lst:=[[csc(x)^5/(a+a*csc(x)),x,6,3/2*arctanh(cos(x))/a-4*cot(x)/a-4/3*cot(x)^3/a+3/2*cot(x)*csc(x)/a+cot(x)*csc(x)^3/(a+a*csc(x)),1],
[csc(x)^4/(a+a*csc(x)),x,6,-3/2*arctanh(cos(x))/a+2*cot(x)/a-3/2*cot(x)*csc(x)/a+cot(x)*csc(x)^2/(a+a*csc(x)),1],
[csc(x)^3/(a+a*csc(x)),x,4,arctanh(cos(x))/a-cot(x)/a-cot(x)/(a+a*csc(x)),1],
[csc(x)^2/(a+a*csc(x)),x,3,-arctanh(cos(x))/a+cot(x)/(a+a*csc(x)),1],
[csc(x)/(a+a*csc(x)),x,1,-cot(x)/(a+a*csc(x)),1],
[1/(a+a*csc(d*x+c)),x,2,x/a+cot(d*x+c)/d/(a+a*csc(d*x+c)),1],
[sin(x)/(a+a*csc(x)),x,4,-x/a-2*cos(x)/a+cos(x)/(a+a*csc(x)),1],
[sin(x)^2/(a+a*csc(x)),x,5,3/2*x/a+2*cos(x)/a-3/2*cos(x)*sin(x)/a+cos(x)*sin(x)/(a+a*csc(x)),1],
[sin(x)^3/(a+a*csc(x)),x,6,-3/2*x/a-4*cos(x)/a+4/3*cos(x)^3/a+3/2*cos(x)*sin(x)/a+cos(x)*sin(x)^2/(a+a*csc(x)),1],
[sin(x)^4/(a+a*csc(x)),x,7,15/8*x/a+4*cos(x)/a-4/3*cos(x)^3/a-15/8*cos(x)*sin(x)/a-5/4*cos(x)*sin(x)^3/a+cos(x)*sin(x)^3/(a+a*csc(x)),1],
[1/(a+a*csc(d*x+c))^2,x,3,x/a^2+4/3*cot(d*x+c)/a^2/d/(1+csc(d*x+c))+1/3*cot(d*x+c)/d/(a+a*csc(d*x+c))^2,1],
[1/(a+a*csc(d*x+c))^3,x,4,x/a^3+1/5*cot(d*x+c)/d/(a+a*csc(d*x+c))^3+7/15*cot(d*x+c)/a/d/(a+a*csc(d*x+c))^2+22/15*cot(d*x+c)/d/(a^3+a^3*csc(d*x+c)),1],
[(a+a*csc(x))^(5/2),x,5,-2*a^(5/2)*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x)))-14/3*a^3*cot(x)/sqrt(a+a*csc(x))-2/3*a^2*cot(x)*sqrt(a+a*csc(x)),1],
[(a+a*csc(x))^(3/2),x,4,-2*a^(3/2)*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x)))-2*a^2*cot(x)/sqrt(a+a*csc(x)),1],
[sqrt(a+a*csc(x)),x,2,-2*sqrt(a)*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x))),1],
[1/sqrt(a+a*csc(x)),x,5,-2*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x)))/sqrt(a)+sqrt(2)*arctan(sqrt(a)*cot(x)/sqrt(2)/sqrt(a+a*csc(x)))/sqrt(a),1],
[1/(a+a*csc(x))^(3/2),x,6,-2*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x)))/a^(3/2)+5/2*arctan(sqrt(a)*cot(x)/sqrt(2)/sqrt(a+a*csc(x)))/sqrt(2)/a^(3/2)+1/2*cot(x)/(a+a*csc(x))^(3/2),1],
[1/(a+a*csc(x))^(5/2),x,7,-2*arctan(sqrt(a)*cot(x)/sqrt(a+a*csc(x)))/a^(5/2)+43/16*arctan(sqrt(a)*cot(x)/sqrt(2)/sqrt(a+a*csc(x)))/sqrt(2)/a^(5/2)+1/4*cot(x)/(a+a*csc(x))^(5/2)+11/16*cot(x)/a/(a+a*csc(x))^(3/2),1],
[sqrt(csc(f*x+e))*sqrt(a+a*csc(f*x+e)),x,2,-2*sqrt(a)*arcsinh(sqrt(a)*cot(f*x+e)/sqrt(a+a*csc(f*x+e)))/f,1],
[sqrt(-csc(f*x+e))*sqrt(a-a*csc(f*x+e)),x,2,-2*sqrt(a)*arcsinh(sqrt(a)*cot(f*x+e)/sqrt(a-a*csc(f*x+e)))/f,1],
[csc(d*x+c)^(4/3)*sqrt(a+a*csc(d*x+c)),x,4,-6/5*a*cos(d*x+c)*csc(d*x+c)^(4/3)/d/sqrt(a+a*csc(d*x+c))-4/5*3^(3/4)*sqrt(2+sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[csc(d*x+c)^(1/3)*sqrt(a+a*csc(d*x+c)),x,3,-2*3^(3/4)*sqrt(2+sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[sqrt(a+a*csc(d*x+c))/csc(d*x+c)^(2/3),x,4,-3/2*a*cos(d*x+c)*csc(d*x+c)^(1/3)/d/sqrt(a+a*csc(d*x+c))-1/2*3^(3/4)*sqrt(2+sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[csc(d*x+c)^(5/3)*sqrt(a+a*csc(d*x+c)),x,6,24/7*a*cot(d*x+c)/d/(1+sqrt(3)-csc(d*x+c)^(1/3))/sqrt(a+a*csc(d*x+c))-6/7*a*cos(d*x+c)*csc(d*x+c)^(5/3)/d/sqrt(a+a*csc(d*x+c))-12/7*3^(1/4)*sqrt(2-sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*EllipticE(sin(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3)))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c))+8/7*sqrt(2)*3^(3/4)*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[csc(d*x+c)^(2/3)*sqrt(a+a*csc(d*x+c)),x,5,6*a*cot(d*x+c)/d/(1+sqrt(3)-csc(d*x+c)^(1/3))/sqrt(a+a*csc(d*x+c))-3*3^(1/4)*sqrt(2-sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*EllipticE(sin(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3)))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c))+2*sqrt(2)*3^(3/4)*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[sqrt(a+a*csc(d*x+c))/csc(d*x+c)^(1/3),x,6,-3*a*cot(d*x+c)/d/(1+sqrt(3)-csc(d*x+c)^(1/3))/sqrt(a+a*csc(d*x+c))-3*a*cos(d*x+c)*csc(d*x+c)^(2/3)/d/sqrt(a+a*csc(d*x+c))+3/2*3^(1/4)*sqrt(2-sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*EllipticE(sin(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3)))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c))-sqrt(2)*3^(3/4)*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[sqrt(a+a*csc(d*x+c))/csc(d*x+c)^(4/3),x,7,-15/8*a*cot(d*x+c)/d/(1+sqrt(3)-csc(d*x+c)^(1/3))/sqrt(a+a*csc(d*x+c))-3/4*a*cos(d*x+c)/d/csc(d*x+c)^(1/3)/sqrt(a+a*csc(d*x+c))-15/8*a*cos(d*x+c)*csc(d*x+c)^(2/3)/d/sqrt(a+a*csc(d*x+c))+15/16*3^(1/4)*sqrt(2-sqrt(3))*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*EllipticE(sin(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3)))),sqrt(-7-4*sqrt(3)))/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c))-5/4*3^(3/4)*a^2*cot(d*x+c)*(1-csc(d*x+c)^(1/3))*sqrt((1+csc(d*x+c)^(1/3)+csc(d*x+c)^(2/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)*InverseJacobiAM(arcsin((1-sqrt(3)-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))),sqrt(-7-4*sqrt(3)))/sqrt(2)/d/sqrt((1-csc(d*x+c)^(1/3))/(1+sqrt(3)-csc(d*x+c)^(1/3))^2)/(a-a*csc(d*x+c))/sqrt(a+a*csc(d*x+c)),1],
[csc(d*x+c)^n*sqrt(a+a*csc(d*x+c)),x,2,-2*a*cot(d*x+c)*hypergeom([1/2, 1-n],[3/2],1-csc(d*x+c))/d/sqrt(a+a*csc(d*x+c)),1],
[csc(d*x+c)^n*sqrt(a-a*csc(d*x+c)),x,3,-2*a*cos(d*x+c)*csc(d*x+c)^(1+n)*hypergeom([1/2, 1-n],[3/2],1+csc(d*x+c))/d/((-csc(d*x+c))^n)/sqrt(a-a*csc(d*x+c)),1],
[csc(f*x+e)^3*(a+a*csc(f*x+e))^m,x,5,cot(f*x+e)*(a+a*csc(f*x+e))^m/f/(m^2+3*m+2)-cot(f*x+e)*(a+a*csc(f*x+e))^(1+m)/a/f/(2+m)-2^(1/2+m)*(m^2+m+1)*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m*hypergeom([1/2, 1/2-m],[3/2],1/2-1/2*csc(f*x+e))/f/(1+m)/(2+m),1],
[csc(f*x+e)^2*(a+a*csc(f*x+e))^m,x,4,-cot(f*x+e)*(a+a*csc(f*x+e))^m/f/(1+m)-2^(1/2+m)*m*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m*hypergeom([1/2, 1/2-m],[3/2],1/2-1/2*csc(f*x+e))/f/(1+m),1],
[csc(f*x+e)*(a+a*csc(f*x+e))^m,x,3,-2^(1/2+m)*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m*hypergeom([1/2, 1/2-m],[3/2],1/2-1/2*csc(f*x+e))/f,1],
[(a+a*csc(f*x+e))^m,x,3,-2^(1/2+m)*AppellF1(1/2,1/2-m,1,3/2,1/2-1/2*csc(f*x+e),1-csc(f*x+e))*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m/f,1],
[(a+a*csc(f*x+e))^m*sin(f*x+e),x,3,-2^(1/2+m)*AppellF1(1/2,1/2-m,2,3/2,1/2-1/2*csc(f*x+e),1-csc(f*x+e))*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m/f,1],
[(a+a*csc(f*x+e))^m*sin(f*x+e)^2,x,3,-2^(1/2+m)*AppellF1(1/2,1/2-m,3,3/2,1/2-1/2*csc(f*x+e),1-csc(f*x+e))*cot(f*x+e)*(1+csc(f*x+e))^(-1/2-m)*(a+a*csc(f*x+e))^m/f,1],
[(a+b*csc(d*x+c))^4,x,6,a^4*x-2*a*b*(2*a^2+b^2)*arctanh(cos(d*x+c))/d-1/3*b^2*(17*a^2+2*b^2)*cot(d*x+c)/d-4/3*a*b^3*cot(d*x+c)*csc(d*x+c)/d-1/3*b^2*cot(d*x+c)*(a+b*csc(d*x+c))^2/d,1],
[(a+b*csc(d*x+c))^3,x,5,a^3*x-1/2*b*(6*a^2+b^2)*arctanh(cos(d*x+c))/d-5/2*a*b^2*cot(d*x+c)/d-1/2*b^2*cot(d*x+c)*(a+b*csc(d*x+c))/d,1],
[(a+b*csc(d*x+c))^2,x,4,a^2*x-2*a*b*arctanh(cos(d*x+c))/d-b^2*cot(d*x+c)/d,1],
[csc(x)^5/(a+b*csc(x)),x,9,1/2*a*(2*a^2+b^2)*arctanh(cos(x))/b^4-2*a^4*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/b^4/sqrt(a^2-b^2)-1/3*(3*a^2+2*b^2)*cot(x)/b^3+1/2*a*cot(x)*csc(x)/b^2-1/3*cot(x)*csc(x)^2/b,1],
[csc(x)^4/(a+b*csc(x)),x,8,-1/2*(2*a^2+b^2)*arctanh(cos(x))/b^3+2*a^3*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/b^3/sqrt(a^2-b^2)+a*cot(x)/b^2-1/2*cot(x)*csc(x)/b,1],
[csc(x)^3/(a+b*csc(x)),x,7,a*arctanh(cos(x))/b^2-2*a^2*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/b^2/sqrt(a^2-b^2)-cot(x)/b,1],
[csc(x)^2/(a+b*csc(x)),x,6,-arctanh(cos(x))/b+2*a*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/b/sqrt(a^2-b^2),1],
[csc(x)/(a+b*csc(x)),x,4,-2*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/sqrt(a^2-b^2),1],
[1/(a+b*csc(d*x+c)),x,4,x/a+2*b*arctanh((a+b*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a/sqrt(a^2-b^2)/d,1],
[sin(x)/(a+b*csc(x)),x,6,-b*x/a^2-2*b^2*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/a^2/sqrt(a^2-b^2)-cos(x)/a,1],
[sin(x)^2/(a+b*csc(x)),x,7,1/2*(a^2+2*b^2)*x/a^3+2*b^3*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/a^3/sqrt(a^2-b^2)+b*cos(x)/a^2-1/2*cos(x)*sin(x)/a,1],
[sin(x)^3/(a+b*csc(x)),x,8,-1/2*b*(a^2+2*b^2)*x/a^4-2*b^4*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/a^4/sqrt(a^2-b^2)-1/3*(2*a^2+3*b^2)*cos(x)/a^3+1/2*b*cos(x)*sin(x)/a^2-1/3*cos(x)*sin(x)^2/a,1],
[sin(x)^4/(a+b*csc(x)),x,9,1/8*(3*a^4+4*a^2*b^2+8*b^4)*x/a^5+2*b^5*arctanh((a+b*tan(1/2*x))/sqrt(a^2-b^2))/a^5/sqrt(a^2-b^2)+1/3*b*(2*a^2+3*b^2)*cos(x)/a^4-1/8*(3*a^2+4*b^2)*cos(x)*sin(x)/a^3+1/3*b*cos(x)*sin(x)^2/a^2-1/4*cos(x)*sin(x)^3/a,1],
[1/(a+b*csc(d*x+c))^2,x,6,x/a^2+2*b*(2*a^2-b^2)*arctanh((a+b*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^2/(a^2-b^2)^(3/2)/d-b^2*cot(d*x+c)/a/(a^2-b^2)/d/(a+b*csc(d*x+c)),1],
[1/(a+b*csc(d*x+c))^3,x,7,x/a^3+b*(6*a^4-5*a^2*b^2+2*b^4)*arctanh((a+b*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^3/(a^2-b^2)^(5/2)/d-1/2*b^2*cot(d*x+c)/a/(a^2-b^2)/d/(a+b*csc(d*x+c))^2-1/2*b^2*(5*a^2-2*b^2)*cot(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*csc(d*x+c)),1],
[1/(a+b*csc(d*x+c))^4,x,8,x/a^4+b*(8*a^6-8*a^4*b^2+7*a^2*b^4-2*b^6)*arctanh((a+b*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/a^4/(a^2-b^2)^(7/2)/d-1/3*b^2*cot(d*x+c)/a/(a^2-b^2)/d/(a+b*csc(d*x+c))^3-1/6*b^2*(8*a^2-3*b^2)*cot(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*csc(d*x+c))^2-1/6*b^2*(26*a^4-17*a^2*b^2+6*b^4)*cot(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*csc(d*x+c)),1],
[1/(3+5*csc(d*x+c)),x,2,-1/12*x-5/6*arctan(cos(d*x+c)/(3+sin(d*x+c)))/d,1],
[1/(5+3*csc(d*x+c)),x,4,1/5*x+3/20*ln(3*cos(1/2*d*x+1/2*c)+sin(1/2*d*x+1/2*c))/d-3/20*ln(cos(1/2*d*x+1/2*c)+3*sin(1/2*d*x+1/2*c))/d,1],
[csc(f*x+e)^3*(a+b*csc(f*x+e))^m,x,6,-cot(f*x+e)*(a+b*csc(f*x+e))^(1+m)/b/f/(2+m)+sqrt(2)*a*AppellF1(1/2,1/2,-1-m,3/2,1/2-1/2*csc(f*x+e),b*(1-csc(f*x+e))/(a+b))*cot(f*x+e)*(a+b*csc(f*x+e))^(1+m)*((a+b*csc(f*x+e))/(a+b))^(-1-m)/b^2/f/(2+m)/sqrt(1+csc(f*x+e))-sqrt(2)*(a^2+b^2*(1+m))*AppellF1(1/2,1/2,-m,3/2,1/2-1/2*csc(f*x+e),b*(1-csc(f*x+e))/(a+b))*cot(f*x+e)*(a+b*csc(f*x+e))^m/b^2/f/(2+m)/sqrt(1+csc(f*x+e))/(((a+b*csc(f*x+e))/(a+b))^m),1],
[csc(f*x+e)^2*(a+b*csc(f*x+e))^m,x,5,-sqrt(2)*AppellF1(1/2,1/2,-1-m,3/2,1/2-1/2*csc(f*x+e),b*(1-csc(f*x+e))/(a+b))*cot(f*x+e)*(a+b*csc(f*x+e))^(1+m)*((a+b*csc(f*x+e))/(a+b))^(-1-m)/b/f/sqrt(1+csc(f*x+e))+sqrt(2)*a*AppellF1(1/2,1/2,-m,3/2,1/2-1/2*csc(f*x+e),b*(1-csc(f*x+e))/(a+b))*cot(f*x+e)*(a+b*csc(f*x+e))^m/b/f/sqrt(1+csc(f*x+e))/(((a+b*csc(f*x+e))/(a+b))^m),1],
[csc(f*x+e)*(a+b*csc(f*x+e))^m,x,2,-sqrt(2)*AppellF1(1/2,1/2,-m,3/2,1/2-1/2*csc(f*x+e),b*(1-csc(f*x+e))/(a+b))*cot(f*x+e)*(a+b*csc(f*x+e))^m/f/sqrt(1+csc(f*x+e))/(((a+b*csc(f*x+e))/(a+b))^m),1],
[(a+b*csc(f*x+e))^m,x,0,Defer(Int)((a+b*csc(f*x+e))^m,x),0],
[(a+b*csc(f*x+e))^m*sin(f*x+e),x,0,Defer(Int)((a+b*csc(f*x+e))^m*sin(f*x+e),x),0],
[(a+b*csc(f*x+e))^m*sin(f*x+e)^2,x,0,Defer(Int)((a+b*csc(f*x+e))^m*sin(f*x+e)^2,x),0]]: