lst:=[[sin(x)^4/(I+tan(x)),x,5,-1/16*I*x-1/32/(I-tan(x))^2-1/8*I/(I-tan(x))+1/24*I/(I+tan(x))^3-5/32/(I+tan(x))^2-3/16*I/(I+tan(x)),1],
[sin(x)^3/(I+tan(x)),x,9,1/3*I*cos(x)^3-1/5*I*cos(x)^5+1/5*sin(x)^5,1],
[sin(x)^2/(I+tan(x)),x,5,-1/8*I*x-1/8*I/(I-tan(x))-1/8/(I+tan(x))^2-1/4*I/(I+tan(x)),1],
[sin(x)/(I+tan(x)),x,8,1/3*I*cos(x)^3+1/3*sin(x)^3,1],
[csc(x)/(I+tan(x)),x,8,I*arctanh(cos(x))-I*cos(x)+sin(x),1],
[csc(x)^2/(I+tan(x)),x,3,I*x+I*cot(x)+ln(cos(x))+ln(tan(x)),1],
[csc(x)^3/(I+tan(x)),x,8,-1/2*I*arctanh(cos(x))-csc(x)+1/2*I*cot(x)*csc(x),1],
[csc(x)^4/(I+tan(x)),x,4,-1/2*cot(x)^2+1/3*I*cot(x)^3,1],
[csc(x)^5/(I+tan(x)),x,9,-1/8*I*arctanh(cos(x))-1/8*I*cot(x)*csc(x)-1/3*csc(x)^3+1/4*I*cot(x)*csc(x)^3,1],
[csc(x)^6/(I+tan(x)),x,4,-1/2*cot(x)^2+1/3*I*cot(x)^3-1/4*cot(x)^4+1/5*I*cot(x)^5,1],
[sin(d*x+c)^5*(a+b*tan(d*x+c)),x,8,b*arctanh(sin(d*x+c))/d-a*cos(d*x+c)/d+2/3*a*cos(d*x+c)^3/d-1/5*a*cos(d*x+c)^5/d-b*sin(d*x+c)/d-1/3*b*sin(d*x+c)^3/d-1/5*b*sin(d*x+c)^5/d,1],
[sin(d*x+c)^4*(a+b*tan(d*x+c)),x,8,3/8*a*x+b*cos(d*x+c)^2/d-b*ln(cos(d*x+c))/d-5/8*a*cos(d*x+c)*sin(d*x+c)/d-1/4*cos(d*x+c)^4*(b-a*tan(d*x+c))/d,1],
[sin(d*x+c)^3*(a+b*tan(d*x+c)),x,8,b*arctanh(sin(d*x+c))/d-a*cos(d*x+c)/d+1/3*a*cos(d*x+c)^3/d-b*sin(d*x+c)/d-1/3*b*sin(d*x+c)^3/d,1],
[sin(d*x+c)^2*(a+b*tan(d*x+c)),x,5,1/2*a*x-b*ln(cos(d*x+c))/d+1/2*cos(d*x+c)^2*(b-a*tan(d*x+c))/d,1],
[sin(d*x+c)*(a+b*tan(d*x+c)),x,6,b*arctanh(sin(d*x+c))/d-a*cos(d*x+c)/d-b*sin(d*x+c)/d,1],
[csc(d*x+c)*(a+b*tan(d*x+c)),x,4,-a*arctanh(cos(d*x+c))/d+b*arctanh(sin(d*x+c))/d,1],
[csc(d*x+c)^2*(a+b*tan(d*x+c)),x,3,-a*cot(d*x+c)/d+b*ln(tan(d*x+c))/d,1],
[csc(d*x+c)^3*(a+b*tan(d*x+c)),x,7,-1/2*a*arctanh(cos(d*x+c))/d+b*arctanh(sin(d*x+c))/d-b*csc(d*x+c)/d-1/2*a*cot(d*x+c)*csc(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*tan(d*x+c)),x,3,-a*cot(d*x+c)/d-1/2*b*cot(d*x+c)^2/d-1/3*a*cot(d*x+c)^3/d+b*ln(tan(d*x+c))/d,1],
[csc(d*x+c)^5*(a+b*tan(d*x+c)),x,9,-3/8*a*arctanh(cos(d*x+c))/d+b*arctanh(sin(d*x+c))/d-b*csc(d*x+c)/d-3/8*a*cot(d*x+c)*csc(d*x+c)/d-1/3*b*csc(d*x+c)^3/d-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d,1],
[csc(d*x+c)^6*(a+b*tan(d*x+c)),x,3,-a*cot(d*x+c)/d-b*cot(d*x+c)^2/d-2/3*a*cot(d*x+c)^3/d-1/4*b*cot(d*x+c)^4/d-1/5*a*cot(d*x+c)^5/d+b*ln(tan(d*x+c))/d,1],
[sin(d*x+c)^4*(a+b*tan(d*x+c))^2,x,9,3/8*(a^2-5*b^2)*x+3/2*a*b*cos(d*x+c)^2/d-2*a*b*ln(cos(d*x+c))/d-1/8*(5*a^2-7*b^2)*cos(d*x+c)*sin(d*x+c)/d+b^2*tan(d*x+c)/d+1/4*cos(d*x+c)^3*sin(d*x+c)*(a+b*tan(d*x+c))^2/d,1],
[sin(d*x+c)^3*(a+b*tan(d*x+c))^2,x,11,2*a*b*arctanh(sin(d*x+c))/d-a^2*cos(d*x+c)/d+2*b^2*cos(d*x+c)/d+1/3*a^2*cos(d*x+c)^3/d-1/3*b^2*cos(d*x+c)^3/d+b^2*sec(d*x+c)/d-2*a*b*sin(d*x+c)/d-2/3*a*b*sin(d*x+c)^3/d,1],
[sin(d*x+c)^2*(a+b*tan(d*x+c))^2,x,7,1/2*(a^2-3*b^2)*x-2*a*b*ln(cos(d*x+c))/d+3/2*b^2*tan(d*x+c)/d-1/2*cos(d*x+c)*sin(d*x+c)*(a+b*tan(d*x+c))^2/d,1],
[sin(d*x+c)*(a+b*tan(d*x+c))^2,x,9,2*a*b*arctanh(sin(d*x+c))/d-a^2*cos(d*x+c)/d+b^2*cos(d*x+c)/d+b^2*sec(d*x+c)/d-2*a*b*sin(d*x+c)/d,1],
[csc(d*x+c)*(a+b*tan(d*x+c))^2,x,6,-a^2*arctanh(cos(d*x+c))/d+2*a*b*arctanh(sin(d*x+c))/d+b^2*sec(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*tan(d*x+c))^2,x,3,-a^2*cot(d*x+c)/d+2*a*b*ln(tan(d*x+c))/d+b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^3*(a+b*tan(d*x+c))^2,x,10,-1/2*a^2*arctanh(cos(d*x+c))/d-b^2*arctanh(cos(d*x+c))/d+2*a*b*arctanh(sin(d*x+c))/d-2*a*b*csc(d*x+c)/d-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d+b^2*sec(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*tan(d*x+c))^2,x,3,-(a^2+b^2)*cot(d*x+c)/d-a*b*cot(d*x+c)^2/d-1/3*a^2*cot(d*x+c)^3/d+2*a*b*ln(tan(d*x+c))/d+b^2*tan(d*x+c)/d,1],
[csc(d*x+c)^5*(a+b*tan(d*x+c))^2,x,13,-3/8*a^2*arctanh(cos(d*x+c))/d-3/2*b^2*arctanh(cos(d*x+c))/d+2*a*b*arctanh(sin(d*x+c))/d-2*a*b*csc(d*x+c)/d-3/8*a^2*cot(d*x+c)*csc(d*x+c)/d-2/3*a*b*csc(d*x+c)^3/d-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d+3/2*b^2*sec(d*x+c)/d-1/2*b^2*csc(d*x+c)^2*sec(d*x+c)/d,1],
[csc(d*x+c)^6*(a+b*tan(d*x+c))^2,x,3,-(a^2+2*b^2)*cot(d*x+c)/d-2*a*b*cot(d*x+c)^2/d-1/3*(2*a^2+b^2)*cot(d*x+c)^3/d-1/2*a*b*cot(d*x+c)^4/d-1/5*a^2*cot(d*x+c)^5/d+2*a*b*ln(tan(d*x+c))/d+b^2*tan(d*x+c)/d,1],
[sin(d*x+c)^3*(a+b*tan(d*x+c))^3,x,16,3*a^2*b*arctanh(sin(d*x+c))/d-5/2*b^3*arctanh(sin(d*x+c))/d-a^3*cos(d*x+c)/d+6*a*b^2*cos(d*x+c)/d+1/3*a^3*cos(d*x+c)^3/d-a*b^2*cos(d*x+c)^3/d+3*a*b^2*sec(d*x+c)/d-3*a^2*b*sin(d*x+c)/d+5/2*b^3*sin(d*x+c)/d-a^2*b*sin(d*x+c)^3/d+5/6*b^3*sin(d*x+c)^3/d+1/2*b^3*sin(d*x+c)^3*tan(d*x+c)^2/d,1],
[sin(d*x+c)^2*(a+b*tan(d*x+c))^3,x,7,1/2*a*(a^2-9*b^2)*x-b*(3*a^2-2*b^2)*ln(cos(d*x+c))/d+9/2*a*b^2*tan(d*x+c)/d+b^3*tan(d*x+c)^2/d-1/2*cos(d*x+c)*sin(d*x+c)*(a+b*tan(d*x+c))^3/d,1],
[sin(d*x+c)*(a+b*tan(d*x+c))^3,x,13,3*a^2*b*arctanh(sin(d*x+c))/d-3/2*b^3*arctanh(sin(d*x+c))/d-a^3*cos(d*x+c)/d+3*a*b^2*cos(d*x+c)/d+3*a*b^2*sec(d*x+c)/d-3*a^2*b*sin(d*x+c)/d+3/2*b^3*sin(d*x+c)/d+1/2*b^3*sin(d*x+c)*tan(d*x+c)^2/d,1],
[csc(d*x+c)*(a+b*tan(d*x+c))^3,x,8,-a^3*arctanh(cos(d*x+c))/d+3*a^2*b*arctanh(sin(d*x+c))/d-1/2*b^3*arctanh(sin(d*x+c))/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*tan(d*x+c))^3,x,3,-a^3*cot(d*x+c)/d+3*a^2*b*ln(tan(d*x+c))/d+3*a*b^2*tan(d*x+c)/d+1/2*b^3*tan(d*x+c)^2/d,1],
[csc(d*x+c)^3*(a+b*tan(d*x+c))^3,x,12,-1/2*a^3*arctanh(cos(d*x+c))/d-3*a*b^2*arctanh(cos(d*x+c))/d+3*a^2*b*arctanh(sin(d*x+c))/d+1/2*b^3*arctanh(sin(d*x+c))/d-3*a^2*b*csc(d*x+c)/d-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+3*a*b^2*sec(d*x+c)/d+1/2*b^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*tan(d*x+c))^3,x,3,-a*(a^2+3*b^2)*cot(d*x+c)/d-3/2*a^2*b*cot(d*x+c)^2/d-1/3*a^3*cot(d*x+c)^3/d+b*(3*a^2+b^2)*ln(tan(d*x+c))/d+3*a*b^2*tan(d*x+c)/d+1/2*b^3*tan(d*x+c)^2/d,1],
[csc(d*x+c)^5*(a+b*tan(d*x+c))^3,x,17,-3/8*a^3*arctanh(cos(d*x+c))/d-9/2*a*b^2*arctanh(cos(d*x+c))/d+3*a^2*b*arctanh(sin(d*x+c))/d+3/2*b^3*arctanh(sin(d*x+c))/d-3*a^2*b*csc(d*x+c)/d-3/2*b^3*csc(d*x+c)/d-3/8*a^3*cot(d*x+c)*csc(d*x+c)/d-a^2*b*csc(d*x+c)^3/d-1/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d+9/2*a*b^2*sec(d*x+c)/d-3/2*a*b^2*csc(d*x+c)^2*sec(d*x+c)/d+1/2*b^3*csc(d*x+c)*sec(d*x+c)^2/d,1],
[csc(d*x+c)^6*(a+b*tan(d*x+c))^3,x,3,-a*(a^2+6*b^2)*cot(d*x+c)/d-1/2*b*(6*a^2+b^2)*cot(d*x+c)^2/d-1/3*a*(2*a^2+3*b^2)*cot(d*x+c)^3/d-3/4*a^2*b*cot(d*x+c)^4/d-1/5*a^3*cot(d*x+c)^5/d+b*(3*a^2+2*b^2)*ln(tan(d*x+c))/d+3*a*b^2*tan(d*x+c)/d+1/2*b^3*tan(d*x+c)^2/d,1],
[sin(d*x+c)^3*(a+b*tan(d*x+c))^4,x,19,4*a^3*b*arctanh(sin(d*x+c))/d-10*a*b^3*arctanh(sin(d*x+c))/d-a^4*cos(d*x+c)/d+12*a^2*b^2*cos(d*x+c)/d-3*b^4*cos(d*x+c)/d+1/3*a^4*cos(d*x+c)^3/d-2*a^2*b^2*cos(d*x+c)^3/d+1/3*b^4*cos(d*x+c)^3/d+6*a^2*b^2*sec(d*x+c)/d-3*b^4*sec(d*x+c)/d+1/3*b^4*sec(d*x+c)^3/d-4*a^3*b*sin(d*x+c)/d+10*a*b^3*sin(d*x+c)/d-4/3*a^3*b*sin(d*x+c)^3/d+10/3*a*b^3*sin(d*x+c)^3/d+2*a*b^3*sin(d*x+c)^3*tan(d*x+c)^2/d,1],
[sin(d*x+c)^2*(a+b*tan(d*x+c))^4,x,7,1/2*(a^4-18*a^2*b^2+5*b^4)*x-4*a*b*(a^2-2*b^2)*ln(cos(d*x+c))/d+1/2*b^2*(18*a^2-5*b^2)*tan(d*x+c)/d+4*a*b^3*tan(d*x+c)^2/d+5/6*b^4*tan(d*x+c)^3/d-1/2*cos(d*x+c)*sin(d*x+c)*(a+b*tan(d*x+c))^4/d,1],
[sin(d*x+c)*(a+b*tan(d*x+c))^4,x,16,4*a^3*b*arctanh(sin(d*x+c))/d-6*a*b^3*arctanh(sin(d*x+c))/d-a^4*cos(d*x+c)/d+6*a^2*b^2*cos(d*x+c)/d-b^4*cos(d*x+c)/d+6*a^2*b^2*sec(d*x+c)/d-2*b^4*sec(d*x+c)/d+1/3*b^4*sec(d*x+c)^3/d-4*a^3*b*sin(d*x+c)/d+6*a*b^3*sin(d*x+c)/d+2*a*b^3*sin(d*x+c)*tan(d*x+c)^2/d,1],
[csc(d*x+c)*(a+b*tan(d*x+c))^4,x,10,-a^4*arctanh(cos(d*x+c))/d+4*a^3*b*arctanh(sin(d*x+c))/d-2*a*b^3*arctanh(sin(d*x+c))/d+6*a^2*b^2*sec(d*x+c)/d-b^4*sec(d*x+c)/d+1/3*b^4*sec(d*x+c)^3/d+2*a*b^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^2*(a+b*tan(d*x+c))^4,x,3,-a^4*cot(d*x+c)/d+4*a^3*b*ln(tan(d*x+c))/d+6*a^2*b^2*tan(d*x+c)/d+2*a*b^3*tan(d*x+c)^2/d+1/3*b^4*tan(d*x+c)^3/d,1],
[csc(d*x+c)^3*(a+b*tan(d*x+c))^4,x,14,-1/2*a^4*arctanh(cos(d*x+c))/d-6*a^2*b^2*arctanh(cos(d*x+c))/d+4*a^3*b*arctanh(sin(d*x+c))/d+2*a*b^3*arctanh(sin(d*x+c))/d-4*a^3*b*csc(d*x+c)/d-1/2*a^4*cot(d*x+c)*csc(d*x+c)/d+6*a^2*b^2*sec(d*x+c)/d+1/3*b^4*sec(d*x+c)^3/d+2*a*b^3*sec(d*x+c)*tan(d*x+c)/d,1],
[csc(d*x+c)^4*(a+b*tan(d*x+c))^4,x,3,-a^2*(a^2+6*b^2)*cot(d*x+c)/d-2*a^3*b*cot(d*x+c)^2/d-1/3*a^4*cot(d*x+c)^3/d+4*a*b*(a^2+b^2)*ln(tan(d*x+c))/d+b^2*(6*a^2+b^2)*tan(d*x+c)/d+2*a*b^3*tan(d*x+c)^2/d+1/3*b^4*tan(d*x+c)^3/d,1],
[csc(d*x+c)^5*(a+b*tan(d*x+c))^4,x,21,-3/8*a^4*arctanh(cos(d*x+c))/d-9*a^2*b^2*arctanh(cos(d*x+c))/d-b^4*arctanh(cos(d*x+c))/d+4*a^3*b*arctanh(sin(d*x+c))/d+6*a*b^3*arctanh(sin(d*x+c))/d-4*a^3*b*csc(d*x+c)/d-6*a*b^3*csc(d*x+c)/d-3/8*a^4*cot(d*x+c)*csc(d*x+c)/d-4/3*a^3*b*csc(d*x+c)^3/d-1/4*a^4*cot(d*x+c)*csc(d*x+c)^3/d+9*a^2*b^2*sec(d*x+c)/d+b^4*sec(d*x+c)/d-3*a^2*b^2*csc(d*x+c)^2*sec(d*x+c)/d+2*a*b^3*csc(d*x+c)*sec(d*x+c)^2/d+1/3*b^4*sec(d*x+c)^3/d,1],
[csc(d*x+c)^6*(a+b*tan(d*x+c))^4,x,3,-(a^4+12*a^2*b^2+b^4)*cot(d*x+c)/d-2*a*b*(2*a^2+b^2)*cot(d*x+c)^2/d-2/3*a^2*(a^2+3*b^2)*cot(d*x+c)^3/d-a^3*b*cot(d*x+c)^4/d-1/5*a^4*cot(d*x+c)^5/d+4*a*b*(a^2+2*b^2)*ln(tan(d*x+c))/d+2*b^2*(3*a^2+b^2)*tan(d*x+c)/d+2*a*b^3*tan(d*x+c)^2/d+1/3*b^4*tan(d*x+c)^3/d,1],
[csc(d*x+c)^7*(a+b*tan(d*x+c))^4,x,25,-5/16*a^4*arctanh(cos(d*x+c))/d-45/4*a^2*b^2*arctanh(cos(d*x+c))/d-5/2*b^4*arctanh(cos(d*x+c))/d+4*a^3*b*arctanh(sin(d*x+c))/d+10*a*b^3*arctanh(sin(d*x+c))/d-4*a^3*b*csc(d*x+c)/d-10*a*b^3*csc(d*x+c)/d-5/16*a^4*cot(d*x+c)*csc(d*x+c)/d-4/3*a^3*b*csc(d*x+c)^3/d-10/3*a*b^3*csc(d*x+c)^3/d-5/24*a^4*cot(d*x+c)*csc(d*x+c)^3/d-4/5*a^3*b*csc(d*x+c)^5/d-1/6*a^4*cot(d*x+c)*csc(d*x+c)^5/d+45/4*a^2*b^2*sec(d*x+c)/d+5/2*b^4*sec(d*x+c)/d-15/4*a^2*b^2*csc(d*x+c)^2*sec(d*x+c)/d-3/2*a^2*b^2*csc(d*x+c)^4*sec(d*x+c)/d+2*a*b^3*csc(d*x+c)^3*sec(d*x+c)^2/d+5/6*b^4*sec(d*x+c)^3/d-1/2*b^4*csc(d*x+c)^2*sec(d*x+c)^3/d,1],
[sin(d*x+c)^5/(a+b*tan(d*x+c)),x,13,a^5*b*arctanh((b*cos(d*x+c)-a*sin(d*x+c))/sqrt(a^2+b^2))/(a^2+b^2)^(7/2)/d+a^3*b^2*cos(d*x+c)/(a^2+b^2)^3/d+a*b^2*cos(d*x+c)/(a^2+b^2)^2/d-a*cos(d*x+c)/(a^2+b^2)/d-1/3*a*b^2*cos(d*x+c)^3/(a^2+b^2)^2/d+2/3*a*cos(d*x+c)^3/(a^2+b^2)/d-1/5*a*cos(d*x+c)^5/(a^2+b^2)/d+a^4*b*sin(d*x+c)/(a^2+b^2)^3/d+1/3*a^2*b*sin(d*x+c)^3/(a^2+b^2)^2/d+1/5*b*sin(d*x+c)^5/(a^2+b^2)/d,1],
[sin(d*x+c)^3/(a+b*tan(d*x+c)),x,10,a^3*b*arctanh((b*cos(d*x+c)-a*sin(d*x+c))/sqrt(a^2+b^2))/(a^2+b^2)^(5/2)/d+a*b^2*cos(d*x+c)/(a^2+b^2)^2/d-a*cos(d*x+c)/(a^2+b^2)/d+1/3*a*cos(d*x+c)^3/(a^2+b^2)/d+a^2*b*sin(d*x+c)/(a^2+b^2)^2/d+1/3*b*sin(d*x+c)^3/(a^2+b^2)/d,1],
[sin(d*x+c)/(a+b*tan(d*x+c)),x,6,a*b*arctanh((b*cos(d*x+c)-a*sin(d*x+c))/sqrt(a^2+b^2))/(a^2+b^2)^(3/2)/d-a*cos(d*x+c)/(a^2+b^2)/d+b*sin(d*x+c)/(a^2+b^2)/d,1],
[csc(d*x+c)/(a+b*tan(d*x+c)),x,6,-arctanh(cos(d*x+c))/a/d+b*arctanh((b*cos(d*x+c)-a*sin(d*x+c))/sqrt(a^2+b^2))/a/sqrt(a^2+b^2)/d,1],
[csc(d*x+c)^3/(a+b*tan(d*x+c)),x,15,-1/2*arctanh(cos(d*x+c))/a/d-b^2*arctanh(cos(d*x+c))/a^3/d+b*sqrt(a^2+b^2)*arctanh((b*cos(d*x+c)-a*sin(d*x+c))/sqrt(a^2+b^2))/a^3/d+b*csc(d*x+c)/a^2/d-1/2*cot(d*x+c)*csc(d*x+c)/a/d,1],
[sin(d*x+c)^4/(a+b*tan(d*x+c)),x,8,1/8*a*(3*a^4-6*a^2*b^2-b^4)*x/(a^2+b^2)^3+a^4*b*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d+1/4*cos(d*x+c)^4*(b+a*tan(d*x+c))/(a^2+b^2)/d-1/8*cos(d*x+c)^2*(4*b*(2*a^2+b^2)+a*(5*a^2+b^2)*tan(d*x+c))/(a^2+b^2)^2/d,1],
[sin(d*x+c)^2/(a+b*tan(d*x+c)),x,7,1/2*a*(a^2-b^2)*x/(a^2+b^2)^2+a^2*b*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^2/d-1/2*cos(d*x+c)^2*(b+a*tan(d*x+c))/(a^2+b^2)/d,1],
[csc(d*x+c)^2/(a+b*tan(d*x+c)),x,3,-cot(d*x+c)/a/d-b*ln(tan(d*x+c))/a^2/d+b*ln(a+b*tan(d*x+c))/a^2/d,1],
[csc(d*x+c)^4/(a+b*tan(d*x+c)),x,3,-(a^2+b^2)*cot(d*x+c)/a^3/d+1/2*b*cot(d*x+c)^2/a^2/d-1/3*cot(d*x+c)^3/a/d-b*(a^2+b^2)*ln(tan(d*x+c))/a^4/d+b*(a^2+b^2)*ln(a+b*tan(d*x+c))/a^4/d,1],
[csc(d*x+c)^6/(a+b*tan(d*x+c)),x,3,-(a^2+b^2)^2*cot(d*x+c)/a^5/d+1/2*b*(2*a^2+b^2)*cot(d*x+c)^2/a^4/d-1/3*(2*a^2+b^2)*cot(d*x+c)^3/a^3/d+1/4*b*cot(d*x+c)^4/a^2/d-1/5*cot(d*x+c)^5/a/d-b*(a^2+b^2)^2*ln(tan(d*x+c))/a^6/d+b*(a^2+b^2)^2*ln(a+b*tan(d*x+c))/a^6/d,1],
[sin(d*x+c)^6/(a+b*tan(d*x+c))^2,x,9,1/16*(5*a^8-80*a^6*b^2+50*a^4*b^4+8*a^2*b^6+b^8)*x/(a^2+b^2)^5+2*a^5*b*(a^2-3*b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^5/d-a^6*b/(a^2+b^2)^4/d/(a+b*tan(d*x+c))-1/6*cos(d*x+c)^6*(2*a*b+(a^2-b^2)*tan(d*x+c))/(a^2+b^2)^2/d+1/24*cos(d*x+c)^4*(12*a*b*(3*a^2+b^2)+(13*a^4-18*a^2*b^2-7*b^4)*tan(d*x+c))/(a^2+b^2)^3/d-1/16*cos(d*x+c)^2*(48*a^5*b+(11*a^6-43*a^4*b^2-7*a^2*b^4-b^6)*tan(d*x+c))/(a^2+b^2)^4/d,1],
[sin(d*x+c)^4/(a+b*tan(d*x+c))^2,x,8,1/8*(3*a^6-33*a^4*b^2+13*a^2*b^4+b^6)*x/(a^2+b^2)^4+2*a^3*b*(a^2-2*b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))+1/4*cos(d*x+c)^4*(2*a*b+(a^2-b^2)*tan(d*x+c))/(a^2+b^2)^2/d-1/8*cos(d*x+c)^2*(16*a^3*b+(5*a^4-12*a^2*b^2-b^4)*tan(d*x+c))/(a^2+b^2)^3/d,1],
[sin(d*x+c)^2/(a+b*tan(d*x+c))^2,x,7,1/2*(a^4-6*a^2*b^2+b^4)*x/(a^2+b^2)^3+2*a*b*(a^2-b^2)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^3/d-a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))-1/2*cos(d*x+c)^2*(2*a*b+(a^2-b^2)*tan(d*x+c))/(a^2+b^2)^2/d,1],
[csc(d*x+c)^2/(a+b*tan(d*x+c))^2,x,3,-cot(d*x+c)/a^2/d-2*b*ln(tan(d*x+c))/a^3/d+2*b*ln(a+b*tan(d*x+c))/a^3/d-b/a^2/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^4/(a+b*tan(d*x+c))^2,x,3,-(a^2+3*b^2)*cot(d*x+c)/a^4/d+b*cot(d*x+c)^2/a^3/d-1/3*cot(d*x+c)^3/a^2/d-2*b*(a^2+2*b^2)*ln(tan(d*x+c))/a^5/d+2*b*(a^2+2*b^2)*ln(a+b*tan(d*x+c))/a^5/d-b*(a^2+b^2)/a^4/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^6/(a+b*tan(d*x+c))^2,x,3,-(a^2+b^2)*(a^2+5*b^2)*cot(d*x+c)/a^6/d+2*b*(a^2+b^2)*cot(d*x+c)^2/a^5/d-1/3*(2*a^2+3*b^2)*cot(d*x+c)^3/a^4/d+1/2*b*cot(d*x+c)^4/a^3/d-1/5*cot(d*x+c)^5/a^2/d-2*b*(a^2+b^2)*(a^2+3*b^2)*ln(tan(d*x+c))/a^7/d+2*b*(a^2+b^2)*(a^2+3*b^2)*ln(a+b*tan(d*x+c))/a^7/d-b*(a^2+b^2)^2/a^6/d/(a+b*tan(d*x+c)),1],
[sin(d*x+c)^6/(a+b*tan(d*x+c))^3,x,9,1/16*a*(5*a^8-180*a^6*b^2+390*a^4*b^4-68*a^2*b^6-3*b^8)*x/(a^2+b^2)^6+a^4*b*(3*a^4-22*a^2*b^2+15*b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^6/d-1/2*a^6*b/(a^2+b^2)^4/d/(a+b*tan(d*x+c))^2-2*a^5*b*(a^2-3*b^2)/(a^2+b^2)^5/d/(a+b*tan(d*x+c))-1/6*cos(d*x+c)^6*(b*(3*a^2-b^2)+a*(a^2-3*b^2)*tan(d*x+c))/(a^2+b^2)^3/d+1/24*cos(d*x+c)^4*(6*b*(9*a^4-4*a^2*b^2-b^4)+a*(13*a^4-62*a^2*b^2-3*b^4)*tan(d*x+c))/(a^2+b^2)^4/d-1/16*a*cos(d*x+c)^2*(24*a^3*b*(3*a^2-5*b^2)+(11*a^6-119*a^4*b^2+65*a^2*b^4+3*b^6)*tan(d*x+c))/(a^2+b^2)^5/d,1],
[sin(d*x+c)^4/(a+b*tan(d*x+c))^3,x,8,3/8*a*(a^6-25*a^4*b^2+35*a^2*b^4-3*b^6)*x/(a^2+b^2)^5+3*a^2*b*(a^4-5*a^2*b^2+2*b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^5/d-1/2*a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))^2-2*a^3*b*(a^2-2*b^2)/(a^2+b^2)^4/d/(a+b*tan(d*x+c))+1/4*cos(d*x+c)^4*(b*(3*a^2-b^2)+a*(a^2-3*b^2)*tan(d*x+c))/(a^2+b^2)^3/d-1/8*a*cos(d*x+c)^2*(24*a*b*(a^2-b^2)+(5*a^4-34*a^2*b^2+9*b^4)*tan(d*x+c))/(a^2+b^2)^4/d,1],
[sin(d*x+c)^2/(a+b*tan(d*x+c))^3,x,7,1/2*a*(a^4-14*a^2*b^2+9*b^4)*x/(a^2+b^2)^4+b*(3*a^4-8*a^2*b^2+b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^4/d-1/2*a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2-2*a*b*(a^2-b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c))-1/2*cos(d*x+c)^2*(b*(3*a^2-b^2)+a*(a^2-3*b^2)*tan(d*x+c))/(a^2+b^2)^3/d,1],
[csc(d*x+c)^2/(a+b*tan(d*x+c))^3,x,3,-cot(d*x+c)/a^3/d-3*b*ln(tan(d*x+c))/a^4/d+3*b*ln(a+b*tan(d*x+c))/a^4/d-1/2*b/a^2/d/(a+b*tan(d*x+c))^2-2*b/a^3/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^4/(a+b*tan(d*x+c))^3,x,3,-(a^2+6*b^2)*cot(d*x+c)/a^5/d+3/2*b*cot(d*x+c)^2/a^4/d-1/3*cot(d*x+c)^3/a^3/d-b*(3*a^2+10*b^2)*ln(tan(d*x+c))/a^6/d+b*(3*a^2+10*b^2)*ln(a+b*tan(d*x+c))/a^6/d-1/2*b*(a^2+b^2)/a^4/d/(a+b*tan(d*x+c))^2-2*b*(a^2+2*b^2)/a^5/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^6/(a+b*tan(d*x+c))^3,x,3,-(a^4+12*a^2*b^2+15*b^4)*cot(d*x+c)/a^7/d+b*(3*a^2+5*b^2)*cot(d*x+c)^2/a^6/d-2/3*(a^2+3*b^2)*cot(d*x+c)^3/a^5/d+3/4*b*cot(d*x+c)^4/a^4/d-1/5*cot(d*x+c)^5/a^3/d-b*(3*a^4+20*a^2*b^2+21*b^4)*ln(tan(d*x+c))/a^8/d+b*(3*a^4+20*a^2*b^2+21*b^4)*ln(a+b*tan(d*x+c))/a^8/d-1/2*b*(a^2+b^2)^2/a^6/d/(a+b*tan(d*x+c))^2-2*b*(a^2+b^2)*(a^2+3*b^2)/a^7/d/(a+b*tan(d*x+c)),1],
[sin(d*x+c)^4/(a+b*tan(d*x+c))^4,x,8,1/8*(3*a^8-132*a^6*b^2+370*a^4*b^4-132*a^2*b^6+3*b^8)*x/(a^2+b^2)^6+4*a*b*(a^2-b^2)*(a^4-8*a^2*b^2+b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^6/d-1/3*a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))^3-a^3*b*(a^2-2*b^2)/(a^2+b^2)^4/d/(a+b*tan(d*x+c))^2-3*a^2*b*(a^4-5*a^2*b^2+2*b^4)/(a^2+b^2)^5/d/(a+b*tan(d*x+c))+1/4*cos(d*x+c)^4*(4*a*b*(a^2-b^2)+(a^4-6*a^2*b^2+b^4)*tan(d*x+c))/(a^2+b^2)^4/d-1/8*cos(d*x+c)^2*(16*a*b*(2*a^4-5*a^2*b^2+b^4)+(5*a^6-65*a^4*b^2+55*a^2*b^4-3*b^6)*tan(d*x+c))/(a^2+b^2)^5/d,1],
[sin(d*x+c)^2/(a+b*tan(d*x+c))^4,x,7,1/2*(a^6-25*a^4*b^2+35*a^2*b^4-3*b^6)*x/(a^2+b^2)^5+4*a*b*(a^4-5*a^2*b^2+2*b^4)*ln(a*cos(d*x+c)+b*sin(d*x+c))/(a^2+b^2)^5/d-1/3*a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^3-a*b*(a^2-b^2)/(a^2+b^2)^3/d/(a+b*tan(d*x+c))^2-b*(3*a^4-8*a^2*b^2+b^4)/(a^2+b^2)^4/d/(a+b*tan(d*x+c))-1/2*cos(d*x+c)^2*(4*a*b*(a^2-b^2)+(a^4-6*a^2*b^2+b^4)*tan(d*x+c))/(a^2+b^2)^4/d,1],
[csc(d*x+c)^2/(a+b*tan(d*x+c))^4,x,3,-cot(d*x+c)/a^4/d-4*b*ln(tan(d*x+c))/a^5/d+4*b*ln(a+b*tan(d*x+c))/a^5/d-1/3*b/a^2/d/(a+b*tan(d*x+c))^3-b/a^3/d/(a+b*tan(d*x+c))^2-3*b/a^4/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^4/(a+b*tan(d*x+c))^4,x,3,-(a^2+10*b^2)*cot(d*x+c)/a^6/d+2*b*cot(d*x+c)^2/a^5/d-1/3*cot(d*x+c)^3/a^4/d-4*b*(a^2+5*b^2)*ln(tan(d*x+c))/a^7/d+4*b*(a^2+5*b^2)*ln(a+b*tan(d*x+c))/a^7/d-1/3*b*(a^2+b^2)/a^4/d/(a+b*tan(d*x+c))^3-b*(a^2+2*b^2)/a^5/d/(a+b*tan(d*x+c))^2-b*(3*a^2+10*b^2)/a^6/d/(a+b*tan(d*x+c)),1],
[csc(d*x+c)^6/(a+b*tan(d*x+c))^4,x,3,-(a^4+20*a^2*b^2+35*b^4)*cot(d*x+c)/a^8/d+2*b*(2*a^2+5*b^2)*cot(d*x+c)^2/a^7/d-2/3*(a^2+5*b^2)*cot(d*x+c)^3/a^6/d+b*cot(d*x+c)^4/a^5/d-1/5*cot(d*x+c)^5/a^4/d-4*b*(a^4+10*a^2*b^2+14*b^4)*ln(tan(d*x+c))/a^9/d+4*b*(a^4+10*a^2*b^2+14*b^4)*ln(a+b*tan(d*x+c))/a^9/d-1/3*b*(a^2+b^2)^2/a^6/d/(a+b*tan(d*x+c))^3-b*(a^2+b^2)*(a^2+3*b^2)/a^7/d/(a+b*tan(d*x+c))^2-b*(3*a^4+20*a^2*b^2+21*b^4)/a^8/d/(a+b*tan(d*x+c)),1],
[csc(x)/(1+tan(x)),x,6,-arctanh(cos(x))+arctanh((cos(x)-sin(x))/sqrt(2))/sqrt(2),1],
[sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x,8,a^3*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(1+m)/d/(1+m)/sqrt(cos(d*x+c)^2)+3*a^2*b*hypergeom([1, 1+1/2*m],[2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(2+m)/d/(2+m)+3*a*b^2*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 3/2+1/2*m],[5/2+1/2*m],sin(d*x+c)^2)*sec(d*x+c)*sin(d*x+c)^(3+m)/d/(3+m)+b^3*hypergeom([2, 2+1/2*m],[3+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(4+m)/d/(4+m),1],
[sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x,6,a^2*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(1+m)/d/(1+m)/sqrt(cos(d*x+c)^2)+2*a*b*hypergeom([1, 1+1/2*m],[2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(2+m)/d/(2+m)+b^2*sqrt(cos(d*x+c)^2)*hypergeom([3/2, 3/2+1/2*m],[5/2+1/2*m],sin(d*x+c)^2)*sec(d*x+c)*sin(d*x+c)^(3+m)/d/(3+m),1],
[sin(d*x+c)^m*(a+b*tan(d*x+c)),x,5,a*cos(d*x+c)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(1+m)/d/(1+m)/sqrt(cos(d*x+c)^2)+b*hypergeom([1, 1+1/2*m],[2+1/2*m],sin(d*x+c)^2)*sin(d*x+c)^(2+m)/d/(2+m),1],
[sin(d*x+c)^m/(a+b*tan(d*x+c)),x,14,2^(1+m)*hypergeom([1/2+1/2*m, 1+m],[3/2+1/2*m],-tan(1/2*d*x+1/2*c)^2)*tan(1/2*d*x+1/2*c)*(tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2))^m*(1+tan(1/2*d*x+1/2*c)^2)^m/a/d/(1+m)+2^(1+m)*b*AppellF1(1+1/2*m,1+m,1,2+1/2*m,-tan(1/2*d*x+1/2*c)^2,a^2*tan(1/2*d*x+1/2*c)^2/(b-sqrt(a^2+b^2))^2)*tan(1/2*d*x+1/2*c)^2*(tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2))^m*(1+tan(1/2*d*x+1/2*c)^2)^m/sqrt(a^2+b^2)/(b-sqrt(a^2+b^2))/d/(2+m)-2^(1+m)*b*AppellF1(1+1/2*m,1+m,1,2+1/2*m,-tan(1/2*d*x+1/2*c)^2,a^2*tan(1/2*d*x+1/2*c)^2/(b+sqrt(a^2+b^2))^2)*tan(1/2*d*x+1/2*c)^2*(tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2))^m*(1+tan(1/2*d*x+1/2*c)^2)^m/sqrt(a^2+b^2)/(b+sqrt(a^2+b^2))/d/(2+m)+2^(1+m)*a*b*AppellF1(3/2+1/2*m,1+m,1,5/2+1/2*m,-tan(1/2*d*x+1/2*c)^2,a^2*tan(1/2*d*x+1/2*c)^2/(b-sqrt(a^2+b^2))^2)*tan(1/2*d*x+1/2*c)^3*(tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2))^m*(1+tan(1/2*d*x+1/2*c)^2)^m/sqrt(a^2+b^2)/(b-sqrt(a^2+b^2))^2/d/(3+m)-2^(1+m)*a*b*AppellF1(3/2+1/2*m,1+m,1,5/2+1/2*m,-tan(1/2*d*x+1/2*c)^2,a^2*tan(1/2*d*x+1/2*c)^2/(b+sqrt(a^2+b^2))^2)*tan(1/2*d*x+1/2*c)^3*(tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2))^m*(1+tan(1/2*d*x+1/2*c)^2)^m/sqrt(a^2+b^2)/(b+sqrt(a^2+b^2))^2/d/(3+m),1],
[sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x,0,Defer(Int)(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x),0],
[sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x,7,-1/16*(a*b^2*n*(5*a^2+b^2*(3+2*n))+sqrt(-b^2)*(3*a^4+a^2*b^2*(-n^2+6*n+6)+b^4*(n^2+4*n+3)))*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a^2+b^2)^2/(a-sqrt(-b^2))/d/(1+n)-1/16*(a*b^2*n*(5*a^2+b^2*(3+2*n))-sqrt(-b^2)*(3*a^4+a^2*b^2*(-n^2+6*n+6)+b^4*(n^2+4*n+3)))*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a^2+b^2)^2/(a+sqrt(-b^2))/d/(1+n)+1/4*cos(d*x+c)^4*(b+a*tan(d*x+c))*(a+b*tan(d*x+c))^(1+n)/(a^2+b^2)/d-1/8*cos(d*x+c)^2*(a+b*tan(d*x+c))^(1+n)*(b*(a^2*(7-n)+b^2*(5+n))+a*(5*a^2+b^2*(3+2*n))*tan(d*x+c))/(a^2+b^2)^2/d,1],
[sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x,6,-1/4*(a*b^2*n+sqrt(-b^2)*(a^2+b^2*(1+n)))*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a-sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a^2+b^2)/(a-sqrt(-b^2))/d/(1+n)-1/4*(a*b^2*n-sqrt(-b^2)*(a^2+b^2*(1+n)))*hypergeom([1, 1+n],[2+n],(a+b*tan(d*x+c))/(a+sqrt(-b^2)))*(a+b*tan(d*x+c))^(1+n)/b/(a^2+b^2)/(a+sqrt(-b^2))/d/(1+n)-1/2*cos(d*x+c)^2*(b+a*tan(d*x+c))*(a+b*tan(d*x+c))^(1+n)/(a^2+b^2)/d,1],
[csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x,2,b*hypergeom([2, 1+n],[2+n],(a+b*tan(d*x+c))/a)*(a+b*tan(d*x+c))^(1+n)/a^2/d/(1+n),1],
[csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x,4,1/6*b*(2-n)*cot(d*x+c)^2*(a+b*tan(d*x+c))^(1+n)/a^2/d-1/3*cot(d*x+c)^3*(a+b*tan(d*x+c))^(1+n)/a/d+1/6*b*(6*a^2+b^2*(n^2-3*n+2))*hypergeom([2, 1+n],[2+n],(a+b*tan(d*x+c))/a)*(a+b*tan(d*x+c))^(1+n)/a^4/d/(1+n),1],
[sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x,0,Defer(Int)(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x),0],
[sin(d*x+c)*(a+b*tan(d*x+c))^n,x,0,Defer(Int)(sin(d*x+c)*(a+b*tan(d*x+c))^n,x),0],
[csc(d*x+c)*(a+b*tan(d*x+c))^n,x,0,Defer(Int)(csc(d*x+c)*(a+b*tan(d*x+c))^n,x),0],
[csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x,0,Defer(Int)(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x),0]]: