*(a^2-b^2)^2*sin(d*x+c)^2/b^6/d+1/3*(a^2-b^2)^2*sin(d*x+c)^3/b^5/d-1/4*a*(a^2-2*b^2)*sin(d*x+c)^4/b^4/d+1/5*(a^2-2*b^2)*sin(d*x+c)^5/b^3/d-1/6*a*sin(d*x+c)^6/b^2/d+1/7*sin(d*x+c)^7/b/d,1],
[cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,4,a^2*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/b^7/d-a*(a^2-b^2)^2*sin(d*x+c)/b^6/d+1/2*(a^2-b^2)^2*sin(d*x+c)^2/b^5/d-1/3*a*(a^2-2*b^2)*sin(d*x+c)^3/b^4/d+1/4*(a^2-2*b^2)*sin(d*x+c)^4/b^3/d-1/5*a*sin(d*x+c)^5/b^2/d+1/6*sin(d*x+c)^6/b/d,1],
[cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x,4,-a*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/b^6/d+(a^2-b^2)^2*sin(d*x+c)/b^5/d-1/2*a*(a^2-2*b^2)*sin(d*x+c)^2/b^4/d+1/3*(a^2-2*b^2)*sin(d*x+c)^3/b^3/d-1/4*a*sin(d*x+c)^4/b^2/d+1/5*sin(d*x+c)^5/b/d,1],
[cos(d*x+c)^4*cot(d*x+c)/(a+b*sin(d*x+c)),x,4,ln(sin(d*x+c))/a/d-(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a/b^4/d+(a^2-2*b^2)*sin(d*x+c)/b^3/d-1/2*a*sin(d*x+c)^2/b^2/d+1/3*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-b*ln(sin(d*x+c))/a^2/d+(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^2/b^3/d-a*sin(d*x+c)/b^2/d+1/2*sin(d*x+c)^2/b/d,1],
[cos(d*x+c)^2*cot(d*x+c)^3/(a+b*sin(d*x+c)),x,4,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-(2*a^2-b^2)*ln(sin(d*x+c))/a^3/d-(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^3/b^2/d+sin(d*x+c)/b/d,1],
[cos(d*x+c)*cot(d*x+c)^4/(a+b*sin(d*x+c)),x,4,(2*a^2-b^2)*csc(d*x+c)/a^3/d+1/2*b*csc(d*x+c)^2/a^2/d-1/3*csc(d*x+c)^3/a/d+b*(2*a^2-b^2)*ln(sin(d*x+c))/a^4/d+(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^4/b/d,1],
[cot(d*x+c)^5/(a+b*sin(d*x+c)),x,3,-b*(2*a^2-b^2)*csc(d*x+c)/a^4/d+1/2*(2*a^2-b^2)*csc(d*x+c)^2/a^3/d+1/3*b*csc(d*x+c)^3/a^2/d-1/4*csc(d*x+c)^4/a/d+(a^2-b^2)^2*ln(sin(d*x+c))/a^5/d-(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^5/d,1],
[cot(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c)),x,4,-(a^2-b^2)^2*csc(d*x+c)/a^5/d-1/2*b*(2*a^2-b^2)*csc(d*x+c)^2/a^4/d+1/3*(2*a^2-b^2)*csc(d*x+c)^3/a^3/d+1/4*b*csc(d*x+c)^4/a^2/d-1/5*csc(d*x+c)^5/a/d-b*(a^2-b^2)^2*ln(sin(d*x+c))/a^6/d+b*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^6/d,1],
[cot(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c)),x,4,b*(a^2-b^2)^2*csc(d*x+c)/a^6/d-1/2*(a^2-b^2)^2*csc(d*x+c)^2/a^5/d-1/3*b*(2*a^2-b^2)*csc(d*x+c)^3/a^4/d+1/4*(2*a^2-b^2)*csc(d*x+c)^4/a^3/d+1/5*b*csc(d*x+c)^5/a^2/d-1/6*csc(d*x+c)^6/a/d+b^2*(a^2-b^2)^2*ln(sin(d*x+c))/a^7/d-b^2*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/a^7/d,1],
[cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c)),x,11,-1/128*(128*a^8-320*a^6*b^2+240*a^4*b^4-40*a^2*b^6-5*b^8)*x/b^9+2*a^3*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^9/d-1/105*a*(105*a^6-245*a^4*b^2+161*a^2*b^4-15*b^6)*cos(d*x+c)/b^8/d+1/128*(64*a^6-144*a^4*b^2+88*a^2*b^4-5*b^6)*cos(d*x+c)*sin(d*x+c)/b^7/d-1/105*a*(35*a^4-77*a^2*b^2+45*b^4)*cos(d*x+c)*sin(d*x+c)^2/b^6/d+1/192*(48*a^4-104*a^2*b^2+59*b^4)*cos(d*x+c)*sin(d*x+c)^3/b^5/d+1/4*cos(d*x+c)*sin(d*x+c)^4/a/d-1/140*(28*a^4-60*a^2*b^2+35*b^4)*cos(d*x+c)*sin(d*x+c)^4/a/b^4/d-1/5*b*cos(d*x+c)*sin(d*x+c)^5/a^2/d+1/240*(40*a^4-85*a^2*b^2+48*b^4)*cos(d*x+c)*sin(d*x+c)^5/a^2/b^3/d-1/7*a*cos(d*x+c)*sin(d*x+c)^6/b^2/d+1/8*cos(d*x+c)*sin(d*x+c)^7/b/d,1],
[cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c)),x,10,1/16*a*(16*a^6-40*a^4*b^2+30*a^2*b^4-5*b^6)*x/b^8-2*a^2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^8/d+1/105*(105*a^6-245*a^4*b^2+161*a^2*b^4-15*b^6)*cos(d*x+c)/b^7/d-1/16*a*(8*a^4-18*a^2*b^2+11*b^4)*cos(d*x+c)*sin(d*x+c)/b^6/d+1/105*(35*a^4-77*a^2*b^2+45*b^4)*cos(d*x+c)*sin(d*x+c)^2/b^5/d+1/3*cos(d*x+c)*sin(d*x+c)^3/a/d-1/24*(6*a^4-13*a^2*b^2+8*b^4)*cos(d*x+c)*sin(d*x+c)^3/a/b^4/d-1/4*b*cos(d*x+c)*sin(d*x+c)^4/a^2/d+1/140*(28*a^4-60*a^2*b^2+35*b^4)*cos(d*x+c)*sin(d*x+c)^4/a^2/b^3/d-1/6*a*cos(d*x+c)*sin(d*x+c)^5/b^2/d+1/7*cos(d*x+c)*sin(d*x+c)^6/b/d,1],
[cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c)),x,7,-1/16*(16*a^6-40*a^4*b^2+30*a^2*b^4-5*b^6)*x/b^7+2*a*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^7/d-1/30*cos(d*x+c)^5*(6*a-5*b*sin(d*x+c))/b^2/d+1/24*cos(d*x+c)^3*(8*a*(a^2-b^2)-b*(6*a^2-5*b^2)*sin(d*x+c))/b^4/d-1/16*cos(d*x+c)*(16*a*(a^2-b^2)^2-b*(8*a^4-14*a^2*b^2+5*b^4)*sin(d*x+c))/b^6/d,1],
[cos(d*x+c)^5*cot(d*x+c)/(a+b*sin(d*x+c)),x,14,-3/8*x/b-1/2*(a^2-3*b^2)*x/b^3-(a^4-3*a^2*b^2+3*b^4)*x/b^5+2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/b^5/d-arctanh(cos(d*x+c))/a/d-a*cos(d*x+c)/b^2/d-a*(a^2-3*b^2)*cos(d*x+c)/b^4/d+1/3*a*cos(d*x+c)^3/b^2/d+3/8*cos(d*x+c)*sin(d*x+c)/b/d+1/2*(a^2-3*b^2)*cos(d*x+c)*sin(d*x+c)/b^3/d+1/4*cos(d*x+c)*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)^4*cot(d*x+c)^2/(a+b*sin(d*x+c)),x,13,1/2*a*x/b^2+a*(a^2-3*b^2)*x/b^4-2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/b^4/d+b*arctanh(cos(d*x+c))/a^2/d+cos(d*x+c)/b/d+(a^2-3*b^2)*cos(d*x+c)/b^3/d-1/3*cos(d*x+c)^3/b/d-cot(d*x+c)/a/d-1/2*a*cos(d*x+c)*sin(d*x+c)/b^2/d,1],
[cos(d*x+c)^3*cot(d*x+c)^3/(a+b*sin(d*x+c)),x,6,-1/2*(2*a^2-5*b^2)*x/b^3+2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/b^3/d+1/2*(5*a^2-2*b^2)*arctanh(cos(d*x+c))/a^3/d-a*cos(d*x+c)/b^2/d+b*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d+1/2*cos(d*x+c)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*cot(d*x+c)^4/(a+b*sin(d*x+c)),x,13,a*x/b^2-2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/b^2/d+1/2*b*arctanh(cos(d*x+c))/a^2/d-b*(3*a^2-b^2)*arctanh(cos(d*x+c))/a^4/d+cos(d*x+c)/b/d-cot(d*x+c)/a/d+(3*a^2-b^2)*cot(d*x+c)/a^3/d-1/3*cot(d*x+c)^3/a/d+1/2*b*cot(d*x+c)*csc(d*x+c)/a^2/d,1],
[cos(d*x+c)*cot(d*x+c)^5/(a+b*sin(d*x+c)),x,15,-x/b+2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/b/d-1/8*(15*a^4-20*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^5/d+b*(-2*a^2+b^2)*cot(d*x+c)/a^4/d+1/3*b*cot(d*x+c)^3/a^2/d+1/8*(7*a^2-4*b^2)*cot(d*x+c)*csc(d*x+c)/a^3/d-1/4*cot(d*x+c)^3*csc(d*x+c)/a/d,1],
[cot(d*x+c)^6/(a+b*sin(d*x+c)),x,9,-2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^6/d+1/8*b*(15*a^4-20*a^2*b^2+8*b^4)*arctanh(cos(d*x+c))/a^6/d-1/15*(23*a^4-35*a^2*b^2+15*b^4)*cot(d*x+c)/a^5/d+1/8*b*(-9*a^2+4*b^2)*cot(d*x+c)*csc(d*x+c)/a^4/d+1/15*(11*a^2-5*b^2)*cot(d*x+c)*csc(d*x+c)^2/a^3/d+1/4*b*cot(d*x+c)*csc(d*x+c)^3/a^2/d-1/5*cot(d*x+c)*csc(d*x+c)^4/a/d,1],
[cot(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c)),x,10,2*b*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^7/d+1/16*(5*a^6-30*a^4*b^2+40*a^2*b^4-16*b^6)*arctanh(cos(d*x+c))/a^7/d+1/15*b*(23*a^4-35*a^2*b^2+15*b^4)*cot(d*x+c)/a^6/d-1/16*(11*a^4-18*a^2*b^2+8*b^4)*cot(d*x+c)*csc(d*x+c)/a^5/d-1/2*cot(d*x+c)*csc(d*x+c)^2/b/d+1/30*(15*a^4-22*a^2*b^2+10*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^4/b/d+1/3*a*cot(d*x+c)*csc(d*x+c)^3/b^2/d-1/24*(8*a^4-13*a^2*b^2+6*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^3/b^2/d+1/5*b*cot(d*x+c)*csc(d*x+c)^4/a^2/d-1/6*cot(d*x+c)*csc(d*x+c)^5/a/d,1],
[cot(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c)),x,11,-2*b^2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^8/d-1/16*b*(5*a^6-30*a^4*b^2+40*a^2*b^4-16*b^6)*arctanh(cos(d*x+c))/a^8/d+1/105*(15*a^6-161*a^4*b^2+245*a^2*b^4-105*b^6)*cot(d*x+c)/a^7/d+1/16*b*(11*a^4-18*a^2*b^2+8*b^4)*cot(d*x+c)*csc(d*x+c)/a^6/d-1/105*(45*a^4-77*a^2*b^2+35*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^5/d-1/3*cot(d*x+c)*csc(d*x+c)^3/b/d+1/24*(8*a^4-13*a^2*b^2+6*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^4/b/d+1/4*a*cot(d*x+c)*csc(d*x+c)^4/b^2/d-1/140*(35*a^4-60*a^2*b^2+28*b^4)*cot(d*x+c)*csc(d*x+c)^4/a^3/b^2/d+1/6*b*cot(d*x+c)*csc(d*x+c)^5/a^2/d-1/7*cot(d*x+c)*csc(d*x+c)^6/a/d,1],
[cot(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c)),x,12,2*b^3*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^9/d+1/128*(5*a^8+40*a^6*b^2-240*a^4*b^4+320*a^2*b^6-128*b^8)*arctanh(cos(d*x+c))/a^9/d-1/105*b*(15*a^6-161*a^4*b^2+245*a^2*b^4-105*b^6)*cot(d*x+c)/a^8/d+1/128*(5*a^6-88*a^4*b^2+144*a^2*b^4-64*b^6)*cot(d*x+c)*csc(d*x+c)/a^7/d+1/105*b*(45*a^4-77*a^2*b^2+35*b^4)*cot(d*x+c)*csc(d*x+c)^2/a^6/d-1/192*(59*a^4-104*a^2*b^2+48*b^4)*cot(d*x+c)*csc(d*x+c)^3/a^5/d-1/4*cot(d*x+c)*csc(d*x+c)^4/b/d+1/140*(35*a^4-60*a^2*b^2+28*b^4)*cot(d*x+c)*csc(d*x+c)^4/a^4/b/d+1/5*a*cot(d*x+c)*csc(d*x+c)^5/b^2/d-1/240*(48*a^4-85*a^2*b^2+40*b^4)*cot(d*x+c)*csc(d*x+c)^5/a^3/b^2/d+1/7*b*cot(d*x+c)*csc(d*x+c)^6/a^2/d-1/8*cot(d*x+c)*csc(d*x+c)^7/a/d,1],
[sin(d*x+c)^2*tan(d*x+c)/(a+b*sin(d*x+c)),x,4,-1/2*ln(1-sin(d*x+c))/(a+b)/d-1/2*ln(1+sin(d*x+c))/(a-b)/d+a^3*ln(a+b*sin(d*x+c))/b^2/(a^2-b^2)/d-sin(d*x+c)/b/d,1],
[sin(d*x+c)*tan(d*x+c)/(a+b*sin(d*x+c)),x,4,-1/2*ln(1-sin(d*x+c))/(a+b)/d+1/2*ln(1+sin(d*x+c))/(a-b)/d-a^2*ln(a+b*sin(d*x+c))/b/(a^2-b^2)/d,1],
[tan(d*x+c)/(a+b*sin(d*x+c)),x,3,-1/2*ln(1-sin(d*x+c))/(a+b)/d-1/2*ln(1+sin(d*x+c))/(a-b)/d+a*ln(a+b*sin(d*x+c))/(a^2-b^2)/d,1],
[csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x,4,-1/2*ln(1-sin(d*x+c))/(a+b)/d+ln(sin(d*x+c))/a/d-1/2*ln(1+sin(d*x+c))/(a-b)/d+b^2*ln(a+b*sin(d*x+c))/a/(a^2-b^2)/d,1],
[csc(d*x+c)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-1/2*ln(1-sin(d*x+c))/(a+b)/d-b*ln(sin(d*x+c))/a^2/d+1/2*ln(1+sin(d*x+c))/(a-b)/d-b^3*ln(a+b*sin(d*x+c))/a^2/(a^2-b^2)/d,1],
[csc(d*x+c)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x,4,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-1/2*ln(1-sin(d*x+c))/(a+b)/d+(a^2+b^2)*ln(sin(d*x+c))/a^3/d-1/2*ln(1+sin(d*x+c))/(a-b)/d+b^4*ln(a+b*sin(d*x+c))/a^3/(a^2-b^2)/d,1],
[sin(d*x+c)^3*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,15,3*b*x/(2*a^2-2*b^2)-1/2*a^2*(2*a^2+b^2)*x/b^3/(a^2-b^2)+2*a^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^3/(a^2-b^2)^(3/2)/d+a*cos(d*x+c)/(a^2-b^2)/d-a^3*cos(d*x+c)/b^2/(a^2-b^2)/d+a*sec(d*x+c)/(a^2-b^2)/d+1/2*a^2*cos(d*x+c)*sin(d*x+c)/b/(a^2-b^2)/d-1/2*b*cos(d*x+c)*sin(d*x+c)/(a^2-b^2)/d-b*tan(d*x+c)/(a^2-b^2)/d,1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,12,-a*x/(a^2-b^2)+a^3*x/b^2/(a^2-b^2)-2*a^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(3/2)/d+a^2*cos(d*x+c)/b/(a^2-b^2)/d-b*cos(d*x+c)/(a^2-b^2)/d-b*sec(d*x+c)/(a^2-b^2)/d+a*tan(d*x+c)/(a^2-b^2)/d,1],
[sin(d*x+c)*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,9,-a^2*x/b/(a^2-b^2)+b*x/(a^2-b^2)+2*a^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b/(a^2-b^2)^(3/2)/d+a*sec(d*x+c)/(a^2-b^2)/d-b*tan(d*x+c)/(a^2-b^2)/d,1],
[tan(d*x+c)^2/(a+b*sin(d*x+c)),x,8,-2*a^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)/d-b*sec(d*x+c)/(a^2-b^2)/d+a*tan(d*x+c)/(a^2-b^2)/d,1],
[sec(d*x+c)*tan(d*x+c)/(a+b*sin(d*x+c)),x,5,2*a*b*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)/d+sec(d*x+c)*(a-b*sin(d*x+c))/(a^2-b^2)/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x,10,2*b^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/(a^2-b^2)^(3/2)/d-arctanh(cos(d*x+c))/a/d+sec(d*x+c)/a/d+b*sec(d*x+c)*(b-a*sin(d*x+c))/a/(a^2-b^2)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x,13,-2*b^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(3/2)/d+b*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a/d-b*sec(d*x+c)/(a^2-b^2)/d+a*tan(d*x+c)/(a^2-b^2)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x,17,2*b^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(3/2)/d-1/2*(3*a^2+2*b^2)*arctanh(cos(d*x+c))/a^3/d+b*cot(d*x+c)/a^2/d+1/2*(3*a^2-b^2)*sec(d*x+c)/a/(a^2-b^2)/d-1/2*csc(d*x+c)^2*sec(d*x+c)/a/d-b*tan(d*x+c)/(a^2-b^2)/d,1],
[tan(d*x+c)^3/(a+b*sin(d*x+c)),x,4,1/4*(2*a+b)*ln(1-sin(d*x+c))/(a+b)^2/d+1/4*(2*a-b)*ln(1+sin(d*x+c))/(a-b)^2/d-a^3*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+1/2*sec(d*x+c)^2*(a/(a^2-b^2)-b*sin(d*x+c)/(a^2-b^2))/d,1],
[sec(d*x+c)*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,5,1/4*a*ln(1-sin(d*x+c))/(a+b)^2/d-1/4*a*ln(1+sin(d*x+c))/(a-b)^2/d+a^2*b*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d-1/2*sec(d*x+c)^2*(b-a*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^2*tan(d*x+c)/(a+b*sin(d*x+c)),x,5,-1/4*b*ln(1-sin(d*x+c))/(a+b)^2/d+1/4*b*ln(1+sin(d*x+c))/(a-b)^2/d-a*b^2*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+1/2*sec(d*x+c)^2*(a-b*sin(d*x+c))/(a^2-b^2)/d,1],
[csc(d*x+c)*sec(d*x+c)^3/(a+b*sin(d*x+c)),x,4,-1/4*(2*a+3*b)*ln(1-sin(d*x+c))/(a+b)^2/d+ln(sin(d*x+c))/a/d-1/4*(2*a-3*b)*ln(1+sin(d*x+c))/(a-b)^2/d-b^4*ln(a+b*sin(d*x+c))/a/(a^2-b^2)^2/d+1/4/(a+b)/d/(1-sin(d*x+c))+1/4/(a-b)/d/(1+sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^3/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-1/4*(3*a+4*b)*ln(1-sin(d*x+c))/(a+b)^2/d-b*ln(sin(d*x+c))/a^2/d+1/4*(3*a-4*b)*ln(1+sin(d*x+c))/(a-b)^2/d+b^5*ln(a+b*sin(d*x+c))/a^2/(a^2-b^2)^2/d+1/4/(a+b)/d/(1-sin(d*x+c))-1/4/(a-b)/d/(1+sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^3/(a+b*sin(d*x+c)),x,4,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-1/4*(4*a+5*b)*ln(1-sin(d*x+c))/(a+b)^2/d+(2*a^2+b^2)*ln(sin(d*x+c))/a^3/d-1/4*(4*a-5*b)*ln(1+sin(d*x+c))/(a-b)^2/d-b^6*ln(a+b*sin(d*x+c))/a^3/(a^2-b^2)^2/d+1/4/(a+b)/d/(1-sin(d*x+c))+1/4/(a-b)/d/(1+sin(d*x+c)),1],
[tan(d*x+c)^4/(a+b*sin(d*x+c)),x,13,2*a^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+a^2*b*sec(d*x+c)/(a^2-b^2)^2/d+b*sec(d*x+c)/(a^2-b^2)/d-1/3*b*sec(d*x+c)^3/(a^2-b^2)/d-a^3*tan(d*x+c)/(a^2-b^2)^2/d+1/3*a*tan(d*x+c)^3/(a^2-b^2)/d,1],
[sec(d*x+c)*tan(d*x+c)^3/(a+b*sin(d*x+c)),x,10,-2*a^3*b*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+1/3*a*sec(d*x+c)^3/(a^2-b^2)/d-a^2*sec(d*x+c)*(a-b*sin(d*x+c))/(a^2-b^2)^2/d-1/3*b*tan(d*x+c)^3/(a^2-b^2)/d,1],
[sec(d*x+c)^2*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,10,2*a^2*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d-1/3*b*sec(d*x+c)^3/(a^2-b^2)/d+a^2*sec(d*x+c)*(b-a*sin(d*x+c))/(a^2-b^2)^2/d+a*tan(d*x+c)/(a^2-b^2)/d+1/3*a*tan(d*x+c)^3/(a^2-b^2)/d,1],
[sec(d*x+c)^3*tan(d*x+c)/(a+b*sin(d*x+c)),x,6,-2*a*b^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+1/3*sec(d*x+c)^3*(a-b*sin(d*x+c))/(a^2-b^2)/d-1/3*sec(d*x+c)*(3*a*b^2-b*(a^2+2*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[csc(d*x+c)*sec(d*x+c)^4/(a+b*sin(d*x+c)),x,12,-2*b^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/(a^2-b^2)^(5/2)/d-arctanh(cos(d*x+c))/a/d+sec(d*x+c)/a/d+1/3*sec(d*x+c)^3/a/d+1/3*b*sec(d*x+c)^3*(b-a*sin(d*x+c))/a/(a^2-b^2)/d-1/3*b*sec(d*x+c)*(3*b^3+a*(2*a^2-5*b^2)*sin(d*x+c))/a/(a^2-b^2)^2/d,1],
[csc(d*x+c)^2*sec(d*x+c)^4/(a+b*sin(d*x+c)),x,15,2*b^6*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(5/2)/d+b*arctanh(cos(d*x+c))/a^2/d-cot(d*x+c)/a/d+b*(-a^2+2*b^2)*sec(d*x+c)/(a^2-b^2)^2/d+1/3*b*sec(d*x+c)^3*(-a+b*sin(d*x+c))/a/(a^2-b^2)/d+1/3*(6*a^4-10*a^2*b^2+b^4)*tan(d*x+c)/a/(a^2-b^2)^2/d+1/3*tan(d*x+c)^3/a/d,1],
[csc(d*x+c)^3*sec(d*x+c)^4/(a+b*sin(d*x+c)),x,20,-2*b^7*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(5/2)/d-5/2*arctanh(cos(d*x+c))/a/d-b^2*arctanh(cos(d*x+c))/a^3/d+b*cot(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d+2*sec(d*x+c)/a/d+b^2*sec(d*x+c)/a^3/d+1/3*sec(d*x+c)^3/a/d+1/3*b^2*sec(d*x+c)^3/a^3/d+1/3*b^3*sec(d*x+c)^3*(b-a*sin(d*x+c))/a^3/(a^2-b^2)/d-1/3*b^3*sec(d*x+c)*(3*b^3+a*(2*a^2-5*b^2)*sin(d*x+c))/a^3/(a^2-b^2)^2/d-2*b*tan(d*x+c)/a^2/d-1/3*b*tan(d*x+c)^3/a^2/d,1],
[sin(d*x+c)^3*tan(d*x+c)^5/(a+b*sin(d*x+c)),x,5,-1/16*(35*a^2+57*a*b+24*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*(35*a^2-57*a*b+24*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d-a^8*ln(a+b*sin(d*x+c))/b^3/(a^2-b^2)^3/d-1/16*(13*a^2-3*a*b-12*b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))+a*sin(d*x+c)/b^2/d-1/2*sin(d*x+c)^2/b/d+1/16*(13*a^2+3*a*b-12*b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d,1],
[sin(d*x+c)^2*tan(d*x+c)^5/(a+b*sin(d*x+c)),x,5,-1/16*(24*a^2+37*a*b+15*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d-1/16*(24*a^2-37*a*b+15*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d+a^7*ln(a+b*sin(d*x+c))/b^2/(a^2-b^2)^3/d-1/16*(12*a^2-a*b-9*b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))-sin(d*x+c)/b/d-1/16*(12*a^2+a*b-9*b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a-b*sin(d*x+c))/(a^2-b^2)/d,1],
[sin(d*x+c)*tan(d*x+c)^5/(a+b*sin(d*x+c)),x,5,-1/16*(15*a^2+21*a*b+8*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*(15*a^2-21*a*b+8*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d-a^6*ln(a+b*sin(d*x+c))/b/(a^2-b^2)^3/d-1/16*(9*a^2-3*a*b-8*b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))+1/16*(9*a^2+3*a*b-8*b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d,1],
[tan(d*x+c)^5/(a+b*sin(d*x+c)),x,4,-1/16*(8*a^2+9*a*b+3*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d-1/16*(8*a^2-9*a*b+3*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d+a^5*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/16*(8*a^2-a*b-5*b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))-1/16*(8*a^2+a*b-5*b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a/(a^2-b^2)-b*sin(d*x+c)/(a^2-b^2))/d,1],
[sec(d*x+c)*tan(d*x+c)^4/(a+b*sin(d*x+c)),x,6,-1/16*a*(3*a+b)*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*a*(3*a-b)*ln(1+sin(d*x+c))/(a-b)^3/d-a^4*b*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d+1/8*sec(d*x+c)^2*(4*b*(2*a^2-b^2)-a*(5*a^2-b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[sec(d*x+c)^2*tan(d*x+c)^3/(a+b*sin(d*x+c)),x,5,1/16*b*(3*a+b)*ln(1-sin(d*x+c))/(a+b)^3/d-1/16*(3*a-b)*b*ln(1+sin(d*x+c))/(a-b)^3/d+a^3*b^2*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/16*(4*a^2-a*b-b^2)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))-1/16*(4*a^2+a*b-b^2)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a-b*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^3*tan(d*x+c)^2/(a+b*sin(d*x+c)),x,5,1/16*a*(a+3*b)*ln(1-sin(d*x+c))/(a+b)^3/d-1/16*a*(a-3*b)*ln(1+sin(d*x+c))/(a-b)^3/d-a^2*b^3*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d-1/16*a*(a-3*b)/(a-b)/(a+b)^2/d/(1-sin(d*x+c))+1/16*a*(a+3*b)/(a-b)^2/(a+b)/d/(1+sin(d*x+c))-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^4*tan(d*x+c)/(a+b*sin(d*x+c)),x,5,-1/16*b*(a+3*b)*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*(a-3*b)*b*ln(1+sin(d*x+c))/(a-b)^3/d+a*b^4*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/4*sec(d*x+c)^4*(a-b*sin(d*x+c))/(a^2-b^2)/d+1/16*(a-3*b)*b^5/(a-b)/(a+b)^2/d/(b^4-b^4*sin(d*x+c))-1/16*b^5*(a+3*b)/(a-b)^2/(a+b)/d/(b^4+b^4*sin(d*x+c)),1],
[csc(d*x+c)*sec(d*x+c)^5/(a+b*sin(d*x+c)),x,4,-1/16*(8*a^2+21*a*b+15*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d+ln(sin(d*x+c))/a/d-1/16*(8*a^2-21*a*b+15*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d+b^6*ln(a+b*sin(d*x+c))/a/(a^2-b^2)^3/d+1/16/(a+b)/d/(1-sin(d*x+c))^2+1/16*(5*a+7*b)/(a+b)^2/d/(1-sin(d*x+c))+1/16/(a-b)/d/(1+sin(d*x+c))^2+1/16*(5*a-7*b)/(a-b)^2/d/(1+sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^5/(a+b*sin(d*x+c)),x,4,-csc(d*x+c)/a/d-1/16*(15*a^2+37*a*b+24*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d-b*ln(sin(d*x+c))/a^2/d+1/16*(15*a^2-37*a*b+24*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d-b^7*ln(a+b*sin(d*x+c))/a^2/(a^2-b^2)^3/d+1/16/(a+b)/d/(1-sin(d*x+c))^2+1/16*(7*a+9*b)/(a+b)^2/d/(1-sin(d*x+c))-1/16/(a-b)/d/(1+sin(d*x+c))^2-1/16*(7*a-9*b)/(a-b)^2/d/(1+sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^5/(a+b*sin(d*x+c)),x,4,b*csc(d*x+c)/a^2/d-1/2*csc(d*x+c)^2/a/d-1/16*(24*a^2+57*a*b+35*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d+(3*a^2+b^2)*ln(sin(d*x+c))/a^3/d-1/16*(24*a^2-57*a*b+35*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d+b^8*ln(a+b*sin(d*x+c))/a^3/(a^2-b^2)^3/d+1/16/(a+b)/d/(1-sin(d*x+c))^2+1/16*(9*a+11*b)/(a+b)^2/d/(1-sin(d*x+c))+1/16/(a-b)/d/(1+sin(d*x+c))^2+1/16*(9*a-11*b)/(a-b)^2/d/(1+sin(d*x+c)),1],
[sqrt(g*cos(f*x+e))*sin(f*x+e)^4/(a+b*sin(f*x+e)),x,21,a^4*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/(-a^2+b^2)^(1/4)/f-a^4*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/(-a^2+b^2)^(1/4)/f-2/3*a^2*(g*cos(f*x+e))^(3/2)/b^3/f/g-2/3*(g*cos(f*x+e))^(3/2)/b/f/g+2/7*(g*cos(f*x+e))^(7/2)/b/f/g^3-2*a^3*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^4/f/sqrt(cos(f*x+e))-4/5*a*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^2/f/sqrt(cos(f*x+e))+a^5*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+a^5*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+2/5*a*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/b^2/f/g,1],
[sqrt(g*cos(f*x+e))*sin(f*x+e)^3/(a+b*sin(f*x+e)),x,18,-a^3*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/(-a^2+b^2)^(1/4)/f+a^3*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/(-a^2+b^2)^(1/4)/f+2/3*a*(g*cos(f*x+e))^(3/2)/b^2/f/g+2*a^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^3/f/sqrt(cos(f*x+e))+4/5*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b/f/sqrt(cos(f*x+e))-a^4*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-a^4*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-2/5*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/b/f/g,1],
[sqrt(g*cos(f*x+e))*sin(f*x+e)^2/(a+b*sin(f*x+e)),x,15,a^2*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(1/4)/f-a^2*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(1/4)/f-2/3*(g*cos(f*x+e))^(3/2)/b/f/g-2*a*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^2/f/sqrt(cos(f*x+e))+a^3*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+a^3*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[sqrt(g*cos(f*x+e))*sin(f*x+e)/(a+b*sin(f*x+e)),x,12,-a*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(1/4)/f+a*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(1/4)/f+2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b/f/sqrt(cos(f*x+e))-a^2*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-a^2*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[sqrt(g*cos(f*x+e))*csc(f*x+e)/(a+b*sin(f*x+e)),x,16,sqrt(g)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-sqrt(b)*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(1/4)/f-sqrt(g)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+sqrt(b)*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(1/4)/f-g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[sqrt(g*cos(f*x+e))*csc(f*x+e)^2/(a+b*sin(f*x+e)),x,19,-b*sqrt(g)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f+b^(3/2)*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(1/4)/f+b*sqrt(g)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f-b^(3/2)*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(1/4)/f-(g*cos(f*x+e))^(3/2)*csc(f*x+e)/a/f/g-sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(cos(f*x+e))+b*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+b*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[sqrt(g*cos(f*x+e))*csc(f*x+e)^3/(a+b*sin(f*x+e)),x,25,1/4*sqrt(g)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+b^2*sqrt(g)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f-b^(5/2)*sqrt(g)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/(-a^2+b^2)^(1/4)/f-1/4*sqrt(g)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-b^2*sqrt(g)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f+b^(5/2)*sqrt(g)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/(-a^2+b^2)^(1/4)/f+b*(g*cos(f*x+e))^(3/2)*csc(f*x+e)/a^2/f/g-1/2*(g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/a/f/g+b*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(cos(f*x+e))-b^2*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a^2/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-b^2*g*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a^2/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x,24,a^3*(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/f+a^3*(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/f-2*a^3*g*sqrt(g*cos(f*x+e))/b^4/f+2/5*a*(g*cos(f*x+e))^(5/2)/b^2/f/g-2*a^4*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^5/f/sqrt(g*cos(f*x+e))+2/3*a^2*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^3/f/sqrt(g*cos(f*x+e))+4/21*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b/f/sqrt(g*cos(f*x+e))+a^4*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+a^4*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+2/3*a^2*g*sqrt(g*cos(f*x+e))*sin(f*x+e)/b^3/f+4/21*g*sqrt(g*cos(f*x+e))*sin(f*x+e)/b/f-2/7*(g*cos(f*x+e))^(5/2)*sin(f*x+e)/b/f/g,1],
[(g*cos(f*x+e))^(3/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x,20,-a^2*(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/f-a^2*(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/f+2*a^2*g*sqrt(g*cos(f*x+e))/b^3/f-2/5*(g*cos(f*x+e))^(5/2)/b/f/g+2*a^3*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^4/f/sqrt(g*cos(f*x+e))-2/3*a*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^2/f/sqrt(g*cos(f*x+e))-a^3*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-a^3*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-2/3*a*g*sqrt(g*cos(f*x+e))*sin(f*x+e)/b^2/f,1],
[(g*cos(f*x+e))^(3/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x,13,a*(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/f+a*(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/f-2/3*(3*a^2-b^2)*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^3/f/sqrt(g*cos(f*x+e))+a^2*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+a^2*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-2/3*g*sqrt(g*cos(f*x+e))*(3*a-b*sin(f*x+e))/b^2/f,1],
[(g*cos(f*x+e))^(3/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x,21,-g^(3/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/sqrt(b)/f-g^(3/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/sqrt(b)/f-2*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b/f/sqrt(g*cos(f*x+e))+(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x,24,b*g^(3/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f-sqrt(b)*(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/f+b*g^(3/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f-sqrt(b)*(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/f-g*sqrt(g*cos(f*x+e))*csc(f*x+e)/a/f+g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a/f/sqrt(g*cos(f*x+e))-(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x,30,1/4*g^(3/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-b^2*g^(3/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f+b^(3/2)*(-a^2+b^2)^(1/4)*g^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/f+1/4*g^(3/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-b^2*g^(3/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f+b^(3/2)*(-a^2+b^2)^(1/4)*g^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/f+b*g*sqrt(g*cos(f*x+e))*csc(f*x+e)/a^2/f-1/2*g*sqrt(g*cos(f*x+e))*csc(f*x+e)^2/a/f-b*g^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a^2/f/sqrt(g*cos(f*x+e))+b*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a^2/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+b*(a^2-b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a^2/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(5/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x,24,-a^3*(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(11/2)/f+a^3*(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(11/2)/f-2/3*a^3*g*(g*cos(f*x+e))^(3/2)/b^4/f+2/7*a*(g*cos(f*x+e))^(7/2)/b^2/f/g-2*a^4*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^5/f/sqrt(cos(f*x+e))+6/5*a^2*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^3/f/sqrt(cos(f*x+e))+4/15*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b/f/sqrt(cos(f*x+e))+a^4*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^6/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+a^4*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^6/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+2/5*a^2*g*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/b^3/f+4/45*g*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/b/f-2/9*(g*cos(f*x+e))^(7/2)*sin(f*x+e)/b/f/g,1],
[(g*cos(f*x+e))^(5/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x,20,a^2*(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/f-a^2*(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(9/2)/f+2/3*a^2*g*(g*cos(f*x+e))^(3/2)/b^3/f-2/7*(g*cos(f*x+e))^(7/2)/b/f/g+2*a^3*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^4/f/sqrt(cos(f*x+e))-6/5*a*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^2/f/sqrt(cos(f*x+e))-a^3*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-a^3*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-2/5*a*g*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/b^2/f,1],
[(g*cos(f*x+e))^(5/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x,13,-a*(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/f+a*(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/f-2/5*(5*a^2-3*b^2)*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^3/f/sqrt(cos(f*x+e))+a^2*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+a^2*(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-2/15*g*(g*cos(f*x+e))^(3/2)*(5*a-3*b*sin(f*x+e))/b^2/f,1],
[(g*cos(f*x+e))^(5/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x,21,g^(5/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/b^(3/2)/f-g^(5/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/b^(3/2)/f-2*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b/f/sqrt(cos(f*x+e))+(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(5/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x,24,-b*g^(5/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f+(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/sqrt(b)/f+b*g^(5/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f-(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/sqrt(b)/f-g*(g*cos(f*x+e))^(3/2)*csc(f*x+e)/a/f-g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/sqrt(cos(f*x+e))-(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/b/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/b/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[(g*cos(f*x+e))^(5/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x,30,-3/4*g^(5/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f+b^2*g^(5/2)*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f-sqrt(b)*(-a^2+b^2)^(3/4)*g^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/f+3/4*g^(5/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f-b^2*g^(5/2)*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f+sqrt(b)*(-a^2+b^2)^(3/4)*g^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/f+b*g*(g*cos(f*x+e))^(3/2)*csc(f*x+e)/a^2/f-1/2*g*(g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/a/f+b*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a^2/f/sqrt(cos(f*x+e))+(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a^2/(b-sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+(a^2-b^2)*g^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a^2/(b+sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)^4/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,23,-a^4*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)-a^4*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(7/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)-2*a^2*sqrt(g*cos(f*x+e))/b^3/f/g-2*sqrt(g*cos(f*x+e))/b/f/g+2/5*(g*cos(f*x+e))^(5/2)/b/f/g^3-2*a^3*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^4/f/sqrt(g*cos(f*x+e))-4/3*a*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^2/f/sqrt(g*cos(f*x+e))+a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+2/3*a*sqrt(g*cos(f*x+e))*sin(f*x+e)/b^2/f/g,1],
[sin(f*x+e)^3/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,19,a^3*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)+a^3*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)+2*a*sqrt(g*cos(f*x+e))/b^2/f/g+2*a^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^3/f/sqrt(g*cos(f*x+e))+4/3*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b/f/sqrt(g*cos(f*x+e))-a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-2/3*sqrt(g*cos(f*x+e))*sin(f*x+e)/b/f/g,1],
[sin(f*x+e)^2/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,15,-a^2*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)-a^2*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(3/4)/f/sqrt(g)-2*sqrt(g*cos(f*x+e))/b/f/g-2*a*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^2/f/sqrt(g*cos(f*x+e))+a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))+a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,12,a*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(3/4)/f/sqrt(g)+a*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(3/4)/f/sqrt(g)+2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b/f/sqrt(g*cos(f*x+e))-a^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2+b*sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))-a^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[csc(f*x+e)/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,16,-arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/sqrt(g)+b^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(3/4)/f/sqrt(g)-arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/sqrt(g)+b^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(3/4)/f/sqrt(g)-b*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-b*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[csc(f*x+e)^2/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,19,b*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/sqrt(g)-b^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(3/4)/f/sqrt(g)+b*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/sqrt(g)-b^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(3/4)/f/sqrt(g)-sqrt(g*cos(f*x+e))*csc(f*x+e)/a/f/g+sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a/f/sqrt(g*cos(f*x+e))+b^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b^2+b*sqrt(-a^2+b^2))/f/sqrt(g*cos(f*x+e))+b^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[csc(f*x+e)^3/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,25,-3/4*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/sqrt(g)-b^2*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f/sqrt(g)+b^(7/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/(-a^2+b^2)^(3/4)/f/sqrt(g)-3/4*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/sqrt(g)-b^2*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^3/f/sqrt(g)+b^(7/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^3/(-a^2+b^2)^(3/4)/f/sqrt(g)+b*sqrt(g*cos(f*x+e))*csc(f*x+e)/a^2/f/g-1/2*sqrt(g*cos(f*x+e))*csc(f*x+e)^2/a/f/g-b*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a^2/f/sqrt(g*cos(f*x+e))-b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a^2/(a^2-b*(b-sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e))-b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a^2/(a^2-b*(b+sqrt(-a^2+b^2)))/f/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)^4/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,22,a^4*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(5/4)/f/g^(3/2)-a^4*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(5/2)/(-a^2+b^2)^(5/4)/f/g^(3/2)-2*b/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))+2/3*a^2*(g*cos(f*x+e))^(3/2)/b/(a^2-b^2)/f/g^3-2/3*b*(g*cos(f*x+e))^(3/2)/(a^2-b^2)/f/g^3-4*a*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))+2*a^3*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b^2/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))-a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))-a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+2*a*sin(f*x+e)/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)^3/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,18,-a^3*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(5/4)/f/g^(3/2)+a^3*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(5/4)/f/g^(3/2)+2*a/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))-2*a^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/b/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))+4*b*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))+a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))-2*b*sin(f*x+e)/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,15,a^2*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(5/4)/f/g^(3/2)-a^2*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(5/4)/f/g^(3/2)-2*b/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))-2*a*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))-a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))-a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+2*a*sin(f*x+e)/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,13,-a*sqrt(b)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(5/4)/f/g^(3/2)+a*sqrt(b)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(5/4)/f/g^(3/2)+2*b*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))+a^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+a^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+2*(a-b*sin(f*x+e))/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[csc(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,21,arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/g^(3/2)-b^(5/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(5/4)/f/g^(3/2)-arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/g^(3/2)+b^(5/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(5/4)/f/g^(3/2)+2/a/f/g/sqrt(g*cos(f*x+e))+2*b*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))+b^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+b^2*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+2*b*(b-a*sin(f*x+e))/a/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[csc(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,25,-b*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/g^(3/2)+b^(7/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(5/4)/f/g^(3/2)+b*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/g^(3/2)-b^(7/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(5/4)/f/g^(3/2)-2*b/a^2/f/g/sqrt(g*cos(f*x+e))-csc(f*x+e)/a/f/g/sqrt(g*cos(f*x+e))-3*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/f/g^2/sqrt(cos(f*x+e))-2*b^2*sqrt(g*cos(f*x+e))*EllipticE(sin(1/2*f*x+1/2*e),sqrt(2))/a/(a^2-b^2)/f/g^2/sqrt(cos(f*x+e))-b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b^2)/(b-sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))-b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b^2)/(b+sqrt(-a^2+b^2))/f/g/sqrt(g*cos(f*x+e))+3*sin(f*x+e)/a/f/g/sqrt(g*cos(f*x+e))-2*b^2*(b-a*sin(f*x+e))/a^2/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e)),1],
[sin(f*x+e)^4/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,22,-a^4*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(7/4)/f/g^(5/2)-a^4*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/b^(3/2)/(-a^2+b^2)^(7/4)/f/g^(5/2)-2/3*b/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2)+2*a^2*sqrt(g*cos(f*x+e))/b/(a^2-b^2)/f/g^3-2*b*sqrt(g*cos(f*x+e))/(a^2-b^2)/f/g^3-4/3*a*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))+2*a^3*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b^2/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))-a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))-a^5*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+2/3*a*sin(f*x+e)/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[sin(f*x+e)^3/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,18,a^3*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(7/4)/f/g^(5/2)+a^3*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/sqrt(b)/(-a^2+b^2)^(7/4)/f/g^(5/2)+2/3*a/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2)-2*a^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/b/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))+4/3*b*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))+a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+a^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))-2/3*b*sin(f*x+e)/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[sin(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,15,-a^2*sqrt(b)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(7/4)/f/g^(5/2)-a^2*sqrt(b)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(7/4)/f/g^(5/2)-2/3*b/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2)+2/3*a*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))-a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))-a^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+2/3*a*sin(f*x+e)/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[sin(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,13,a*b^(3/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(7/4)/f/g^(5/2)+a*b^(3/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/(-a^2+b^2)^(7/4)/f/g^(5/2)-2/3*b*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))+a^2*b*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+a^2*b*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+2/3*(a-b*sin(f*x+e))/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[csc(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,21,-arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/g^(5/2)+b^(7/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(7/4)/f/g^(5/2)-arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a/f/g^(5/2)+b^(7/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a/(-a^2+b^2)^(7/4)/f/g^(5/2)+2/3/a/f/g/(g*cos(f*x+e))^(3/2)-2/3*b*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))+b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+b^3*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+2/3*b*(b-a*sin(f*x+e))/a/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[csc(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,25,b*arctan(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/g^(5/2)-b^(9/2)*arctan(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(7/4)/f/g^(5/2)+b*arctanh(sqrt(g*cos(f*x+e))/sqrt(g))/a^2/f/g^(5/2)-b^(9/2)*arctanh(sqrt(b)*sqrt(g*cos(f*x+e))/(-a^2+b^2)^(1/4)/sqrt(g))/a^2/(-a^2+b^2)^(7/4)/f/g^(5/2)-2/3*b/a^2/f/g/(g*cos(f*x+e))^(3/2)-csc(f*x+e)/a/f/g/(g*cos(f*x+e))^(3/2)+5/3*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a/f/g^2/sqrt(g*cos(f*x+e))+2/3*b^2*sqrt(cos(f*x+e))*InverseJacobiAM(1/2*f*x+1/2*e,sqrt(2))/a/(a^2-b^2)/f/g^2/sqrt(g*cos(f*x+e))-b^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))-b^4*sqrt(cos(f*x+e))*EllipticPi(sin(1/2*f*x+1/2*e),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/a/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/f/g^2/sqrt(g*cos(f*x+e))+5/3*sin(f*x+e)/a/f/g/(g*cos(f*x+e))^(3/2)-2/3*b^2*(b-a*sin(f*x+e))/a^2/(a^2-b^2)/f/g/(g*cos(f*x+e))^(3/2),1],
[sqrt(g*cos(f*x+e))*(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,29,a^2*d^(5/2)*sqrt(g)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f+1/4*d^(5/2)*sqrt(g)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-a^2*d^(5/2)*sqrt(g)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f-1/4*d^(5/2)*sqrt(g)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f+a^2*d^(5/2)*sqrt(g)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f+1/4*d^(5/2)*sqrt(g)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-2*sqrt(2)*a^3*d^3*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^3/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*a^3*d^3*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^3/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))-1/2*d^2*(g*cos(f*x+e))^(3/2)*sqrt(d*sin(f*x+e))/b/f/g-a*d^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/b^2/f/sqrt(sin(2*f*x+2*e)),1],
[sqrt(g*cos(f*x+e))*(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,18,-a*d^(3/2)*sqrt(g)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/f+a*d^(3/2)*sqrt(g)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/f-a*d^(3/2)*sqrt(g)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/f+2*sqrt(2)*a^2*d^2*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^2/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*a^2*d^2*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^2/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))+d*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/b/f/sqrt(sin(2*f*x+2*e)),1],
[sqrt(g*cos(f*x+e))*sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,15,sqrt(d)*sqrt(g)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-sqrt(d)*sqrt(g)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f+sqrt(d)*sqrt(g)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-2*sqrt(2)*a*d*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*a*d*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e)),1],
[sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,5,2*sqrt(2)*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/sqrt(-a+b)/sqrt(a+b)/f/sqrt(d*sin(f*x+e)),1],
[sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,9,-2*(g*cos(f*x+e))^(3/2)/a/d/f/g/sqrt(d*sin(f*x+e))-2*sqrt(2)*b*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/sqrt(-a+b)/sqrt(a+b)/d/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*b*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/sqrt(-a+b)/sqrt(a+b)/d/f/sqrt(d*sin(f*x+e))-2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/d^2/f/sqrt(sin(2*f*x+2*e)),1],
[sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,11,-2/3*(g*cos(f*x+e))^(3/2)/a/d/f/g/(d*sin(f*x+e))^(3/2)+2*b*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/g/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^2*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/sqrt(-a+b)/sqrt(a+b)/d^2/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^2*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/sqrt(-a+b)/sqrt(a+b)/d^2/f/sqrt(d*sin(f*x+e))+2*b*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^2/d^3/f/sqrt(sin(2*f*x+2*e)),1],
[sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x,16,-2/5*(g*cos(f*x+e))^(3/2)/a/d/f/g/(d*sin(f*x+e))^(5/2)+2/3*b*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/g/(d*sin(f*x+e))^(3/2)-4/5*(g*cos(f*x+e))^(3/2)/a/d^3/f/g/sqrt(d*sin(f*x+e))-2*b^2*(g*cos(f*x+e))^(3/2)/a^3/d^3/f/g/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^3*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^3/sqrt(-a+b)/sqrt(a+b)/d^3/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^3*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^3/sqrt(-a+b)/sqrt(a+b)/d^3/f/sqrt(d*sin(f*x+e))-4/5*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/d^4/f/sqrt(sin(2*f*x+2*e))-2*b^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^3/d^4/f/sqrt(sin(2*f*x+2*e)),1],
[sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x,19,-2/7*(g*cos(f*x+e))^(3/2)/a/d/f/g/(d*sin(f*x+e))^(7/2)+2/5*b*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/g/(d*sin(f*x+e))^(5/2)-8/21*(g*cos(f*x+e))^(3/2)/a/d^3/f/g/(d*sin(f*x+e))^(3/2)-2/3*b^2*(g*cos(f*x+e))^(3/2)/a^3/d^3/f/g/(d*sin(f*x+e))^(3/2)+4/5*b*(g*cos(f*x+e))^(3/2)/a^2/d^4/f/g/sqrt(d*sin(f*x+e))+2*b^3*(g*cos(f*x+e))^(3/2)/a^4/d^4/f/g/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^4*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^4/sqrt(-a+b)/sqrt(a+b)/d^4/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^4*sqrt(g)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^4/sqrt(-a+b)/sqrt(a+b)/d^4/f/sqrt(d*sin(f*x+e))+4/5*b*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^2/d^5/f/sqrt(sin(2*f*x+2*e))+2*b^3*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^4/d^5/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,29,3/4*d^(3/2)*g^(3/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/f+(a^2-b^2)*d^(3/2)*g^(3/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^3/f-3/4*d^(3/2)*g^(3/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/f-(a^2-b^2)*d^(3/2)*g^(3/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^3/f+3/4*d^(3/2)*g^(3/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b/f+(a^2-b^2)*d^(3/2)*g^(3/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b^3/f+2*sqrt(2)*a*sqrt(-a^2+b^2)*d^(3/2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/b^3/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*a*sqrt(-a^2+b^2)*d^(3/2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/b^3/f/sqrt(g*cos(f*x+e))-a*d*g*sqrt(g*cos(f*x+e))*sqrt(d*sin(f*x+e))/b^2/f+1/2*g*sqrt(g*cos(f*x+e))*(d*sin(f*x+e))^(3/2)/b/f+1/2*a*d^2*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/b^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)*sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,18,-a*sqrt(d)*g^(3/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^2/f+a*sqrt(d)*g^(3/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^2/f-a*sqrt(d)*g^(3/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b^2/f-2*sqrt(2)*sqrt(-a^2+b^2)*sqrt(d)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/b^2/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*sqrt(-a^2+b^2)*sqrt(d)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/b^2/f/sqrt(g*cos(f*x+e))+g*sqrt(g*cos(f*x+e))*sqrt(d*sin(f*x+e))/b/f-1/2*d*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/b/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,17,g^(3/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/sqrt(d)/f-g^(3/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/sqrt(d)/f+g^(3/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b/sqrt(d)/f+2*sqrt(2)*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a/b/sqrt(d)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a/b/sqrt(d)/f/sqrt(g*cos(f*x+e))+g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,8,-2*sqrt(2)*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^2/d^(3/2)/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^2/d^(3/2)/f/sqrt(g*cos(f*x+e))-2*g*sqrt(g*cos(f*x+e))/a/d/f/sqrt(d*sin(f*x+e))-b*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^2/d/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,12,2*sqrt(2)*b*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^3/d^(5/2)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*b*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^3/d^(5/2)/f/sqrt(g*cos(f*x+e))-2/3*g*sqrt(g*cos(f*x+e))/a/d/f/(d*sin(f*x+e))^(3/2)+2*b*g*sqrt(g*cos(f*x+e))/a^2/d^2/f/sqrt(d*sin(f*x+e))+2/3*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a/d^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))-(a^2-b^2)*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^3/d^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x,15,-2*sqrt(2)*b^2*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^4/d^(7/2)/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*b^2*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^4/d^(7/2)/f/sqrt(g*cos(f*x+e))-2/5*g*sqrt(g*cos(f*x+e))/a/d/f/(d*sin(f*x+e))^(5/2)+2/3*b*g*sqrt(g*cos(f*x+e))/a^2/d^2/f/(d*sin(f*x+e))^(3/2)-8/5*g*sqrt(g*cos(f*x+e))/a/d^3/f/sqrt(d*sin(f*x+e))+2*(a^2-b^2)*g*sqrt(g*cos(f*x+e))/a^3/d^3/f/sqrt(d*sin(f*x+e))-2/3*b*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^2/d^3/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))+b*(a^2-b^2)*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^4/d^3/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x,20,2*sqrt(2)*b^3*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^5/d^(9/2)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*b^3*sqrt(-a^2+b^2)*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^5/d^(9/2)/f/sqrt(g*cos(f*x+e))-2/7*g*sqrt(g*cos(f*x+e))/a/d/f/(d*sin(f*x+e))^(7/2)+2/5*b*g*sqrt(g*cos(f*x+e))/a^2/d^2/f/(d*sin(f*x+e))^(5/2)-4/7*g*sqrt(g*cos(f*x+e))/a/d^3/f/(d*sin(f*x+e))^(3/2)+2/3*(a^2-b^2)*g*sqrt(g*cos(f*x+e))/a^3/d^3/f/(d*sin(f*x+e))^(3/2)+8/5*b*g*sqrt(g*cos(f*x+e))/a^2/d^4/f/sqrt(d*sin(f*x+e))-2*b*(a^2-b^2)*g*sqrt(g*cos(f*x+e))/a^4/d^4/f/sqrt(d*sin(f*x+e))+4/7*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a/d^4/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))-2/3*(a^2-b^2)*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^3/d^4/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))-b^2*(a^2-b^2)*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^5/d^4/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(g*cos(f*x+e))^(5/2)*sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,29,-1/4*sqrt(d)*g^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-(a^2-b^2)*sqrt(d)*g^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f+1/4*sqrt(d)*g^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f+(a^2-b^2)*sqrt(d)*g^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f-1/4*sqrt(d)*g^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b/f-(a^2-b^2)*sqrt(d)*g^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b^3/f-2*sqrt(2)*a*sqrt(-a+b)*sqrt(a+b)*d*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^3/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*a*sqrt(-a+b)*sqrt(a+b)*d*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^3/f/sqrt(d*sin(f*x+e))+1/2*g*(g*cos(f*x+e))^(3/2)*sqrt(d*sin(f*x+e))/b/f+a*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/b^2/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,18,a*g^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/sqrt(d)/f-a*g^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/sqrt(d)/f+a*g^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b^2/sqrt(d)/f+2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^2/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b^2/f/sqrt(d*sin(f*x+e))-g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/b/d/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,19,-g^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/d^(3/2)/f+g^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/d^(3/2)/f-g^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b/d^(3/2)/f-2*g*(g*cos(f*x+e))^(3/2)/a/d/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/b/d/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/b/d/f/sqrt(d*sin(f*x+e))-2*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/d^2/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,10,-2/3*g*(g*cos(f*x+e))^(3/2)/a/d/f/(d*sin(f*x+e))^(3/2)+2*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/d^2/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/d^2/f/sqrt(d*sin(f*x+e))+2*b*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^2/d^3/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x,15,-2/5*g*(g*cos(f*x+e))^(3/2)/a/d/f/(d*sin(f*x+e))^(5/2)+2/3*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/(d*sin(f*x+e))^(3/2)-4/5*g*(g*cos(f*x+e))^(3/2)/a/d^3/f/sqrt(d*sin(f*x+e))+2*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^3/d^3/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*b*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^3/d^3/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*b*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^3/d^3/f/sqrt(d*sin(f*x+e))-4/5*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/d^4/f/sqrt(sin(2*f*x+2*e))+2*(a^2-b^2)*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^3/d^4/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x,18,-2/7*g*(g*cos(f*x+e))^(3/2)/a/d/f/(d*sin(f*x+e))^(7/2)+2/5*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/(d*sin(f*x+e))^(5/2)-8/21*g*(g*cos(f*x+e))^(3/2)/a/d^3/f/(d*sin(f*x+e))^(3/2)+2/3*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^3/d^3/f/(d*sin(f*x+e))^(3/2)+4/5*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^4/f/sqrt(d*sin(f*x+e))-2*b*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^4/d^4/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^2*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^4/d^4/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^2*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^4/d^4/f/sqrt(d*sin(f*x+e))+4/5*b*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^2/d^5/f/sqrt(sin(2*f*x+2*e))-2*b*(a^2-b^2)*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^4/d^5/f/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(11/2)/(a+b*sin(f*x+e)),x,24,-2/9*g*(g*cos(f*x+e))^(3/2)/a/d/f/(d*sin(f*x+e))^(9/2)+2/7*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^2/f/(d*sin(f*x+e))^(7/2)-4/15*g*(g*cos(f*x+e))^(3/2)/a/d^3/f/(d*sin(f*x+e))^(5/2)+2/5*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^3/d^3/f/(d*sin(f*x+e))^(5/2)+8/21*b*g*(g*cos(f*x+e))^(3/2)/a^2/d^4/f/(d*sin(f*x+e))^(3/2)-2/3*b*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^4/d^4/f/(d*sin(f*x+e))^(3/2)-8/15*g*(g*cos(f*x+e))^(3/2)/a/d^5/f/sqrt(d*sin(f*x+e))+4/5*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^3/d^5/f/sqrt(d*sin(f*x+e))+2*b^2*(a^2-b^2)*g*(g*cos(f*x+e))^(3/2)/a^5/d^5/f/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^3*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^5/d^5/f/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^3*sqrt(-a+b)*sqrt(a+b)*g^(5/2)*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^5/d^5/f/sqrt(d*sin(f*x+e))-8/15*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/d^6/f/sqrt(sin(2*f*x+2*e))+4/5*(a^2-b^2)*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^3/d^6/f/sqrt(sin(2*f*x+2*e))+2*b^2*(a^2-b^2)*g^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^5/d^6/f/sqrt(sin(2*f*x+2*e)),1],
[(d*sin(f*x+e))^(5/2)/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,18,a*d^(5/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^2/f/sqrt(g)-a*d^(5/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b^2/f/sqrt(g)+a*d^(5/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b^2/f/sqrt(g)-2*sqrt(2)*a^2*d^(5/2)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/b^2/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*a^2*d^(5/2)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/b^2/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e))-d^2*sqrt(g*cos(f*x+e))*sqrt(d*sin(f*x+e))/b/f/g+1/2*d^3*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/b/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(d*sin(f*x+e))^(3/2)/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,14,-d^(3/2)*arctan(1-sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/f/sqrt(g)+d^(3/2)*arctan(1+sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(g*cos(f*x+e)))/sqrt(2)/b/f/sqrt(g)-d^(3/2)*arctanh(sqrt(2)*sqrt(g)*sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(sqrt(d)+sqrt(d)*tan(f*x+e)))/sqrt(2)/b/f/sqrt(g)+2*sqrt(2)*a*d^(3/2)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/b/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*a*d^(3/2)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/b/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e)),1],
[sqrt(d*sin(f*x+e))/sqrt(g*cos(f*x+e))/(a+b*sin(f*x+e)),x,4,-2*sqrt(2)*sqrt(d)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*sqrt(d)*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/sqrt(-a^2+b^2)/f/sqrt(g*cos(f*x+e)),1],
[1/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,7,2*sqrt(2)*b*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a/sqrt(-a^2+b^2)/sqrt(d)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*b*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a/sqrt(-a^2+b^2)/sqrt(d)/f/sqrt(g*cos(f*x+e))+InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[1/sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,9,-2*sqrt(2)*b^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^2/sqrt(-a^2+b^2)/d^(3/2)/f/sqrt(g*cos(f*x+e))+2*sqrt(2)*b^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^2/sqrt(-a^2+b^2)/d^(3/2)/f/sqrt(g*cos(f*x+e))-2*sqrt(g*cos(f*x+e))/a/d/f/g/sqrt(d*sin(f*x+e))-b*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^2/d/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[1/sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,13,2*sqrt(2)*b^3*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^3/sqrt(-a^2+b^2)/d^(5/2)/f/sqrt(g*cos(f*x+e))-2*sqrt(2)*b^3*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^3/sqrt(-a^2+b^2)/d^(5/2)/f/sqrt(g*cos(f*x+e))-2/3*sqrt(g*cos(f*x+e))/a/d/f/g/(d*sin(f*x+e))^(3/2)+2*b*sqrt(g*cos(f*x+e))/a^2/d^2/f/g/sqrt(d*sin(f*x+e))+2/3*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a/d^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))+b^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^3/d^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[(d*sin(f*x+e))^(5/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,29,-a^2*d^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/(a^2-b^2)/f/g^(3/2)+b*d^(5/2)*arctan(1-sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/(a^2-b^2)/f/g^(3/2)+a^2*d^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/b/(a^2-b^2)/f/g^(3/2)-b*d^(5/2)*arctan(1+sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(d*sin(f*x+e)))/sqrt(2)/(a^2-b^2)/f/g^(3/2)-a^2*d^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/b/(a^2-b^2)/f/g^(3/2)+b*d^(5/2)*arctanh(sqrt(2)*sqrt(d)*sqrt(g*cos(f*x+e))/(sqrt(g)+sqrt(g)*cot(f*x+e))/sqrt(d*sin(f*x+e)))/sqrt(2)/(a^2-b^2)/f/g^(3/2)-2*sqrt(2)*a^3*d^3*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))+2*sqrt(2)*a^3*d^3*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/b/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*b*d^2*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))+2*a*d*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))-2*a*d^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[(d*sin(f*x+e))^(3/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,10,2*sqrt(2)*a^2*d^2*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*sqrt(2)*a^2*d^2*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))+2*a*d*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))-2*b*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))+2*b*d*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[sqrt(d*sin(f*x+e))/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,11,-2*sqrt(2)*a*b*d*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))+2*sqrt(2)*a*b*d*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*b*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g/sqrt(g*cos(f*x+e))+2*a*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/d/f/g/sqrt(g*cos(f*x+e))-2*a*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[1/(g*cos(f*x+e))^(3/2)/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e)),x,11,2*sqrt(2)*b^2*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^2*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/(-a+b)^(3/2)/(a+b)^(3/2)/f/g^(3/2)/sqrt(d*sin(f*x+e))+2*a*sqrt(d*sin(f*x+e))/(a^2-b^2)/d/f/g/sqrt(g*cos(f*x+e))-2*b*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/d^2/f/g/sqrt(g*cos(f*x+e))+2*b*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/d/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x,16,-2*a/(a^2-b^2)/d/f/g/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))+2*b^2*(g*cos(f*x+e))^(3/2)/a/(a^2-b^2)/d/f/g^3/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^3*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/(-a+b)^(3/2)/(a+b)^(3/2)/d/f/g^(3/2)/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^3*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a/(-a+b)^(3/2)/(a+b)^(3/2)/d/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*b*sqrt(d*sin(f*x+e))/(a^2-b^2)/d^2/f/g/sqrt(g*cos(f*x+e))+4*a*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/d^3/f/g/sqrt(g*cos(f*x+e))-4*a*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/d^2/f/g^2/sqrt(sin(2*f*x+2*e))+2*b^2*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a/(a^2-b^2)/d^2/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x,19,-2/3*a/(a^2-b^2)/d/f/g/sqrt(g*cos(f*x+e))/(d*sin(f*x+e))^(3/2)+2/3*b^2*(g*cos(f*x+e))^(3/2)/a/(a^2-b^2)/d/f/g^3/(d*sin(f*x+e))^(3/2)+2*b/(a^2-b^2)/d^2/f/g/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e))-2*b^3*(g*cos(f*x+e))^(3/2)/a^2/(a^2-b^2)/d^2/f/g^3/sqrt(d*sin(f*x+e))+2*sqrt(2)*b^4*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),-sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/(-a+b)^(3/2)/(a+b)^(3/2)/d^2/f/g^(3/2)/sqrt(d*sin(f*x+e))-2*sqrt(2)*b^4*EllipticPi(sin(arcsin(sqrt(g*cos(f*x+e))/sqrt(g)/sqrt(1+sin(f*x+e)))),sqrt(-a+b)/sqrt(a+b),sqrt(-1))*sqrt(sin(f*x+e))/a^2/(-a+b)^(3/2)/(a+b)^(3/2)/d^2/f/g^(3/2)/sqrt(d*sin(f*x+e))+8/3*a*sqrt(d*sin(f*x+e))/(a^2-b^2)/d^3/f/g/sqrt(g*cos(f*x+e))-4*b*(d*sin(f*x+e))^(3/2)/(a^2-b^2)/d^4/f/g/sqrt(g*cos(f*x+e))+4*b*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/(a^2-b^2)/d^3/f/g^2/sqrt(sin(2*f*x+2*e))-2*b^3*sqrt(g*cos(f*x+e))*EllipticE(sin(e-1/4*Pi+f*x),sqrt(2))*sqrt(d*sin(f*x+e))/a^2/(a^2-b^2)/d^3/f/g^2/sqrt(sin(2*f*x+2*e)),1],
[(g*cos(f*x+e))^(3/2)/sqrt(d*sin(f*x+e))/(a+b*sin(f*x+e))^2,x,8,sqrt(2)*b*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b-sqrt(-a^2+b^2)),sqrt(-1))/a^2/sqrt(-a^2+b^2)/sqrt(d)/f/sqrt(g*cos(f*x+e))-sqrt(2)*b*g^2*sqrt(cos(f*x+e))*EllipticPi(sin(arcsin(sqrt(d*sin(f*x+e))/sqrt(d)/sqrt(1+cos(f*x+e)))),-a/(b+sqrt(-a^2+b^2)),sqrt(-1))/a^2/sqrt(-a^2+b^2)/sqrt(d)/f/sqrt(g*cos(f*x+e))+g*sqrt(g*cos(f*x+e))*sqrt(d*sin(f*x+e))/a/d/f/(a+b*sin(f*x+e))+1/2*g^2*InverseJacobiAM(e-1/4*Pi+f*x,sqrt(2))*sqrt(sin(2*f*x+2*e))/a^2/f/sqrt(g*cos(f*x+e))/sqrt(d*sin(f*x+e)),1],
[sin(d*x+c)^2*(a+b*sin(d*x+c))*tan(d*x+c)^2,x,9,-3/2*a*x+2*b*cos(d*x+c)/d-1/3*b*cos(d*x+c)^3/d+b*sec(d*x+c)/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d+a*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+b*sin(d*x+c))*tan(d*x+c)^2,x,9,-3/2*b*x+a*cos(d*x+c)/d+a*sec(d*x+c)/d+1/2*b*cos(d*x+c)*sin(d*x+c)/d+b*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))*tan(d*x+c)^2,x,7,-a*x+b*cos(d*x+c)/d+b*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))*tan(d*x+c),x,5,-b*x+a*sec(d*x+c)/d+b*tan(d*x+c)/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c)),x,6,-a*arctanh(cos(d*x+c))/d+a*sec(d*x+c)/d+b*tan(d*x+c)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c)),x,7,-b*arctanh(cos(d*x+c))/d-a*cot(d*x+c)/d+b*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c)),x,9,-3/2*a*arctanh(cos(d*x+c))/d-b*cot(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d+a*sec(d*x+c)/d+b*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+b*sin(d*x+c))^2*tan(d*x+c)^2,x,9,-3*a*b*x+(a^2+2*b^2)*cos(d*x+c)/d-1/3*b^2*cos(d*x+c)^3/d+(a^2+b^2)*sec(d*x+c)/d+a*b*cos(d*x+c)*sin(d*x+c)/d+2*a*b*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c)^2,x,12,-a^2*x-3/2*b^2*x+2*a*b*cos(d*x+c)/d+2*a*b*sec(d*x+c)/d+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d+a^2*tan(d*x+c)/d+b^2*tan(d*x+c)/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^2*tan(d*x+c),x,4,-2*a*b*x+2*b^2*cos(d*x+c)/d+sec(d*x+c)*(a+b*sin(d*x+c))^2/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x,8,-a^2*arctanh(cos(d*x+c))/d+(a^2+b^2)*sec(d*x+c)/d+2*a*b*tan(d*x+c)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x,7,-2*a*b*arctanh(cos(d*x+c))/d-a^2*cot(d*x+c)/d+2*a*b*sec(d*x+c)/d+(a^2+b^2)*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x,10,-1/2*(3*a^2+2*b^2)*arctanh(cos(d*x+c))/d-2*a*b*cot(d*x+c)/d+1/2*(3*a^2+2*b^2)*sec(d*x+c)/d-1/2*a^2*csc(d*x+c)^2*sec(d*x+c)/d+2*a*b*tan(d*x+c)/d,1],
[csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x,9,-3*a*b*arctanh(cos(d*x+c))/d-(2*a^2+b^2)*cot(d*x+c)/d-1/3*a^2*cot(d*x+c)^3/d-a*b*cot(d*x+c)*csc(d*x+c)/d+2*a*b*sec(d*x+c)/d+(a^2+b^2)*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+b*sin(d*x+c))^3*tan(d*x+c)^2,x,19,-9/2*a^2*b*x-15/8*b^3*x+a^3*cos(d*x+c)/d+6*a*b^2*cos(d*x+c)/d-a*b^2*cos(d*x+c)^3/d+a^3*sec(d*x+c)/d+3*a*b^2*sec(d*x+c)/d+3/2*a^2*b*cos(d*x+c)*sin(d*x+c)/d+9/8*b^3*cos(d*x+c)*sin(d*x+c)/d-1/4*b^3*cos(d*x+c)^3*sin(d*x+c)/d+3*a^2*b*tan(d*x+c)/d+b^3*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c)^2,x,15,-a^3*x-9/2*a*b^2*x+3*a^2*b*cos(d*x+c)/d+2*b^3*cos(d*x+c)/d-1/3*b^3*cos(d*x+c)^3/d+3*a^2*b*sec(d*x+c)/d+b^3*sec(d*x+c)/d+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+a^3*tan(d*x+c)/d+3*a*b^2*tan(d*x+c)/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^3*tan(d*x+c),x,3,-3/2*b*(2*a^2+b^2)*x+6*a*b^2*cos(d*x+c)/d+3/2*b^3*cos(d*x+c)*sin(d*x+c)/d+sec(d*x+c)*(a+b*sin(d*x+c))^3/d,1],
[csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x,11,-b^3*x-a^3*arctanh(cos(d*x+c))/d+a^3*sec(d*x+c)/d+3*a*b^2*sec(d*x+c)/d+3*a^2*b*tan(d*x+c)/d+b^3*tan(d*x+c)/d,1],
[csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x,12,-3*a^2*b*arctanh(cos(d*x+c))/d-a^3*cot(d*x+c)/d+3*a^2*b*sec(d*x+c)/d+b^3*sec(d*x+c)/d+a^3*tan(d*x+c)/d+3*a*b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x,15,-3/2*a^3*arctanh(cos(d*x+c))/d-3*a*b^2*arctanh(cos(d*x+c))/d-3*a^2*b*cot(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+a^3*sec(d*x+c)/d+3*a*b^2*sec(d*x+c)/d+3*a^2*b*tan(d*x+c)/d+b^3*tan(d*x+c)/d,1],
[csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x,16,-9/2*a^2*b*arctanh(cos(d*x+c))/d-b^3*arctanh(cos(d*x+c))/d-2*a^3*cot(d*x+c)/d-3*a*b^2*cot(d*x+c)/d-1/3*a^3*cot(d*x+c)^3/d-3/2*a^2*b*cot(d*x+c)*csc(d*x+c)/d+3*a^2*b*sec(d*x+c)/d+b^3*sec(d*x+c)/d+a^3*tan(d*x+c)/d+3*a*b^2*tan(d*x+c)/d,1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x,12,-x/b^2-2*a^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(5/2)/d+4*a^3*(a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(5/2)/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))-a^4*cos(d*x+c)/b/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sin(d*x+c)*tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x,12,2*a^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b/(a^2-b^2)^(5/2)/d-2*a^2*(a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b/(a^2-b^2)^(5/2)/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))+a^3*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x,12,-2*a^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d-4*a*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))-a^2*b*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)*tan(d*x+c)/(a+b*sin(d*x+c))^2,x,6,2*b*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d-a*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))+sec(d*x+c)*(2*a^2+b^2-3*a*b*sin(d*x+c))/(a^2-b^2)^2/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x,13,2*b^3*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+2*b^3*(3*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(5/2)/d-arctanh(cos(d*x+c))/a^2/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))+b^4*cos(d*x+c)/a/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x,15,-2*b^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/(a^2-b^2)^(5/2)/d-4*b^4*(2*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(5/2)/d+2*b*arctanh(cos(d*x+c))/a^3/d-cot(d*x+c)/a^2/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))-b^5*cos(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x,17,2*b^5*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(5/2)/d+2*b^5*(5*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/(a^2-b^2)^(5/2)/d-1/2*arctanh(cos(d*x+c))/a^2/d-(a^2+3*b^2)*arctanh(cos(d*x+c))/a^4/d+2*b*cot(d*x+c)/a^3/d-1/2*cot(d*x+c)*csc(d*x+c)/a^2/d+1/2*cos(d*x+c)/(a+b)^2/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^2/d/(1+sin(d*x+c))+b^6*cos(d*x+c)/a^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sin(d*x+c)^2*tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x,18,4*a^4*(a^2-2*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(7/2)/d-a^4*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(7/2)/d-2*a^2*(a^4-3*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/(a^2-b^2)^(7/2)/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))-1/2*a^4*cos(d*x+c)/b/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2-3/2*a^5*cos(d*x+c)/b/(a^2-b^2)^3/d/(a+b*sin(d*x+c))+2*a^3*(a^2-2*b^2)*cos(d*x+c)/b/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[sin(d*x+c)*tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x,18,-2*a^3*(a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b/(a^2-b^2)^(7/2)/d+a^3*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b/(a^2-b^2)^(7/2)/d+2*a*b*(a^2+3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))+1/2*a^3*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2+3/2*a^4*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))-a^2*(a^2-3*b^2)*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x,18,-4*a^2*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-a^2*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-2*b^2*(3*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))-1/2*a^2*b*cos(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2-3/2*a^3*b*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))-2*a*b^3*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)*tan(d*x+c)/(a+b*sin(d*x+c))^3,x,7,3*a*b*(2*a^2+3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-1/2*a*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))^2-1/2*(3*a^2+2*b^2)*sec(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))+1/2*sec(d*x+c)*(3*a*(2*a^2+3*b^2)-b*(11*a^2+4*b^2)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x,19,2*b^3*(3*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/(a^2-b^2)^(7/2)/d+b^3*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/(a^2-b^2)^(7/2)/d+2*b^3*(6*a^4-3*a^2*b^2+b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(7/2)/d-arctanh(cos(d*x+c))/a^3/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))+1/2*b^4*cos(d*x+c)/a/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2+3/2*b^4*cos(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))+b^4*(3*a^2-b^2)*cos(d*x+c)/a^2/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x,21,-4*b^4*(2*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(7/2)/d-b^4*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(7/2)/d-2*b^4*(10*a^4-9*a^2*b^2+3*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/(a^2-b^2)^(7/2)/d+3*b*arctanh(cos(d*x+c))/a^4/d-cot(d*x+c)/a^3/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))-1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))-1/2*b^5*cos(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2-3/2*b^5*cos(d*x+c)/a/(a^2-b^2)^3/d/(a+b*sin(d*x+c))-2*b^5*(2*a^2-b^2)*cos(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x,23,2*b^5*(5*a^2-3*b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(7/2)/d+b^5*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(7/2)/d+2*b^5*(15*a^4-17*a^2*b^2+6*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^5/(a^2-b^2)^(7/2)/d-1/2*arctanh(cos(d*x+c))/a^3/d-(a^2+6*b^2)*arctanh(cos(d*x+c))/a^5/d+3*b*cot(d*x+c)/a^4/d-1/2*cot(d*x+c)*csc(d*x+c)/a^3/d+1/2*cos(d*x+c)/(a+b)^3/d/(1-sin(d*x+c))+1/2*cos(d*x+c)/(a-b)^3/d/(1+sin(d*x+c))+1/2*b^6*cos(d*x+c)/a^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2+3/2*b^6*cos(d*x+c)/a^2/(a^2-b^2)^3/d/(a+b*sin(d*x+c))+b^6*(5*a^2-3*b^2)*cos(d*x+c)/a^4/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[sec(f*x+e)^2*sqrt(a+b*sin(f*x+e))/sqrt(d*sin(f*x+e)),x,2,sec(f*x+e)*sqrt(d*sin(f*x+e))*sqrt(a+b*sin(f*x+e))/d/f-sqrt(a+b)*sqrt(a*(1-csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/sqrt(d)/f,1],
[sec(f*x+e)^2*(a+b*sin(f*x+e))^(3/2)/sqrt(d*sin(f*x+e)),x,-1,sec(f*x+e)*(b+a*sin(f*x+e))*sqrt(a+b*sin(f*x+e))/f/sqrt(d*sin(f*x+e))-(a+b)^(3/2)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/sqrt(d)/f-b*(a+b)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*sqrt((b+a*csc(f*x+e))/(-a+b))*EllipticE(sin(arcsin(sqrt(-(b+a*csc(f*x+e))/(a-b)))),sqrt((-a+b)/(a+b)))*(1+sin(f*x+e))*tan(f*x+e)/f/sqrt(a*(1+csc(f*x+e))/(a-b))/sqrt(d*sin(f*x+e))/sqrt(a+b*sin(f*x+e)),1],
[sec(f*x+e)^4*(a+b*sin(f*x+e))^(5/2)/sqrt(d*sin(f*x+e)),x,-1,5/6*a*sec(f*x+e)*(b+a*sin(f*x+e))*sqrt(a+b*sin(f*x+e))/f/sqrt(d*sin(f*x+e))+1/3*sec(f*x+e)^3*sqrt(d*sin(f*x+e))*(a+b*sin(f*x+e))^(5/2)/d/f-5/6*a*(a+b)^(3/2)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/sqrt(d)/f-5/6*a*b*(a+b)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*sqrt((b+a*csc(f*x+e))/(-a+b))*EllipticE(sin(arcsin(sqrt(-(b+a*csc(f*x+e))/(a-b)))),sqrt((-a+b)/(a+b)))*(1+sin(f*x+e))*tan(f*x+e)/f/sqrt(a*(1+csc(f*x+e))/(a-b))/sqrt(d*sin(f*x+e))/sqrt(a+b*sin(f*x+e)),1],
[sin(d*x+c)^2*(a+b*sin(d*x+c))*tan(d*x+c)^5,x,11,35/8*b*arctanh(sin(d*x+c))/d+1/2*a*cos(d*x+c)^2/d-3*a*ln(cos(d*x+c))/d-3/2*a*sec(d*x+c)^2/d+1/4*a*sec(d*x+c)^4/d-3*b*sin(d*x+c)/d-1/3*b*sin(d*x+c)^3/d-13/8*b*sec(d*x+c)*tan(d*x+c)/d+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d,1],
[sin(d*x+c)*(a+b*sin(d*x+c))*tan(d*x+c)^5,x,11,15/8*a*arctanh(sin(d*x+c))/d+1/2*b*cos(d*x+c)^2/d-3*b*ln(cos(d*x+c))/d-3/2*b*sec(d*x+c)^2/d+1/4*b*sec(d*x+c)^4/d-a*sin(d*x+c)/d-9/8*a*sec(d*x+c)*tan(d*x+c)/d+1/4*a*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))*tan(d*x+c)^5,x,8,-1/16*(8*a+15*b)*ln(1-sin(d*x+c))/d-1/16*(8*a-15*b)*ln(1+sin(d*x+c))/d-b*sin(d*x+c)/d+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))/d-1/8*sec(d*x+c)^2*(8*a+9*b*sin(d*x+c))/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))*tan(d*x+c)^4,x,7,3/8*a*arctanh(sin(d*x+c))/d-b*ln(cos(d*x+c))/d-3/8*a*sec(d*x+c)*tan(d*x+c)/d-1/2*b*tan(d*x+c)^2/d+1/4*a*sec(d*x+c)*tan(d*x+c)^3/d+1/4*b*tan(d*x+c)^4/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))*tan(d*x+c)^3,x,6,3/8*b*arctanh(sin(d*x+c))/d-3/8*b*sec(d*x+c)*tan(d*x+c)/d+1/4*b*sec(d*x+c)*tan(d*x+c)^3/d+1/4*a*tan(d*x+c)^4/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))*tan(d*x+c)^2,x,6,-1/8*a*arctanh(sin(d*x+c))/d-1/8*a*sec(d*x+c)*tan(d*x+c)/d+1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+1/4*b*tan(d*x+c)^4/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))*tan(d*x+c),x,6,-1/8*b*arctanh(sin(d*x+c))/d+1/4*a*sec(d*x+c)^4/d-1/8*b*sec(d*x+c)*tan(d*x+c)/d+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d,1],
[csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c)),x,8,3/8*b*arctanh(sin(d*x+c))/d+a*ln(tan(d*x+c))/d+3/8*b*sec(d*x+c)*tan(d*x+c)/d+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d+a*tan(d*x+c)^2/d+1/4*a*tan(d*x+c)^4/d,1],
[csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c)),x,11,15/8*a*arctanh(sin(d*x+c))/d-a*csc(d*x+c)/d+b*ln(tan(d*x+c))/d+9/8*a*sec(d*x+c)*tan(d*x+c)/d+b*tan(d*x+c)^2/d+1/4*a*sec(d*x+c)*tan(d*x+c)^3/d+1/4*b*tan(d*x+c)^4/d,1],
[csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c)),x,11,15/8*b*arctanh(sin(d*x+c))/d-1/2*a*cot(d*x+c)^2/d-b*csc(d*x+c)/d+3*a*ln(tan(d*x+c))/d+9/8*b*sec(d*x+c)*tan(d*x+c)/d+3/2*a*tan(d*x+c)^2/d+1/4*b*sec(d*x+c)*tan(d*x+c)^3/d+1/4*a*tan(d*x+c)^4/d,1],
[csc(d*x+c)^4*sec(d*x+c)^5*(a+b*sin(d*x+c)),x,11,35/8*a*arctanh(sin(d*x+c))/d-1/2*b*cot(d*x+c)^2/d-3*a*csc(d*x+c)/d-1/3*a*csc(d*x+c)^3/d+3*b*ln(tan(d*x+c))/d+13/8*a*sec(d*x+c)*tan(d*x+c)/d+3/2*b*tan(d*x+c)^2/d+1/4*a*sec(d*x+c)*tan(d*x+c)^3/d+1/4*b*tan(d*x+c)^4/d,1],
[sin(d*x+c)*(a+b*sin(d*x+c))^2*tan(d*x+c)^5,x,9,-1/16*(15*a^2+48*a*b+35*b^2)*ln(1-sin(d*x+c))/d+1/16*(15*a^2-48*a*b+35*b^2)*ln(1+sin(d*x+c))/d-(a^2+3*b^2)*sin(d*x+c)/d-a*b*sin(d*x+c)^2/d-1/3*b^2*sin(d*x+c)^3/d-1/8*sec(d*x+c)^2*(20*a*b+(9*a^2+11*b^2)*sin(d*x+c))/d+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^2*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))^2*tan(d*x+c)^5,x,8,-1/8*(4*a^2+15*a*b+12*b^2)*ln(1-sin(d*x+c))/d+1/8*(-4*a^2+15*a*b-12*b^2)*ln(1+sin(d*x+c))/d-2*a*b*sin(d*x+c)/d-1/2*b^2*sin(d*x+c)^2/d+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^2/d-1/4*sec(d*x+c)^2*(4*a^2+5*b^2+9*a*b*sin(d*x+c))/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^2*tan(d*x+c)^4,x,9,-1/16*(3*a^2+16*a*b+15*b^2)*ln(1-sin(d*x+c))/d-1/16*(-3*a^2+16*a*b-15*b^2)*ln(1+sin(d*x+c))/d-b^2*sin(d*x+c)/d-1/8*sec(d*x+c)^2*(12*a*b+(5*a^2+7*b^2)*sin(d*x+c))/d+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^2*tan(d*x+c)/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^2*tan(d*x+c)^3,x,7,-1/8*b*(3*a+4*b)*ln(1-sin(d*x+c))/d+1/8*(3*a-4*b)*b*ln(1+sin(d*x+c))/d+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^2/d-1/4*sec(d*x+c)^2*(2*a^2+3*b^2+5*a*b*sin(d*x+c))/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^2*tan(d*x+c)^2,x,6,-1/8*(a^2-3*b^2)*arctanh(sin(d*x+c))/d-1/16*(a+b)*(a+3*b)/d/(1-sin(d*x+c))+1/16*(a-3*b)*(a-b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^2*tan(d*x+c)/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^2*tan(d*x+c),x,5,-1/4*a*b*arctanh(sin(d*x+c))/d-1/4*b*sec(d*x+c)^2*(b+a*sin(d*x+c))/d+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^2/d,1],
[csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x,6,-1/8*a*(4*a+3*b)*ln(1-sin(d*x+c))/d+a^2*ln(sin(d*x+c))/d-1/8*a*(4*a-3*b)*ln(1+sin(d*x+c))/d+1/4*a*sec(d*x+c)^2*(2*a+3*b*sin(d*x+c))/d+1/4*sec(d*x+c)^4*(a^2+b^2+2*a*b*sin(d*x+c))/d,1],
[csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x,10,3/8*(5*a^2+b^2)*arctanh(sin(d*x+c))/d-a^2*csc(d*x+c)/d-2*a*b*ln(cos(d*x+c))/d+2*a*b*ln(sin(d*x+c))/d+a*b*sec(d*x+c)^2/d+1/4*b*sec(d*x+c)^4*(2*a+(a^2+b^2)*sin(d*x+c)/b)/d+1/8*(7*a^2+3*b^2)*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x,10,15/4*a*b*arctanh(sin(d*x+c))/d-2*a*b*csc(d*x+c)/d-1/2*a^2*csc(d*x+c)^2/d-(3*a^2+b^2)*ln(cos(d*x+c))/d+(3*a^2+b^2)*ln(sin(d*x+c))/d+1/2*(2*a^2+b^2)*sec(d*x+c)^2/d+1/4*sec(d*x+c)^4*(a^2+b^2+2*a*b*sin(d*x+c))/d+7/4*a*b*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*sin(d*x+c))^3*tan(d*x+c)^5,x,4,-1/16*(a+b)*(8*a^2+37*a*b+35*b^2)*ln(1-sin(d*x+c))/d-1/16*(a-b)*(8*a^2-37*a*b+35*b^2)*ln(1+sin(d*x+c))/d-1/16*(a+b)^2*(8*a+11*b)/d/(1-sin(d*x+c))-3*b*(a^2+b^2)*sin(d*x+c)/d-3/2*a*b^2*sin(d*x+c)^2/d-1/3*b^3*sin(d*x+c)^3/d-1/16*(8*a-11*b)*(a-b)^2/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^3/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^3*tan(d*x+c)^4,x,5,-3/16*(a+b)*(a^2+7*a*b+8*b^2)*ln(1-sin(d*x+c))/d+3/16*(a-b)*(a^2-7*a*b+8*b^2)*ln(1+sin(d*x+c))/d-1/16*(a+b)^2*(5*a+8*b)/d/(1-sin(d*x+c))-3*a*b^2*sin(d*x+c)/d-1/2*b^3*sin(d*x+c)^2/d+1/16*(5*a-8*b)*(a-b)^2/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^3*tan(d*x+c)/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^3*tan(d*x+c)^3,x,5,-3/16*b*(a+b)*(3*a+5*b)*ln(1-sin(d*x+c))/d+3/16*(3*a-5*b)*(a-b)*b*ln(1+sin(d*x+c))/d-1/16*(a+b)^2*(4*a+7*b)/d/(1-sin(d*x+c))-b^3*sin(d*x+c)/d-1/16*(4*a-7*b)*(a-b)^2/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^3/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^3*tan(d*x+c)^2,x,5,1/16*(a^3-9*a*b^2-8*b^3)*ln(1-sin(d*x+c))/d-1/16*(a^3-9*a*b^2+8*b^3)*ln(1+sin(d*x+c))/d-1/16*(a+b)^2*(a+4*b)/d/(1-sin(d*x+c))+1/16*(a-4*b)*(a-b)^2/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^3*tan(d*x+c)/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^3*tan(d*x+c),x,5,-3/8*b*(a^2-b^2)*arctanh(sin(d*x+c))/d-3/8*b*sec(d*x+c)^2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d+1/4*sec(d*x+c)^4*(a+b*sin(d*x+c))^3/d,1],
[csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x,6,-1/16*(8*a^3+9*a^2*b-b^3)*ln(1-sin(d*x+c))/d+a^3*ln(sin(d*x+c))/d-1/16*(8*a^3-9*a^2*b+b^3)*ln(1+sin(d*x+c))/d+1/8*sec(d*x+c)^2*(4*a^3+b*(9*a^2-b^2)*sin(d*x+c))/d+1/4*sec(d*x+c)^4*(a*(a^2+3*b^2)+b*(3*a^2+b^2)*sin(d*x+c))/d,1],
[csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x,10,3/8*a*(5*a^2+3*b^2)*arctanh(sin(d*x+c))/d-a^3*csc(d*x+c)/d-3*a^2*b*ln(cos(d*x+c))/d+3*a^2*b*ln(sin(d*x+c))/d+3/2*a^2*b*sec(d*x+c)^2/d+1/4*b*sec(d*x+c)^4*(3*a^2+b^2+a*(3+a^2/b^2)*b*sin(d*x+c))/d+1/8*a*(7*a^2+9*b^2)*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x,10,3/8*b*(15*a^2+b^2)*arctanh(sin(d*x+c))/d-3*a^2*b*csc(d*x+c)/d-1/2*a^3*csc(d*x+c)^2/d-3*a*(a^2+b^2)*ln(cos(d*x+c))/d+3*a*(a^2+b^2)*ln(sin(d*x+c))/d+1/2*a*(2*a^2+3*b^2)*sec(d*x+c)^2/d+1/4*b^2*sec(d*x+c)^4*(a*(3+a^2/b^2)+(1+3*a^2/b^2)*b*sin(d*x+c))/d+3/8*b*(7*a^2+b^2)*sec(d*x+c)*tan(d*x+c)/d,1],
[sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x,8,-1/4*(6*a^2*b^2*(-n^2+1)-a^4*(n^2-4*n+3)-b^4*(n^2+4*n+3))*hypergeom([2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(-n^2+1)-b^4*sec(d*x+c)^2*sin(d*x+c)^(1+n)/d/(1-n)+a*b*(a^2*(2-n)-b^2*(2+n))*hypergeom([2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)+1/4*sec(d*x+c)^4*sin(d*x+c)^(1+n)*(a^4+6*a^2*b^2+b^4+4*a*b*(a^2+b^2)*sin(d*x+c))/d,1],
[sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x,7,1/4*a*(a^2*(3-n)-3*b^2*(1+n))*hypergeom([2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)+1/4*b*(3*a^2*(2-n)-b^2*(2+n))*hypergeom([2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)+1/4*sec(d*x+c)^4*sin(d*x+c)^(1+n)*(a*(a^2+3*b^2)+b*(3*a^2+b^2)*sin(d*x+c))/d,1],
[sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x,7,1/4*(a^2*(3-n)-b^2*(1+n))*hypergeom([2, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)+1/2*a*b*(2-n)*hypergeom([2, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n)+1/4*sec(d*x+c)^4*sin(d*x+c)^(1+n)*(a^2+b^2+2*a*b*sin(d*x+c))/d,1],
[sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x,6,a*hypergeom([3, 1/2+1/2*n],[3/2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(1+n)/d/(1+n)+b*hypergeom([3, 1+1/2*n],[2+1/2*n],sin(d*x+c)^2)*sin(d*x+c)^(2+n)/d/(2+n),1],
[sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x,10,1/16*(3*a^2-9*a*b+8*b^2)*hypergeom([1, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/(a-b)^3/d/(1+n)+1/16*(3*a^2+9*a*b+8*b^2)*hypergeom([1, 1+n],[2+n],sin(d*x+c))*sin(d*x+c)^(1+n)/(a+b)^3/d/(1+n)-b^6*hypergeom([1, 1+n],[2+n],-b*sin(d*x+c)/a)*sin(d*x+c)^(1+n)/a/(a^2-b^2)^3/d/(1+n)+1/16*(3*a-5*b)*hypergeom([2, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/(a-b)^2/d/(1+n)+1/16*(3*a+5*b)*hypergeom([2, 1+n],[2+n],sin(d*x+c))*sin(d*x+c)^(1+n)/(a+b)^2/d/(1+n)+1/8*hypergeom([3, 1+n],[2+n],-sin(d*x+c))*sin(d*x+c)^(1+n)/(a-b)/d/(1+n)+1/8*hypergeom([3, 1+n],[2+n],sin(d*x+c))*sin(d*x+c)^(1+n)/(a+b)/d/(1+n),1],
[sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x,17,3/16*AppellF1(1+n,-p,1,2+n,-b*sin(d*x+c)/a,-sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p)+3/16*AppellF1(1+n,-p,1,2+n,-b*sin(d*x+c)/a,sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p)+3/16*AppellF1(1+n,-p,2,2+n,-b*sin(d*x+c)/a,-sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p)+3/16*AppellF1(1+n,-p,2,2+n,-b*sin(d*x+c)/a,sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p)+1/8*AppellF1(1+n,-p,3,2+n,-b*sin(d*x+c)/a,-sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p)+1/8*AppellF1(1+n,-p,3,2+n,-b*sin(d*x+c)/a,sin(d*x+c))*sin(d*x+c)^(1+n)*(a+b*sin(d*x+c))^p/d/(1+n)/((1+b*sin(d*x+c)/a)^p),1],
[sec(f*x+e)^6*(a+b*sin(f*x+e))^(9/2)/sqrt(d*sin(f*x+e)),x,-1,-3/5*a*b*(-2*a^2+b^2)*cos(f*x+e)*sqrt(a+b*sin(f*x+e))/f/sqrt(d*sin(f*x+e))+1/5*sec(f*x+e)^5*sqrt(d*sin(f*x+e))*(a+b*sin(f*x+e))^(9/2)/d/f-3/20*a*sec(f*x+e)^3*sqrt(d*sin(f*x+e))*sqrt(a+b*sin(f*x+e))*(-a*(7*a^2+b^2)+2*b*(-7*a^2+b^2)*sin(f*x+e)+5*a*(a^2-b^2)*sin(f*x+e)^2+(8*a^2*b-4*b^3)*sin(f*x+e)^3)/d/f-3/20*a*(a+b)^(3/2)*(5*a^2+3*a*b-4*b^2)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*sqrt(a*(1+csc(f*x+e))/(a-b))*InverseJacobiAM(arcsin(sqrt(d)*sqrt(a+b*sin(f*x+e))/sqrt(a+b)/sqrt(d*sin(f*x+e))),sqrt(-(a+b)/(a-b)))*tan(f*x+e)/sqrt(d)/f-3/5*b*(2*a^4-3*a^2*b^2+b^4)*sqrt(-a*(-1+csc(f*x+e))/(a+b))*EllipticE(sin(arcsin(sqrt(-(b+a*csc(f*x+e))/(a-b)))),sqrt(1-2*a/(a+b)))*sqrt(d*sin(f*x+e))*sqrt(-a*csc(f*x+e)^2*(1+sin(f*x+e))*(a+b*sin(f*x+e))/(a-b)^2)*tan(f*x+e)/d/f/sqrt(a+b*sin(f*x+e)),1],
[cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x,9,-9/2080*(64*a*b*c*d-26*a^2*d^2-b^2*(18*c^2-13*d^2))*cos(f*x+e)*(c+d*sin(f*x+e))^(7/3)/d^3/f-9/208*b*(-2*a*d+3*b*c)*cos(f*x+e)*sin(f*x+e)*(c+d*sin(f*x+e))^(7/3)/d^2/f+3/16*cos(f*x+e)*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(7/3)/d/f-3/1040*(208*a^2*c*d^2-64*a*b*d*(3*c^2-5*d^2)+b^2*c*(54*c^2+d^2))*AppellF1(1/2,1/2,-7/3,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(7/3)/sqrt(2)/d^4/f/sqrt(1+sin(f*x+e))/((c+d*sin(f*x+e))/(c+d))^(7/3)-3/1040*(c^2-d^2)*(192*a*b*c*d-208*a^2*d^2-b^2*(54*c^2+91*d^2))*AppellF1(1/2,1/2,-4/3,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(4/3)/sqrt(2)/d^4/f/sqrt(1+sin(f*x+e))/((c+d*sin(f*x+e))/(c+d))^(4/3),1],
[cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x,8,-3/130*(-13*a*d+6*b*c)*cos(f*x+e)*(c+d*sin(f*x+e))^(7/3)/d^2/f+3/13*b*cos(f*x+e)*sin(f*x+e)*(c+d*sin(f*x+e))^(7/3)/d/f+3/65*(-13*a*c*d+6*b*c^2-10*b*d^2)*AppellF1(1/2,1/2,-7/3,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(7/3)/sqrt(2)/d^3/f/sqrt(1+sin(f*x+e))/((c+d*sin(f*x+e))/(c+d))^(7/3)-3/65*(-13*a*d+6*b*c)*(c^2-d^2)*AppellF1(1/2,1/2,-4/3,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(4/3)/sqrt(2)/d^3/f/sqrt(1+sin(f*x+e))/((c+d*sin(f*x+e))/(c+d))^(4/3),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x,2,-2/3*sqrt(2)*AppellF1(3/2,-1/2,-4/3,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^(4/3)/f/sqrt(1+sin(f*x+e))/((c+d*sin(f*x+e))/(c+d))^(4/3),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x,0,Defer(Int)(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x),0],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x,0,Defer(Int)(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x),0],
[cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x,0,Defer(Int)(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x),0],
[cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x,0,Defer(Int)(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x),0],
[cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x,9,(2*a^2*d^2*(3+n)-4*a*b*c*d*(4+n)+b^2*(6*c^2-d^2*(3+n)))*cos(f*x+e)*(c+d*sin(f*x+e))^(1+n)/d^3/f/(2+n)/(3+n)/(4+n)-b*(-2*a*d+3*b*c)*cos(f*x+e)*sin(f*x+e)*(c+d*sin(f*x+e))^(1+n)/d^2/f/(3+n)/(4+n)+cos(f*x+e)*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1+n)/d/f/(4+n)-sqrt(2)*(a^2*c*d^2*(n^2+7*n+12)-2*a*b*d*(4+n)*(2*c^2-d^2*(2+n))+b^2*c*(6*c^2-d^2*(-n^2-n+3)))*AppellF1(1/2,1/2,-1-n,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(1+n)*((c+d*sin(f*x+e))/(c+d))^(-1-n)/d^4/f/(2+n)/(3+n)/(4+n)/sqrt(1+sin(f*x+e))-sqrt(2)*(c^2-d^2)*(4*a*b*c*d*(4+n)-a^2*d^2*(n^2+7*n+12)-b^2*(6*c^2+d^2*(n^2+4*n+3)))*AppellF1(1/2,1/2,-n,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^n/d^4/f/(2+n)/(3+n)/(4+n)/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x,8,-(2*b*c-a*d*(3+n))*cos(f*x+e)*(c+d*sin(f*x+e))^(1+n)/d^2/f/(2+n)/(3+n)+b*cos(f*x+e)*sin(f*x+e)*(c+d*sin(f*x+e))^(1+n)/d/f/(3+n)-sqrt(2)*(a*c*d*(3+n)-b*(2*c^2-d^2*(2+n)))*AppellF1(1/2,1/2,-1-n,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^(1+n)*((c+d*sin(f*x+e))/(c+d))^(-1-n)/d^3/f/(2+n)/(3+n)/sqrt(1+sin(f*x+e))-sqrt(2)*(c^2-d^2)*(2*b*c-a*d*(3+n))*AppellF1(1/2,1/2,-n,3/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(c+d*sin(f*x+e))^n/d^3/f/(2+n)/(3+n)/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x,2,-2/3*sqrt(2)*AppellF1(3/2,-1/2,-n,5/2,1/2-1/2*sin(f*x+e),d*(1-sin(f*x+e))/(c+d))*cos(f*x+e)*(1-sin(f*x+e))*(c+d*sin(f*x+e))^n/f/sqrt(1+sin(f*x+e))/(((c+d*sin(f*x+e))/(c+d))^n),1],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x,0,Defer(Int)(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x),0],
[cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x,0,Defer(Int)(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x),0],
[cos(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,a*A*sin(d*x+c)/d+1/2*(A*b+B*a)*sin(d*x+c)^2/d-1/3*(3*A*a-B*b)*sin(d*x+c)^3/d-3/4*(A*b+B*a)*sin(d*x+c)^4/d+3/5*(A*a-B*b)*sin(d*x+c)^5/d+1/2*(A*b+B*a)*sin(d*x+c)^6/d-1/7*(A*a-3*B*b)*sin(d*x+c)^7/d-1/8*(A*b+B*a)*sin(d*x+c)^8/d-1/9*b*B*sin(d*x+c)^9/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,a*A*sin(d*x+c)/d+1/2*(A*b+B*a)*sin(d*x+c)^2/d-1/3*(2*A*a-B*b)*sin(d*x+c)^3/d-1/2*(A*b+B*a)*sin(d*x+c)^4/d+1/5*(A*a-2*B*b)*sin(d*x+c)^5/d+1/6*(A*b+B*a)*sin(d*x+c)^6/d+1/7*b*B*sin(d*x+c)^7/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,a*A*sin(d*x+c)/d+1/2*(A*b+B*a)*sin(d*x+c)^2/d-1/3*(A*a-B*b)*sin(d*x+c)^3/d-1/4*(A*b+B*a)*sin(d*x+c)^4/d-1/5*b*B*sin(d*x+c)^5/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,3,a*A*sin(d*x+c)/d+1/2*(A*b+B*a)*sin(d*x+c)^2/d+1/3*b*B*sin(d*x+c)^3/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,6,-1/2*(a+b)*(A+B)*ln(1-sin(d*x+c))/d+1/2*(a-b)*(A-B)*ln(1+sin(d*x+c))/d-b*B*sin(d*x+c)/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/2*(A*a-B*b)*arctanh(sin(d*x+c))/d+1/4*(a+b)*(A+B)/d/(1-sin(d*x+c))-1/4*(a-b)*(A-B)/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/8*(3*A*a-B*b)*arctanh(sin(d*x+c))/d+1/16*(a+b)*(A+B)/d/(1-sin(d*x+c))^2+1/16*(b*(A-B)+a*(3*A+B))/d/(1-sin(d*x+c))-1/16*(a-b)*(A-B)/d/(1+sin(d*x+c))^2-1/16*(a*(3*A-B)-b*(A+B))/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x,4,1/16*(5*A*a-B*b)*arctanh(sin(d*x+c))/d+1/48*(a+b)*(A+B)/d/(1-sin(d*x+c))^3+1/32*(A*b+a*(2*A+B))/d/(1-sin(d*x+c))^2+1/32*(b*(A-B)+a*(5*A+B))/d/(1-sin(d*x+c))-1/48*(a-b)*(A-B)/d/(1+sin(d*x+c))^3+1/32*(A*b-a*(2*A-B))/d/(1+sin(d*x+c))^2-1/32*(a*(5*A-B)-b*(A+B))/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,-1/3*(a^2-b^2)^3*(A*b-B*a)*(a+b*sin(d*x+c))^3/b^8/d+1/4*(a^2-b^2)^2*(6*A*a*b-7*B*a^2+B*b^2)*(a+b*sin(d*x+c))^4/b^8/d-3/5*(a^2-b^2)*(5*A*a^2*b-A*b^3-7*B*a^3+3*B*a*b^2)*(a+b*sin(d*x+c))^5/b^8/d+1/6*(20*A*a^3*b-12*A*a*b^3-35*B*a^4+30*B*a^2*b^2-3*B*b^4)*(a+b*sin(d*x+c))^6/b^8/d-1/7*(15*A*a^2*b-3*A*b^3-35*B*a^3+15*B*a*b^2)*(a+b*sin(d*x+c))^7/b^8/d+3/8*(2*A*a*b-7*B*a^2+B*b^2)*(a+b*sin(d*x+c))^8/b^8/d-1/9*(A*b-7*B*a)*(a+b*sin(d*x+c))^9/b^8/d-1/10*B*(a+b*sin(d*x+c))^10/b^8/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,1/3*(a^2-b^2)^2*(A*b-B*a)*(a+b*sin(d*x+c))^3/b^6/d-1/4*(a^2-b^2)*(4*A*a*b-5*B*a^2+B*b^2)*(a+b*sin(d*x+c))^4/b^6/d+2/5*(3*A*a^2*b-A*b^3-5*B*a^3+3*B*a*b^2)*(a+b*sin(d*x+c))^5/b^6/d-1/3*(2*A*a*b-5*B*a^2+B*b^2)*(a+b*sin(d*x+c))^6/b^6/d+1/7*(A*b-5*B*a)*(a+b*sin(d*x+c))^7/b^6/d+1/8*B*(a+b*sin(d*x+c))^8/b^6/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,-1/3*(a^2-b^2)*(A*b-B*a)*(a+b*sin(d*x+c))^3/b^4/d+1/4*(2*A*a*b-3*B*a^2+B*b^2)*(a+b*sin(d*x+c))^4/b^4/d-1/5*(A*b-3*B*a)*(a+b*sin(d*x+c))^5/b^4/d-1/6*B*(a+b*sin(d*x+c))^6/b^4/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,1/3*(A*b-B*a)*(a+b*sin(d*x+c))^3/b^2/d+1/4*B*(a+b*sin(d*x+c))^4/b^2/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,6,-1/2*(a+b)^2*(A+B)*ln(1-sin(d*x+c))/d+1/2*(a-b)^2*(A-B)*ln(1+sin(d*x+c))/d-b*(A*b+2*B*a)*sin(d*x+c)/d-1/2*b^2*B*sin(d*x+c)^2/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,3,-1/4*(a+b)*(a*A-b*(A+2*B))*ln(1-sin(d*x+c))/d+1/4*(a-b)*(a*A+b*(A-2*B))*ln(1+sin(d*x+c))/d+1/4*(a+b)^2*(A+B)/d/(1-sin(d*x+c))-1/4*(a-b)^2*(A-B)/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/8*(3*A*a^2-A*b^2-2*B*a*b)*arctanh(sin(d*x+c))/d+1/16*(a+b)^2*(A+B)/d/(1-sin(d*x+c))^2+1/16*(a+b)*(a*(3*A+B)-b*(A+3*B))/d/(1-sin(d*x+c))-1/16*(a-b)^2*(A-B)/d/(1+sin(d*x+c))^2-1/16*(a-b)*(3*A*a+A*b-B*a-3*B*b)/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x,4,1/16*(5*A*a^2-A*b^2-2*B*a*b)*arctanh(sin(d*x+c))/d+1/48*(a+b)^2*(A+B)/d/(1-sin(d*x+c))^3-1/32*(a+b)*(b*B-a*(2*A+B))/d/(1-sin(d*x+c))^2+1/32*(2*a*b*(A-B)-b^2*(A+B)+a^2*(5*A+B))/d/(1-sin(d*x+c))-1/48*(a-b)^2*(A-B)/d/(1+sin(d*x+c))^3-1/32*(a-b)*(2*A*a-B*a-B*b)/d/(1+sin(d*x+c))^2+1/32*(b^2*(A-B)-a^2*(5*A-B)+2*a*b*(A+B))/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-(a^2-b^2)^3*(A*b-B*a)*ln(a+b*sin(d*x+c))/b^8/d+(A*a^5*b-3*A*a^3*b^3+3*A*a*b^5-B*a^6+3*B*a^4*b^2-3*B*a^2*b^4+B*b^6)*sin(d*x+c)/b^7/d-1/2*(a^4-3*a^2*b^2+3*b^4)*(A*b-B*a)*sin(d*x+c)^2/b^6/d+1/3*(A*a^3*b-3*A*a*b^3-B*a^4+3*B*a^2*b^2-3*B*b^4)*sin(d*x+c)^3/b^5/d-1/4*(a^2-3*b^2)*(A*b-B*a)*sin(d*x+c)^4/b^4/d+1/5*(A*a*b-B*a^2+3*B*b^2)*sin(d*x+c)^5/b^3/d-1/6*(A*b-B*a)*sin(d*x+c)^6/b^2/d-1/7*B*sin(d*x+c)^7/b/d,1],
[cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,(a^2-b^2)^2*(A*b-B*a)*ln(a+b*sin(d*x+c))/b^6/d-(A*a^3*b-2*A*a*b^3-B*a^4+2*B*a^2*b^2-B*b^4)*sin(d*x+c)/b^5/d+1/2*(a^2-2*b^2)*(A*b-B*a)*sin(d*x+c)^2/b^4/d-1/3*(A*a*b-B*a^2+2*B*b^2)*sin(d*x+c)^3/b^3/d+1/4*(A*b-B*a)*sin(d*x+c)^4/b^2/d+1/5*B*sin(d*x+c)^5/b/d,1],
[cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-(a^2-b^2)*(A*b-B*a)*ln(a+b*sin(d*x+c))/b^4/d+(A*a*b-B*a^2+B*b^2)*sin(d*x+c)/b^3/d-1/2*(A*b-B*a)*sin(d*x+c)^2/b^2/d-1/3*B*sin(d*x+c)^3/b/d,1],
[cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,(A*b-B*a)*ln(a+b*sin(d*x+c))/b^2/d+B*sin(d*x+c)/b/d,1],
[sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-1/2*(A+B)*ln(1-sin(d*x+c))/(a+b)/d+1/2*(A-B)*ln(1+sin(d*x+c))/(a-b)/d-(A*b-B*a)*ln(a+b*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-1/4*(a*A+b*(2*A+B))*ln(1-sin(d*x+c))/(a+b)^2/d+1/4*(a*A-b*(2*A-B))*ln(1+sin(d*x+c))/(a-b)^2/d+b^2*(A*b-B*a)*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+1/4*(A+B)/(a+b)/d/(1-sin(d*x+c))-1/4*(A-B)/(a-b)/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-1/16*(3*a^2*A+a*b*(9*A+B)+b^2*(8*A+3*B))*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*(3*a^2*A+b^2*(8*A-3*B)-a*b*(9*A-B))*ln(1+sin(d*x+c))/(a-b)^3/d-b^4*(A*b-B*a)*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/16*(A+B)/(a+b)/d/(1-sin(d*x+c))^2+1/16*(3*A*a+5*A*b+B*a+3*B*b)/(a+b)^2/d/(1-sin(d*x+c))-1/16*(A-B)/(a-b)/d/(1+sin(d*x+c))^2-1/16*(3*A*a-5*A*b-B*a+3*B*b)/(a-b)^2/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x,3,-1/32*(5*a^3*A+a^2*b*(20*A+B)+a*b^2*(29*A+4*B)+b^3*(16*A+5*B))*ln(1-sin(d*x+c))/(a+b)^4/d+1/32*(5*a^3*A-b^3*(16*A-5*B)+a*b^2*(29*A-4*B)-a^2*b*(20*A-B))*ln(1+sin(d*x+c))/(a-b)^4/d+b^6*(A*b-B*a)*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d+1/48*(A+B)/(a+b)/d/(1-sin(d*x+c))^3+1/32*(2*A*a+3*A*b+B*a+2*B*b)/(a+b)^2/d/(1-sin(d*x+c))^2+1/32*(a^2*(5*A+B)+2*a*b*(7*A+2*B)+b^2*(11*A+5*B))/(a+b)^3/d/(1-sin(d*x+c))-1/48*(A-B)/(a-b)/d/(1+sin(d*x+c))^3-1/32*(2*A*a-3*A*b-B*a+2*B*b)/(a-b)^2/d/(1+sin(d*x+c))^2-1/32*(b^2*(11*A-5*B)+a^2*(5*A-B)-a*(14*A*b-4*B*b))/(a-b)^3/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,(a^2-b^2)^2*(6*A*a*b-7*B*a^2+B*b^2)*ln(a+b*sin(d*x+c))/b^8/d-(5*A*a^4*b-9*A*a^2*b^3+3*A*b^5-6*B*a^5+12*B*a^3*b^2-6*B*a*b^4)*sin(d*x+c)/b^7/d+1/2*(4*A*a^3*b-6*A*a*b^3-5*B*a^4+9*B*a^2*b^2-3*B*b^4)*sin(d*x+c)^2/b^6/d-1/3*(3*A*a^2*b-3*A*b^3-4*B*a^3+6*B*a*b^2)*sin(d*x+c)^3/b^5/d+1/4*(2*A*a*b-3*B*a^2+3*B*b^2)*sin(d*x+c)^4/b^4/d-1/5*(A*b-2*B*a)*sin(d*x+c)^5/b^3/d-1/6*B*sin(d*x+c)^6/b^2/d+(a^2-b^2)^3*(A*b-B*a)/b^8/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,-(a^2-b^2)*(4*A*a*b-5*B*a^2+B*b^2)*ln(a+b*sin(d*x+c))/b^6/d+(3*A*a^2*b-2*A*b^3-4*B*a^3+4*B*a*b^2)*sin(d*x+c)/b^5/d-1/2*(2*A*a*b-3*B*a^2+2*B*b^2)*sin(d*x+c)^2/b^4/d+1/3*(A*b-2*B*a)*sin(d*x+c)^3/b^3/d+1/4*B*sin(d*x+c)^4/b^2/d-(a^2-b^2)^2*(A*b-B*a)/b^6/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,(2*A*a*b-3*B*a^2+B*b^2)*ln(a+b*sin(d*x+c))/b^4/d-(A*b-2*B*a)*sin(d*x+c)/b^3/d-1/2*B*sin(d*x+c)^2/b^2/d+(a^2-b^2)*(A*b-B*a)/b^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,B*ln(a+b*sin(d*x+c))/b^2/d-(A*b-B*a)/b^2/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,-1/2*(A+B)*ln(1-sin(d*x+c))/(a+b)^2/d+1/2*(A-B)*ln(1+sin(d*x+c))/(a-b)^2/d-(2*A*a*b-B*a^2-B*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+(A*b-B*a)/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,-1/4*(A*a+3*A*b+2*B*b)*ln(1-sin(d*x+c))/(a+b)^3/d+1/4*(A*a-3*A*b+2*B*b)*ln(1+sin(d*x+c))/(a-b)^3/d+b^2*(4*A*a*b-3*B*a^2-B*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/4*(A+B)/(a+b)^2/d/(1-sin(d*x+c))-1/4*(A-B)/(a-b)^2/d/(1+sin(d*x+c))-b^2*(A*b-B*a)/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,-1/16*(3*a^2*A+2*a*b*(6*A+B)+b^2*(15*A+8*B))*ln(1-sin(d*x+c))/(a+b)^4/d+1/16*(3*a^2*A+b^2*(15*A-8*B)-2*a*b*(6*A-B))*ln(1+sin(d*x+c))/(a-b)^4/d-b^4*(6*A*a*b-5*B*a^2-B*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d+1/16*(A+B)/(a+b)^2/d/(1-sin(d*x+c))^2+1/16*(3*A*a+7*A*b+B*a+5*B*b)/(a+b)^3/d/(1-sin(d*x+c))-1/16*(A-B)/(a-b)^2/d/(1+sin(d*x+c))^2-1/16*(3*A*a-7*A*b-B*a+5*B*b)/(a-b)^3/d/(1+sin(d*x+c))+b^4*(A*b-B*a)/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x,3,-1/32*(5*a^3*A+a^2*b*(25*A+2*B)+a*b^2*(47*A+10*B)+b^3*(35*A+16*B))*ln(1-sin(d*x+c))/(a+b)^5/d+1/32*(5*a^3*A-b^3*(35*A-16*B)+a*b^2*(47*A-10*B)-a^2*(25*A*b-2*B*b))*ln(1+sin(d*x+c))/(a-b)^5/d+b^6*(8*A*a*b-7*B*a^2-B*b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^5/d+1/48*(A+B)/(a+b)^2/d/(1-sin(d*x+c))^3+1/32*(2*A*a+4*A*b+B*a+3*B*b)/(a+b)^3/d/(1-sin(d*x+c))^2+1/32*(6*a*b*(3*A+B)+a^2*(5*A+B)+b^2*(19*A+11*B))/(a+b)^4/d/(1-sin(d*x+c))-1/48*(A-B)/(a-b)^2/d/(1+sin(d*x+c))^3-1/32*(2*A*a-4*A*b-B*a+3*B*b)/(a-b)^3/d/(1+sin(d*x+c))^2-1/32*(b^2*(19*A-11*B)-6*a*b*(3*A-B)+a^2*(5*A-B))/(a-b)^4/d/(1+sin(d*x+c))-b^6*(A*b-B*a)/(a^2-b^2)^4/d/(a+b*sin(d*x+c)),1],
[(g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x,0,Defer(Int)((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x),0],
[(g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x,4,-g*AppellF1(1-p,1/2-1/2*p,1/2-1/2*p,2-p,(a+b)/(a+b*sin(f*x+e)),(a-b)/(a+b*sin(f*x+e)))*(g*cos(f*x+e))^(-1+p)*(-b*(1-sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2-1/2*p)*(b*(1+sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2-1/2*p)/(-a*d+b*c)/f/(1-p)+g*AppellF1(1-p,1/2-1/2*p,1/2-1/2*p,2-p,(c+d)/(c+d*sin(f*x+e)),(c-d)/(c+d*sin(f*x+e)))*(g*cos(f*x+e))^(-1+p)*(-d*(1-sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)*(d*(1+sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)/(-a*d+b*c)/f/(1-p),1],
[(g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x,5,-b*g*AppellF1(1-p,1/2-1/2*p,1/2-1/2*p,2-p,(a+b)/(a+b*sin(f*x+e)),(a-b)/(a+b*sin(f*x+e)))*(g*cos(f*x+e))^(-1+p)*(-b*(1-sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2-1/2*p)*(b*(1+sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2-1/2*p)/(-a*d+b*c)^2/f/(1-p)+b*g*AppellF1(1-p,1/2-1/2*p,1/2-1/2*p,2-p,(c+d)/(c+d*sin(f*x+e)),(c-d)/(c+d*sin(f*x+e)))*(g*cos(f*x+e))^(-1+p)*(-d*(1-sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)*(d*(1+sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)/(-a*d+b*c)^2/f/(1-p)+g*AppellF1(2-p,1/2-1/2*p,1/2-1/2*p,3-p,(c+d)/(c+d*sin(f*x+e)),(c-d)/(c+d*sin(f*x+e)))*(g*cos(f*x+e))^(-1+p)*(-d*(1-sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)*(d*(1+sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2-1/2*p)/(-a*d+b*c)/f/(2-p)/(c+d*sin(f*x+e)),1],
[(g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x,5,-AppellF1(p+1,1/2*p+1/2,1/2*p+1/2,2+p,(a+b)/(a+b*sin(f*x+e)),(a-b)/(a+b*sin(f*x+e)))*sec(f*x+e)*(g*sec(f*x+e))^p*(-b*(1-sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2*p+1/2)*(b*(1+sin(f*x+e))/(a+b*sin(f*x+e)))^(1/2*p+1/2)/(-a*d+b*c)/f/(p+1)+AppellF1(p+1,1/2*p+1/2,1/2*p+1/2,2+p,(c+d)/(c+d*sin(f*x+e)),(c-d)/(c+d*sin(f*x+e)))*sec(f*x+e)*(g*sec(f*x+e))^p*(-d*(1-sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2*p+1/2)*(d*(1+sin(f*x+e))/(c+d*sin(f*x+e)))^(1/2*p+1/2)/(-a*d+b*c)/f/(p+1),1]]: