lst:=[[sin(x)^4/(a+a*cos(x)),x,3,1/2*x/a-1/2*cos(x)*sin(x)/a-1/3*sin(x)^3/a,1],
[sin(x)^3/(a+a*cos(x)),x,2,1/2*(a-a*cos(x))^2/a^3,1],
[sin(x)^2/(a+a*cos(x)),x,2,x/a-sin(x)/a,1],
[sin(x)/(a+a*cos(x)),x,2,-ln(1+cos(x))/a,1],
[1/(a+a*cos(x)),x,1,sin(x)/(a+a*cos(x)),1],
[csc(x)/(a+a*cos(x)),x,4,-1/2*arctanh(cos(x))/a+1/(2*a+2*a*cos(x)),1],
[csc(x)^2/(a+a*cos(x)),x,3,-2/3*cot(x)/a+csc(x)/(3*a+3*a*cos(x)),1],
[csc(x)^3/(a+a*cos(x)),x,4,-3/8*arctanh(cos(x))/a-1/(8*a-8*a*cos(x))+1/(4*a+4*a*cos(x))+1/8*a^3/(a^2+a^2*cos(x))^2,1],
[csc(x)^4/(a+a*cos(x)),x,3,-4/5*cot(x)/a-4/15*cot(x)^3/a+csc(x)^3/(5*a+5*a*cos(x)),1],
[sin(2*x)/(1+cos(2*x)),x,2,-ln(cos(x)),1],
[sin(2*x)/(1-cos(2*x)),x,2,ln(sin(x)),1],
[sin(x)/(1+cos(x))^2,x,2,1/(1+cos(x)),1],
[sin(x)/(1-cos(x))^2,x,2,-1/(1-cos(x)),1],
[sin(x)^2/(1+cos(x))^2,x,2,-x+2*sin(x)/(1+cos(x)),1],
[sin(x)^2/(1-cos(x))^2,x,2,-x-2*sin(x)/(1-cos(x)),1],
[sin(x)^3/(1+cos(x))^2,x,3,cos(x)-2*ln(1+cos(x)),1],
[sin(x)^3/(1-cos(x))^2,x,3,cos(x)+2*ln(1-cos(x)),1],
[sin(x)/(1+cos(x))^3,x,2,1/2/(1+cos(x))^2,1],
[sin(x)/(1-cos(x))^3,x,2,-1/2/(1-cos(x))^2,1],
[sin(x)^2/(1+cos(x))^3,x,1,1/3*sin(x)^3/(1+cos(x))^3,1],
[sin(x)^2/(1-cos(x))^3,x,1,-1/3*sin(x)^3/(1-cos(x))^3,1],
[sin(x)^3/(1+cos(x))^3,x,3,2/(1+cos(x))+ln(1+cos(x)),1],
[sin(x)^3/(1-cos(x))^3,x,3,-2/(1-cos(x))-ln(1-cos(x)),1],
[sin(x)^4/(a+b*cos(x)),x,5,-1/2*a*(2*a^2-3*b^2)*x/b^4+2*(a-b)^(3/2)*(a+b)^(3/2)*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/b^4+1/2*(2*a^2-2*b^2-a*b*cos(x))*sin(x)/b^3-1/3*sin(x)^3/b,1],
[sin(x)^3/(a+b*cos(x)),x,3,-a*cos(x)/b^2+1/2*cos(x)^2/b+(a^2-b^2)*ln(a+b*cos(x))/b^3,1],
[sin(x)^2/(a+b*cos(x)),x,4,a*x/b^2-2*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/b^2-sin(x)/b,1],
[sin(x)/(a+b*cos(x)),x,2,-ln(a+b*cos(x))/b,1],
[1/(a+b*cos(x)),x,2,2*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b),1],
[csc(x)/(a+b*cos(x)),x,3,ln(1-cos(x))/(2*a+2*b)-ln(1+cos(x))/(2*a-2*b)+b*ln(a+b*cos(x))/(a^2-b^2),1],
[csc(x)^2/(a+b*cos(x)),x,4,-2*b^2*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)+(b-a*cos(x))*csc(x)/(a^2-b^2),1],
[csc(x)^3/(a+b*cos(x)),x,3,-1/4/(a+b)/(1-cos(x))+1/4/(a-b)/(1+cos(x))+1/4*(a+2*b)*ln(1-cos(x))/(a+b)^2-1/4*(a-2*b)*ln(1+cos(x))/(a-b)^2-b^3*ln(a+b*cos(x))/(a^2-b^2)^2,1],
[csc(x)^4/(a+b*cos(x)),x,5,2*b^4*arctan(sqrt(a-b)*tan(1/2*x)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)-1/3*(3*b^3+a*(2*a^2-5*b^2)*cos(x))*csc(x)/(a^2-b^2)^2+(b-a*cos(x))*csc(x)^3/(3*a^2-3*b^2),1],
[(a+b*cos(d*x+c))*(e*sin(d*x+c))^(7/2),x,5,10/21*a*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-10/21*a*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/d-2/7*a*e*cos(d*x+c)*(e*sin(d*x+c))^(5/2)/d+2/9*b*(e*sin(d*x+c))^(9/2)/d/e,1],
[(a+b*cos(d*x+c))*(e*sin(d*x+c))^(5/2),x,4,6/5*a*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))-2/5*a*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/d+2/7*b*(e*sin(d*x+c))^(7/2)/d/e,1],
[(a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2),x,4,2/3*a*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-2/3*a*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/d+2/5*b*(e*sin(d*x+c))^(5/2)/d/e,1],
[(a+b*cos(d*x+c))*sqrt(e*sin(d*x+c)),x,3,2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))+2/3*b*(e*sin(d*x+c))^(3/2)/d/e,1],
[(a+b*cos(d*x+c))/sqrt(e*sin(d*x+c)),x,3,2*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))+2*b*sqrt(e*sin(d*x+c))/d/e,1],
[(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x,4,-2*b/d/e/sqrt(e*sin(d*x+c))-2*a*cos(d*x+c)/d/e/sqrt(e*sin(d*x+c))-2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^2/sqrt(sin(d*x+c)),1],
[(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x,4,-2/3*b/d/e/(e*sin(d*x+c))^(3/2)-2/3*a*cos(d*x+c)/d/e/(e*sin(d*x+c))^(3/2)+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^2/sqrt(e*sin(d*x+c)),1],
[(a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x,5,-2/5*b/d/e/(e*sin(d*x+c))^(5/2)-2/5*a*cos(d*x+c)/d/e/(e*sin(d*x+c))^(5/2)-6/5*a*cos(d*x+c)/d/e^3/sqrt(e*sin(d*x+c))-6/5*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^4/sqrt(sin(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(7/2),x,6,10/231*(11*a^2+2*b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-10/231*(11*a^2+2*b^2)*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/d-2/77*(11*a^2+2*b^2)*e*cos(d*x+c)*(e*sin(d*x+c))^(5/2)/d+26/99*a*b*(e*sin(d*x+c))^(9/2)/d/e+2/11*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(9/2)/d/e,1],
[(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(5/2),x,5,2/15*(9*a^2+2*b^2)*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))-2/45*(9*a^2+2*b^2)*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/d+22/63*a*b*(e*sin(d*x+c))^(7/2)/d/e+2/9*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(7/2)/d/e,1],
[(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(3/2),x,5,2/21*(7*a^2+2*b^2)*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-2/21*(7*a^2+2*b^2)*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/d+18/35*a*b*(e*sin(d*x+c))^(5/2)/d/e+2/7*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/d/e,1],
[(a+b*cos(d*x+c))^2*sqrt(e*sin(d*x+c)),x,4,2/5*(5*a^2+2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))+14/15*a*b*(e*sin(d*x+c))^(3/2)/d/e+2/5*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/d/e,1],
[(a+b*cos(d*x+c))^2/sqrt(e*sin(d*x+c)),x,4,2/3*(3*a^2+2*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))+10/3*a*b*sqrt(e*sin(d*x+c))/d/e+2/3*b*(a+b*cos(d*x+c))*sqrt(e*sin(d*x+c))/d/e,1],
[(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x,4,-2*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))/d/e/sqrt(e*sin(d*x+c))-2*(a^2+2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^2/sqrt(sin(d*x+c))-2*a*b*(e*sin(d*x+c))^(3/2)/d/e^3,1],
[(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x,4,-2/3*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))/d/e/(e*sin(d*x+c))^(3/2)+2/3*(a^2-2*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^2/sqrt(e*sin(d*x+c))-2/3*a*b*sqrt(e*sin(d*x+c))/d/e^3,1],
[(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x,5,-2/5*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))/d/e/(e*sin(d*x+c))^(5/2)-2/5*a*b/d/e^3/sqrt(e*sin(d*x+c))-2/5*(3*a^2-2*b^2)*cos(d*x+c)/d/e^3/sqrt(e*sin(d*x+c))-2/5*(3*a^2-2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^4/sqrt(sin(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(7/2),x,7,10/231*a*(11*a^2+6*b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-10/231*a*(11*a^2+6*b^2)*e^3*cos(d*x+c)*sqrt(e*sin(d*x+c))/d-2/77*a*(11*a^2+6*b^2)*e*cos(d*x+c)*(e*sin(d*x+c))^(5/2)/d+2/1287*b*(177*a^2+44*b^2)*(e*sin(d*x+c))^(9/2)/d/e+34/143*a*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(9/2)/d/e+2/13*b*(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(9/2)/d/e,1],
[(a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(5/2),x,6,2/5*a*(3*a^2+2*b^2)*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))-2/15*a*(3*a^2+2*b^2)*e*cos(d*x+c)*(e*sin(d*x+c))^(3/2)/d+2/231*b*(43*a^2+12*b^2)*(e*sin(d*x+c))^(7/2)/d/e+10/33*a*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(7/2)/d/e+2/11*b*(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(7/2)/d/e,1],
[(a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(3/2),x,6,2/21*a*(7*a^2+6*b^2)*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))-2/21*a*(7*a^2+6*b^2)*e*cos(d*x+c)*sqrt(e*sin(d*x+c))/d+2/315*b*(89*a^2+28*b^2)*(e*sin(d*x+c))^(5/2)/d/e+26/63*a*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/d/e+2/9*b*(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(5/2)/d/e,1],
[(a+b*cos(d*x+c))^3*sqrt(e*sin(d*x+c)),x,5,2/5*a*(5*a^2+6*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/sqrt(sin(d*x+c))+2/105*b*(57*a^2+20*b^2)*(e*sin(d*x+c))^(3/2)/d/e+22/35*a*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/d/e+2/7*b*(a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(3/2)/d/e,1],
[(a+b*cos(d*x+c))^3/sqrt(e*sin(d*x+c)),x,5,2*a*(a^2+2*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/sqrt(e*sin(d*x+c))+2/5*b*(11*a^2+4*b^2)*sqrt(e*sin(d*x+c))/d/e+6/5*a*b*(a+b*cos(d*x+c))*sqrt(e*sin(d*x+c))/d/e+2/5*b*(a+b*cos(d*x+c))^2*sqrt(e*sin(d*x+c))/d/e,1],
[(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x,5,-2*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))^2/d/e/sqrt(e*sin(d*x+c))-2*a*(a^2+6*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^2/sqrt(sin(d*x+c))-2/3*b*(3*a^2+4*b^2)*(e*sin(d*x+c))^(3/2)/d/e^3-2*a*b*(a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/d/e^3,1],
[(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x,5,-2/3*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))^2/d/e/(e*sin(d*x+c))^(3/2)+2/3*a*(a^2-6*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^2/sqrt(e*sin(d*x+c))-2/3*b*(a^2+4*b^2)*sqrt(e*sin(d*x+c))/d/e^3-2/3*a*b*(a+b*cos(d*x+c))*sqrt(e*sin(d*x+c))/d/e^3,1],
[(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x,5,-2/5*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))^2/d/e/(e*sin(d*x+c))^(5/2)+2/5*(a+b*cos(d*x+c))*(a*b-(3*a^2-4*b^2)*cos(d*x+c))/d/e^3/sqrt(e*sin(d*x+c))-6/5*a*(a^2-2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/d/e^4/sqrt(sin(d*x+c))-2/5*b*(3*a^2-4*b^2)*(e*sin(d*x+c))^(3/2)/d/e^5,1],
[(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(9/2),x,5,-2/7*(b+a*cos(d*x+c))*(a+b*cos(d*x+c))^2/d/e/(e*sin(d*x+c))^(7/2)-2/21*(a+b*cos(d*x+c))*(a*b+(5*a^2-4*b^2)*cos(d*x+c))/d/e^3/(e*sin(d*x+c))^(3/2)+2/21*a*(5*a^2-6*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/d/e^4/sqrt(e*sin(d*x+c))-2/21*b*(5*a^2-4*b^2)*sqrt(e*sin(d*x+c))/d/e^5,1],
[(e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c)),x,15,(-a^2+b^2)^(9/4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d+(-a^2+b^2)^(9/4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d+2/21*a*(21*a^4-49*a^2*b^2+33*b^4)*e^6*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^6/d/sqrt(e*sin(d*x+c))-a*(a^2-b^2)^3*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-a*(a^2-b^2)^3*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-2/21*e^5*(21*(a^2-b^2)^2-a*b*(7*a^2-12*b^2)*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^5/d+2/35*e^3*(7*a^2-7*b^2-5*a*b*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/b^3/d-2/9*e*(e*sin(d*x+c))^(9/2)/b/d,1],
[(e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c)),x,14,-(-a^2+b^2)^(7/4)*e^(9/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d+(-a^2+b^2)^(7/4)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d+a*(a^2-b^2)^2*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+a*(a^2-b^2)^2*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-2/5*a*(5*a^2-8*b^2)*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^4/d/sqrt(sin(d*x+c))+2/15*e^3*(5*a^2-5*b^2-3*a*b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/b^3/d-2/7*e*(e*sin(d*x+c))^(7/2)/b/d,1],
[(e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c)),x,14,(-a^2+b^2)^(5/4)*e^(7/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d+(-a^2+b^2)^(5/4)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d-2/3*a*(3*a^2-4*b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^4/d/sqrt(e*sin(d*x+c))+a*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+a*(a^2-b^2)^2*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+2/3*e^3*(3*a^2-3*b^2-a*b*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^3/d-2/5*e*(e*sin(d*x+c))^(5/2)/b/d,1],
[(e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c)),x,13,-(-a^2+b^2)^(3/4)*e^(5/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/d+(-a^2+b^2)^(3/4)*e^(5/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/d-a*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-a*(a^2-b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+2*a*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^2/d/sqrt(sin(d*x+c))-2/3*e*(e*sin(d*x+c))^(3/2)/b/d,1],
[(e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c)),x,13,(-a^2+b^2)^(1/4)*e^(3/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/d+(-a^2+b^2)^(1/4)*e^(3/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/d+2*a*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^2/d/sqrt(e*sin(d*x+c))-a*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-a*(a^2-b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-2*e*sqrt(e*sin(d*x+c))/b/d,1],
[sqrt(e*sin(d*x+c))/(a+b*cos(d*x+c)),x,9,-sqrt(e)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(1/4)/d+sqrt(e)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(1/4)/d+a*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+a*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))/sqrt(e*sin(d*x+c)),x,9,sqrt(b)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(3/4)/d/sqrt(e)+sqrt(b)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(3/4)/d/sqrt(e)+a*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+a*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x,13,-b^(3/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(5/4)/d/e^(3/2)+b^(3/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(5/4)/d/e^(3/2)+2*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/sqrt(e*sin(d*x+c))-a*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-a*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-2*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x,13,b^(5/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/e^(5/2)+b^(5/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/e^(5/2)+2/3*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/(e*sin(d*x+c))^(3/2)+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/d/e^2/sqrt(e*sin(d*x+c))-a*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c))-a*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x,14,-b^(7/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(7/2)+b^(7/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(7/2)+2/5*(b-a*cos(d*x+c))/(a^2-b^2)/d/e/(e*sin(d*x+c))^(5/2)-2/5*(5*b^3+a*(3*a^2-8*b^2)*cos(d*x+c))/(a^2-b^2)^2/d/e^3/sqrt(e*sin(d*x+c))+a*b^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))+a*b^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))-2/5*a*(3*a^2-8*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^2/d/e^4/sqrt(sin(d*x+c)),1],
[(e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^2,x,15,9/2*a*(-a^2+b^2)^(5/4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d+9/2*a*(-a^2+b^2)^(5/4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d-3/7*(21*a^4-28*a^2*b^2+5*b^4)*e^6*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^6/d/sqrt(e*sin(d*x+c))+9/2*a^2*(a^2-b^2)^2*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+9/2*a^2*(a^2-b^2)^2*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+3/7*e^5*(21*a*(a^2-b^2)-b*(7*a^2-5*b^2)*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^5/d-9/35*e^3*(7*a-5*b*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/b^3/d+e*(e*sin(d*x+c))^(9/2)/b/d/(a+b*cos(d*x+c)),1],
[(e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^2,x,14,-7/2*a*(-a^2+b^2)^(3/4)*e^(9/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d+7/2*a*(-a^2+b^2)^(3/4)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d-7/2*a^2*(a^2-b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-7/2*a^2*(a^2-b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+7/5*(5*a^2-3*b^2)*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^4/d/sqrt(sin(d*x+c))-7/15*e^3*(5*a-3*b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/b^3/d+e*(e*sin(d*x+c))^(7/2)/b/d/(a+b*cos(d*x+c)),1],
[(e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^2,x,14,5/2*a*(-a^2+b^2)^(1/4)*e^(7/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d+5/2*a*(-a^2+b^2)^(1/4)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d+5/3*(3*a^2-b^2)*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^4/d/sqrt(e*sin(d*x+c))-5/2*a^2*(a^2-b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-5/2*a^2*(a^2-b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-5/3*e^3*(3*a-b*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^3/d+e*(e*sin(d*x+c))^(5/2)/b/d/(a+b*cos(d*x+c)),1],
[(e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^2,x,13,-3/2*a*e^(5/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(1/4)/d+3/2*a*e^(5/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(1/4)/d+3/2*a^2*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+3/2*a^2*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-3*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^2/d/sqrt(sin(d*x+c))+e*(e*sin(d*x+c))^(3/2)/b/d/(a+b*cos(d*x+c)),1],
[(e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^2,x,13,1/2*a*e^(3/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(3/4)/d+1/2*a*e^(3/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(3/4)/d-e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^2/d/sqrt(e*sin(d*x+c))+1/2*a^2*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+1/2*a^2*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+e*sqrt(e*sin(d*x+c))/b/d/(a+b*cos(d*x+c)),1],
[sqrt(e*sin(d*x+c))/(a+b*cos(d*x+c))^2,x,13,1/2*a*sqrt(e)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(5/4)/d-1/2*a*sqrt(e)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(5/4)/d+1/2*a^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+1/2*a^2*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)/d/sqrt(sin(d*x+c))-b*(e*sin(d*x+c))^(3/2)/(a^2-b^2)/d/e/(a+b*cos(d*x+c)),1],
[1/(a+b*cos(d*x+c))^2/sqrt(e*sin(d*x+c)),x,13,-3/2*a*sqrt(b)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/sqrt(e)-3/2*a*sqrt(b)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/sqrt(e)-InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/d/sqrt(e*sin(d*x+c))+3/2*a^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+3/2*a^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-b*sqrt(e*sin(d*x+c))/(a^2-b^2)/d/e/(a+b*cos(d*x+c)),1],
[1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x,14,5/2*a*b^(3/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(3/2)-5/2*a*b^(3/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(3/2)-b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))/sqrt(e*sin(d*x+c))+(5*a*b-(2*a^2+3*b^2)*cos(d*x+c))/(a^2-b^2)^2/d/e/sqrt(e*sin(d*x+c))-5/2*a^2*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-5/2*a^2*b*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-(2*a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^2/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x,14,-7/2*a*b^(5/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/e^(5/2)-7/2*a*b^(5/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/e^(5/2)-b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2)+1/3*(7*a*b-(2*a^2+5*b^2)*cos(d*x+c))/(a^2-b^2)^2/d/e/(e*sin(d*x+c))^(3/2)+1/3*(2*a^2+5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/d/e^2/sqrt(e*sin(d*x+c))-7/2*a^2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c))-7/2*a^2*b^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x,15,9/2*a*b^(7/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(7/2)-9/2*a*b^(7/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(7/2)-b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2)+1/5*(9*a*b-(2*a^2+7*b^2)*cos(d*x+c))/(a^2-b^2)^2/d/e/(e*sin(d*x+c))^(5/2)-3/5*(15*a*b^3+(2*a^4-10*a^2*b^2-7*b^4)*cos(d*x+c))/(a^2-b^2)^3/d/e^3/sqrt(e*sin(d*x+c))+9/2*a^2*b^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))+9/2*a^2*b^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))-3/5*(2*a^4-10*a^2*b^2-7*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^3/d/e^4/sqrt(sin(d*x+c)),1],
[(e*sin(d*x+c))^(13/2)/(a+b*cos(d*x+c))^3,x,15,11/8*(9*a^4-11*a^2*b^2+2*b^4)*e^(13/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d-11/8*(9*a^4-11*a^2*b^2+2*b^4)*e^(13/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d-11/8*a*(9*a^4-11*a^2*b^2+2*b^4)*e^7*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^7/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-11/8*a*(9*a^4-11*a^2*b^2+2*b^4)*e^7*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^7/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+11/20*a*(45*a^2-37*b^2)*e^6*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^6/d/sqrt(sin(d*x+c))-11/60*e^5*(45*a^2-10*b^2-27*a*b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/b^5/d+11/28*e^3*(9*a+2*b*cos(d*x+c))*(e*sin(d*x+c))^(7/2)/b^3/d/(a+b*cos(d*x+c))+1/2*e*(e*sin(d*x+c))^(11/2)/b/d/(a+b*cos(d*x+c))^2,1],
[(e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^3,x,15,-9/8*(7*a^4-9*a^2*b^2+2*b^4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d-9/8*(7*a^4-9*a^2*b^2+2*b^4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d+3/4*a*(21*a^2-13*b^2)*e^6*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^6/d/sqrt(e*sin(d*x+c))-9/8*a*(7*a^4-9*a^2*b^2+2*b^4)*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-9/8*a*(7*a^4-9*a^2*b^2+2*b^4)*e^6*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-3/4*e^5*(21*a^2-6*b^2-7*a*b*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^5/d+9/20*e^3*(7*a+2*b*cos(d*x+c))*(e*sin(d*x+c))^(5/2)/b^3/d/(a+b*cos(d*x+c))+1/2*e*(e*sin(d*x+c))^(9/2)/b/d/(a+b*cos(d*x+c))^2,1],
[(e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^3,x,14,-7/8*(5*a^2-2*b^2)*e^(9/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(1/4)/d+7/8*(5*a^2-2*b^2)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(1/4)/d+7/8*a*(5*a^2-2*b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+7/8*a*(5*a^2-2*b^2)*e^5*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-35/4*a*e^4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^4/d/sqrt(sin(d*x+c))+7/12*e^3*(5*a+2*b*cos(d*x+c))*(e*sin(d*x+c))^(3/2)/b^3/d/(a+b*cos(d*x+c))+1/2*e*(e*sin(d*x+c))^(7/2)/b/d/(a+b*cos(d*x+c))^2,1],
[(e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^3,x,14,5/8*(3*a^2-2*b^2)*e^(7/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(3/4)/d+5/8*(3*a^2-2*b^2)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(3/4)/d-15/4*a*e^4*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^4/d/sqrt(e*sin(d*x+c))+5/8*a*(3*a^2-2*b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+5/8*a*(3*a^2-2*b^2)*e^4*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+5/4*e^3*(3*a+2*b*cos(d*x+c))*sqrt(e*sin(d*x+c))/b^3/d/(a+b*cos(d*x+c))+1/2*e*(e*sin(d*x+c))^(5/2)/b/d/(a+b*cos(d*x+c))^2,1],
[(e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^3,x,14,-3/8*(a^2-2*b^2)*e^(5/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(5/4)/d+3/8*(a^2-2*b^2)*e^(5/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(5/4)/d-3/8*a*(a^2-2*b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))-3/8*a*(a^2-2*b^2)*e^3*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^3/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+3/4*a*e^2*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/b^2/(a^2-b^2)/d/sqrt(sin(d*x+c))+1/2*e*(e*sin(d*x+c))^(3/2)/b/d/(a+b*cos(d*x+c))^2-3/4*a*e*(e*sin(d*x+c))^(3/2)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^3,x,14,-1/8*(a^2+2*b^2)*e^(3/2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(7/4)/d-1/8*(a^2+2*b^2)*e^(3/2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(7/4)/d-1/4*a*e^2*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b^2)/d/sqrt(e*sin(d*x+c))+1/8*a*(a^2+2*b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+1/8*a*(a^2+2*b^2)*e^2*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b^2/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+1/2*e*sqrt(e*sin(d*x+c))/b/d/(a+b*cos(d*x+c))^2-1/4*a*e*sqrt(e*sin(d*x+c))/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[sqrt(e*sin(d*x+c))/(a+b*cos(d*x+c))^3,x,14,-1/8*(3*a^2+2*b^2)*sqrt(e)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(9/4)/d+1/8*(3*a^2+2*b^2)*sqrt(e)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(9/4)/d+1/8*a*(3*a^2+2*b^2)*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+1/8*a*(3*a^2+2*b^2)*e*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/b/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/sqrt(e*sin(d*x+c))+5/4*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^2/d/sqrt(sin(d*x+c))-1/2*b*(e*sin(d*x+c))^(3/2)/(a^2-b^2)/d/e/(a+b*cos(d*x+c))^2-5/4*a*b*(e*sin(d*x+c))^(3/2)/(a^2-b^2)^2/d/e/(a+b*cos(d*x+c)),1],
[1/(a+b*cos(d*x+c))^3/sqrt(e*sin(d*x+c)),x,14,3/8*sqrt(b)*(5*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/sqrt(e)+3/8*sqrt(b)*(5*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/sqrt(e)-7/4*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/d/sqrt(e*sin(d*x+c))+3/8*a*(5*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))+3/8*a*(5*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*sin(d*x+c))-1/2*b*sqrt(e*sin(d*x+c))/(a^2-b^2)/d/e/(a+b*cos(d*x+c))^2-7/4*a*b*sqrt(e*sin(d*x+c))/(a^2-b^2)^2/d/e/(a+b*cos(d*x+c)),1],
[1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x,15,-5/8*b^(3/2)*(7*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(3/2)+5/8*b^(3/2)*(7*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(3/2)-1/2*b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))^2/sqrt(e*sin(d*x+c))-9/4*a*b/(a^2-b^2)^2/d/e/(a+b*cos(d*x+c))/sqrt(e*sin(d*x+c))+1/4*(5*b*(7*a^2+2*b^2)-a*(8*a^2+37*b^2)*cos(d*x+c))/(a^2-b^2)^3/d/e/sqrt(e*sin(d*x+c))-5/8*a*b*(7*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-5/8*a*b*(7*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*sin(d*x+c))-1/4*a*(8*a^2+37*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^3/d/e^2/sqrt(sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x,15,7/8*b^(5/2)*(9*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/e^(5/2)+7/8*b^(5/2)*(9*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/e^(5/2)-1/2*b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2)-11/4*a*b/(a^2-b^2)^2/d/e/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2)+1/12*(7*b*(9*a^2+2*b^2)-a*(8*a^2+69*b^2)*cos(d*x+c))/(a^2-b^2)^3/d/e/(e*sin(d*x+c))^(3/2)+1/12*a*(8*a^2+69*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/d/e^2/sqrt(e*sin(d*x+c))-7/8*a*b^2*(9*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c))-7/8*a*b^2*(9*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^3/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*sin(d*x+c)),1],
[1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x,16,-9/8*b^(7/2)*(11*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(7/2)+9/8*b^(7/2)*(11*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*sin(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(7/2)-1/2*b/(a^2-b^2)/d/e/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2)-13/4*a*b/(a^2-b^2)^2/d/e/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2)+1/20*(9*b*(11*a^2+2*b^2)-a*(8*a^2+109*b^2)*cos(d*x+c))/(a^2-b^2)^3/d/e/(e*sin(d*x+c))^(5/2)-3/20*(15*b^3*(11*a^2+2*b^2)+a*(8*a^4-64*a^2*b^2-139*b^4)*cos(d*x+c))/(a^2-b^2)^4/d/e^3/sqrt(e*sin(d*x+c))+9/8*a*b^3*(11*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^4/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))+9/8*a*b^3*(11*a^2+2*b^2)*EllipticPi(sin(1/2*c-1/4*Pi+1/2*d*x),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))*sqrt(sin(d*x+c))/(a^2-b^2)^4/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*sin(d*x+c))-3/20*a*(8*a^4-64*a^2*b^2-139*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2))*sqrt(e*sin(d*x+c))/(a^2-b^2)^4/d/e^4/sqrt(sin(d*x+c)),1],
[(a+b*cos(d*x+c))^m*(g*sin(d*x+c))^p,x,2,-g*AppellF1(1+m,1/2-1/2*p,1/2-1/2*p,2+m,(a+b*cos(d*x+c))/(a-b),(a+b*cos(d*x+c))/(a+b))*(a+b*cos(d*x+c))^(1+m)*(1-(a+b*cos(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*cos(d*x+c))/(a+b))^(1/2-1/2*p)*(g*sin(d*x+c))^(-1+p)/b/d/(1+m),1]]: