lst:=[[(b*tan(f*x+e)^2)^(5/2),x,4,-b^2*cot(f*x+e)*ln(cos(f*x+e))*sqrt(b*tan(f*x+e)^2)/f-1/2*b^2*tan(f*x+e)*sqrt(b*tan(f*x+e)^2)/f+1/4*b^2*tan(f*x+e)^3*sqrt(b*tan(f*x+e)^2)/f,1],
[(b*tan(f*x+e)^2)^(3/2),x,3,b*cot(f*x+e)*ln(cos(f*x+e))*sqrt(b*tan(f*x+e)^2)/f+1/2*b*tan(f*x+e)*sqrt(b*tan(f*x+e)^2)/f,1],
[sqrt(b*tan(f*x+e)^2),x,2,-cot(f*x+e)*ln(cos(f*x+e))*sqrt(b*tan(f*x+e)^2)/f,1],
[1/sqrt(b*tan(f*x+e)^2),x,2,ln(sin(f*x+e))*tan(f*x+e)/f/sqrt(b*tan(f*x+e)^2),1],
[1/(b*tan(f*x+e)^2)^(3/2),x,3,-1/2*cot(f*x+e)/b/f/sqrt(b*tan(f*x+e)^2)-ln(sin(f*x+e))*tan(f*x+e)/b/f/sqrt(b*tan(f*x+e)^2),1],
[1/(b*tan(f*x+e)^2)^(5/2),x,4,1/2*cot(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^2)-1/4*cot(f*x+e)^3/b^2/f/sqrt(b*tan(f*x+e)^2)+ln(sin(f*x+e))*tan(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^2),1],
[(b*tan(f*x+e)^3)^(5/2),x,15,-2*b^2*cot(f*x+e)*sqrt(b*tan(f*x+e)^3)/f-b^2*arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)+b^2*arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)+b^2*arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)+2/5*b^2*tan(f*x+e)*sqrt(b*tan(f*x+e)^3)/f-2/9*b^2*tan(f*x+e)^3*sqrt(b*tan(f*x+e)^3)/f+2/13*b^2*tan(f*x+e)^5*sqrt(b*tan(f*x+e)^3)/f,1],
[(b*tan(f*x+e)^3)^(3/2),x,13,-2/3*b*sqrt(b*tan(f*x+e)^3)/f-b*arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)+b*arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)-b*arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)+2/7*b*tan(f*x+e)^2*sqrt(b*tan(f*x+e)^3)/f,1],
[sqrt(b*tan(f*x+e)^3),x,12,2*cot(f*x+e)*sqrt(b*tan(f*x+e)^3)/f+arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)-arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2)-arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*sqrt(b*tan(f*x+e)^3)/sqrt(2)/f/tan(f*x+e)^(3/2),1],
[1/sqrt(b*tan(f*x+e)^3),x,12,-2*tan(f*x+e)/f/sqrt(b*tan(f*x+e)^3)+arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/f/sqrt(b*tan(f*x+e)^3)-arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/f/sqrt(b*tan(f*x+e)^3)+arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/f/sqrt(b*tan(f*x+e)^3),1],
[1/(b*tan(f*x+e)^3)^(3/2),x,13,2/3/b/f/sqrt(b*tan(f*x+e)^3)-2/7*cot(f*x+e)^2/b/f/sqrt(b*tan(f*x+e)^3)-arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b/f/sqrt(b*tan(f*x+e)^3)+arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b/f/sqrt(b*tan(f*x+e)^3)+arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b/f/sqrt(b*tan(f*x+e)^3),1],
[1/(b*tan(f*x+e)^3)^(5/2),x,15,-2/5*cot(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^3)+2/9*cot(f*x+e)^3/b^2/f/sqrt(b*tan(f*x+e)^3)-2/13*cot(f*x+e)^5/b^2/f/sqrt(b*tan(f*x+e)^3)+2*tan(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^3)-arctan(1-sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b^2/f/sqrt(b*tan(f*x+e)^3)+arctan(1+sqrt(2)*sqrt(tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b^2/f/sqrt(b*tan(f*x+e)^3)-arctanh(sqrt(2)*sqrt(tan(f*x+e))/(1+tan(f*x+e)))*tan(f*x+e)^(3/2)/sqrt(2)/b^2/f/sqrt(b*tan(f*x+e)^3),1],
[(b*tan(f*x+e)^4)^(5/2),x,7,b^2*cot(f*x+e)*sqrt(b*tan(f*x+e)^4)/f-b^2*x*cot(f*x+e)^2*sqrt(b*tan(f*x+e)^4)-1/3*b^2*tan(f*x+e)*sqrt(b*tan(f*x+e)^4)/f+1/5*b^2*tan(f*x+e)^3*sqrt(b*tan(f*x+e)^4)/f-1/7*b^2*tan(f*x+e)^5*sqrt(b*tan(f*x+e)^4)/f+1/9*b^2*tan(f*x+e)^7*sqrt(b*tan(f*x+e)^4)/f,1],
[(b*tan(f*x+e)^4)^(3/2),x,5,b*cot(f*x+e)*sqrt(b*tan(f*x+e)^4)/f-b*x*cot(f*x+e)^2*sqrt(b*tan(f*x+e)^4)-1/3*b*tan(f*x+e)*sqrt(b*tan(f*x+e)^4)/f+1/5*b*tan(f*x+e)^3*sqrt(b*tan(f*x+e)^4)/f,1],
[sqrt(b*tan(f*x+e)^4),x,3,cot(f*x+e)*sqrt(b*tan(f*x+e)^4)/f-x*cot(f*x+e)^2*sqrt(b*tan(f*x+e)^4),1],
[1/sqrt(b*tan(f*x+e)^4),x,3,-tan(f*x+e)/f/sqrt(b*tan(f*x+e)^4)-x*tan(f*x+e)^2/sqrt(b*tan(f*x+e)^4),1],
[1/(b*tan(f*x+e)^4)^(3/2),x,5,1/3*cot(f*x+e)/b/f/sqrt(b*tan(f*x+e)^4)-1/5*cot(f*x+e)^3/b/f/sqrt(b*tan(f*x+e)^4)-tan(f*x+e)/b/f/sqrt(b*tan(f*x+e)^4)-x*tan(f*x+e)^2/b/sqrt(b*tan(f*x+e)^4),1],
[1/(b*tan(f*x+e)^4)^(5/2),x,7,1/3*cot(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^4)-1/5*cot(f*x+e)^3/b^2/f/sqrt(b*tan(f*x+e)^4)+1/7*cot(f*x+e)^5/b^2/f/sqrt(b*tan(f*x+e)^4)-1/9*cot(f*x+e)^7/b^2/f/sqrt(b*tan(f*x+e)^4)-tan(f*x+e)/b^2/f/sqrt(b*tan(f*x+e)^4)-x*tan(f*x+e)^2/b^2/sqrt(b*tan(f*x+e)^4),1],
[(b*tan(f*x+e)^n)^(5/2),x,3,2*b^2*hypergeom([1, 1/2+5/4*n],[3/2+5/4*n],-tan(f*x+e)^2)*tan(f*x+e)^(1+2*n)*sqrt(b*tan(f*x+e)^n)/f/(2+5*n),1],
[(b*tan(f*x+e)^n)^(3/2),x,3,2*b*hypergeom([1, 1/2+3/4*n],[3/2+3/4*n],-tan(f*x+e)^2)*tan(f*x+e)^(1+n)*sqrt(b*tan(f*x+e)^n)/f/(2+3*n),1],
[sqrt(b*tan(f*x+e)^n),x,3,2*hypergeom([1, 1/2+1/4*n],[3/2+1/4*n],-tan(f*x+e)^2)*tan(f*x+e)*sqrt(b*tan(f*x+e)^n)/f/(2+n),1],
[1/sqrt(b*tan(f*x+e)^n),x,3,2*hypergeom([1, 1/2-1/4*n],[3/2-1/4*n],-tan(f*x+e)^2)*tan(f*x+e)/f/(2-n)/sqrt(b*tan(f*x+e)^n),1],
[1/(b*tan(f*x+e)^n)^(3/2),x,3,2*hypergeom([1, 1/2-3/4*n],[3/2-3/4*n],-tan(f*x+e)^2)*tan(f*x+e)^(1-n)/b/f/(2-3*n)/sqrt(b*tan(f*x+e)^n),1],
[1/(b*tan(f*x+e)^n)^(5/2),x,3,2*hypergeom([1, 1/2-5/4*n],[3/2-5/4*n],-tan(f*x+e)^2)*tan(f*x+e)^(1-2*n)/b^2/f/(2-5*n)/sqrt(b*tan(f*x+e)^n),1],
[(b*tan(f*x+e)^n)^p,x,3,hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^n)^p/f/(n*p+1),1],
[(b*tan(f*x+e)^2)^p,x,3,hypergeom([1, 1/2+p],[3/2+p],-tan(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1+2*p),1],
[(b*tan(f*x+e)^3)^p,x,3,hypergeom([1, 1/2+3/2*p],[3/2*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^3)^p/f/(1+3*p),1],
[(b*tan(f*x+e)^4)^p,x,3,hypergeom([1, 1/2+2*p],[3/2+2*p],-tan(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^4)^p/f/(1+4*p),1],
[(b*tan(f*x+e)^n)^(1/n),x,2,-cot(f*x+e)*ln(cos(f*x+e))*(b*tan(f*x+e)^n)^(1/n)/f,1],
[sin(f*x+e)^5*(a+b*tan(f*x+e)^2),x,3,-(a-3*b)*cos(f*x+e)/f+1/3*(2*a-3*b)*cos(f*x+e)^3/f-1/5*(a-b)*cos(f*x+e)^5/f+b*sec(f*x+e)/f,1],
[sin(f*x+e)^3*(a+b*tan(f*x+e)^2),x,3,-(a-2*b)*cos(f*x+e)/f+1/3*(a-b)*cos(f*x+e)^3/f+b*sec(f*x+e)/f,1],
[sin(f*x+e)*(a+b*tan(f*x+e)^2),x,3,-(a-b)*cos(f*x+e)/f+b*sec(f*x+e)/f,1],
[csc(f*x+e)*(a+b*tan(f*x+e)^2),x,3,-a*arctanh(cos(f*x+e))/f+b*sec(f*x+e)/f,1],
[csc(f*x+e)^3*(a+b*tan(f*x+e)^2),x,4,-1/2*(a+2*b)*arctanh(cos(f*x+e))/f-1/2*a*cot(f*x+e)*csc(f*x+e)/f+b*sec(f*x+e)/f,1],
[csc(f*x+e)^5*(a+b*tan(f*x+e)^2),x,5,-3/8*(a+4*b)*arctanh(cos(f*x+e))/f-1/8*(5*a+4*b)*cot(f*x+e)*csc(f*x+e)/f-1/4*a*cot(f*x+e)^3*csc(f*x+e)/f+b*sec(f*x+e)/f,1],
[sin(f*x+e)^6*(a+b*tan(f*x+e)^2),x,6,5/16*(a-7*b)*x-1/16*(11*a-29*b)*cos(f*x+e)*sin(f*x+e)/f+1/24*(13*a-19*b)*cos(f*x+e)^3*sin(f*x+e)/f-1/6*(a-b)*cos(f*x+e)^5*sin(f*x+e)/f+b*tan(f*x+e)/f,1],
[sin(f*x+e)^4*(a+b*tan(f*x+e)^2),x,5,3/8*(a-5*b)*x-1/8*(5*a-9*b)*cos(f*x+e)*sin(f*x+e)/f+1/4*(a-b)*cos(f*x+e)^3*sin(f*x+e)/f+b*tan(f*x+e)/f,1],
[sin(f*x+e)^2*(a+b*tan(f*x+e)^2),x,4,1/2*(a-3*b)*x-1/2*(a-b)*cos(f*x+e)*sin(f*x+e)/f+b*tan(f*x+e)/f,1],
[a+b*tan(f*x+e)^2,x,3,a*x-b*x+b*tan(f*x+e)/f,1],
[csc(f*x+e)^2*(a+b*tan(f*x+e)^2),x,3,-a*cot(f*x+e)/f+b*tan(f*x+e)/f,1],
[csc(f*x+e)^4*(a+b*tan(f*x+e)^2),x,3,-(a+b)*cot(f*x+e)/f-1/3*a*cot(f*x+e)^3/f+b*tan(f*x+e)/f,1],
[csc(f*x+e)^6*(a+b*tan(f*x+e)^2),x,3,-(a+2*b)*cot(f*x+e)/f-1/3*(2*a+b)*cot(f*x+e)^3/f-1/5*a*cot(f*x+e)^5/f+b*tan(f*x+e)/f,1],
[sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x,3,-(a^2-6*a*b+6*b^2)*cos(f*x+e)/f+2/3*(a-2*b)*(a-b)*cos(f*x+e)^3/f-1/5*(a-b)^2*cos(f*x+e)^5/f+2*(a-2*b)*b*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x,3,-(a-3*b)*(a-b)*cos(f*x+e)/f+1/3*(a-b)^2*cos(f*x+e)^3/f+(2*a-3*b)*b*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[sin(f*x+e)*(a+b*tan(f*x+e)^2)^2,x,3,-(a-b)^2*cos(f*x+e)/f+2*(a-b)*b*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[csc(f*x+e)*(a+b*tan(f*x+e)^2)^2,x,4,-a^2*arctanh(cos(f*x+e))/f+(2*a-b)*b*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x,5,-1/2*a*(a+4*b)*arctanh(cos(f*x+e))/f-1/2*a^2*cot(f*x+e)*csc(f*x+e)/f+2*a*b*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x,6,-1/8*(3*a^2+24*a*b+8*b^2)*arctanh(cos(f*x+e))/f-1/8*a*(5*a+8*b)*cot(f*x+e)*csc(f*x+e)/f-1/4*a^2*cot(f*x+e)^3*csc(f*x+e)/f+b*(2*a+b)*sec(f*x+e)/f+1/3*b^2*sec(f*x+e)^3/f,1],
[sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x,6,1/8*(3*a^2-30*a*b+35*b^2)*x-1/8*(5*a-13*b)*(a-b)*cos(f*x+e)*sin(f*x+e)/f+1/4*(a-b)^2*cos(f*x+e)^3*sin(f*x+e)/f+(2*a-3*b)*b*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x,5,1/2*(a-5*b)*(a-b)*x-1/2*(a-b)^2*cos(f*x+e)*sin(f*x+e)/f+2*(a-b)*b*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*x+(2*a-b)*b*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x,3,-a^2*cot(f*x+e)/f+2*a*b*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x,3,-a*(a+2*b)*cot(f*x+e)/f-1/3*a^2*cot(f*x+e)^3/f+b*(2*a+b)*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x,3,-(a^2+4*a*b+b^2)*cot(f*x+e)/f-2/3*a*(a+b)*cot(f*x+e)^3/f-1/5*a^2*cot(f*x+e)^5/f+2*b*(a+b)*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[sin(f*x+e)^5/(a+b*tan(f*x+e)^2),x,4,-a^2*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(7/2)/f-a^2*cos(f*x+e)/(a-b)^3/f+1/3*(2*a-b)*cos(f*x+e)^3/(a-b)^2/f-1/5*cos(f*x+e)^5/(a-b)/f,1],
[sin(f*x+e)^3/(a+b*tan(f*x+e)^2),x,4,-a*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(5/2)/f-a*cos(f*x+e)/(a-b)^2/f+1/3*cos(f*x+e)^3/(a-b)/f,1],
[sin(f*x+e)/(a+b*tan(f*x+e)^2),x,3,-sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(3/2)/f-cos(f*x+e)/(a-b)/f,1],
[csc(f*x+e)/(a+b*tan(f*x+e)^2),x,4,-sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a/sqrt(a-b)/f-arctanh(cos(f*x+e))/a/f,1],
[csc(f*x+e)^3/(a+b*tan(f*x+e)^2),x,5,-sqrt(a-b)*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^2/f-1/2*(a-2*b)*arctanh(cos(f*x+e))/a^2/f-1/2*cot(f*x+e)*csc(f*x+e)/a/f,1],
[csc(f*x+e)^5/(a+b*tan(f*x+e)^2),x,6,-(a-b)^(3/2)*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^3/f-1/8*(3*a^2-12*a*b+8*b^2)*arctanh(cos(f*x+e))/a^3/f-1/8*(5*a-4*b)*cot(f*x+e)*csc(f*x+e)/a^2/f-1/4*cot(f*x+e)^3*csc(f*x+e)/a/f,1],
[sin(f*x+e)^6/(a+b*tan(f*x+e)^2),x,7,1/16*(5*a^3+15*a^2*b-5*a*b^2+b^3)*x/(a-b)^4-a^(5/2)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^4/f-1/16*(11*a^2-4*a*b+b^2)*cos(f*x+e)*sin(f*x+e)/(a-b)^3/f+1/8*(3*a-b)*cos(f*x+e)^3*sin(f*x+e)/(a-b)^2/f+1/6*cos(f*x+e)^3*sin(f*x+e)^3/(a-b)/f,1],
[sin(f*x+e)^4/(a+b*tan(f*x+e)^2),x,6,1/8*(3*a^2+6*a*b-b^2)*x/(a-b)^3-a^(3/2)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^3/f-1/8*(5*a-b)*cos(f*x+e)*sin(f*x+e)/(a-b)^2/f+1/4*cos(f*x+e)^3*sin(f*x+e)/(a-b)/f,1],
[sin(f*x+e)^2/(a+b*tan(f*x+e)^2),x,5,1/2*(a+b)*x/(a-b)^2-sqrt(a)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^2/f-1/2*cos(f*x+e)*sin(f*x+e)/(a-b)/f,1],
[1/(a+b*tan(f*x+e)^2),x,3,x/(a-b)-sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)/f,1],
[csc(f*x+e)^2/(a+b*tan(f*x+e)^2),x,3,-sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/f-cot(f*x+e)/a/f,1],
[csc(f*x+e)^4/(a+b*tan(f*x+e)^2),x,4,-(a-b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/f-(a-b)*cot(f*x+e)/a^2/f-1/3*cot(f*x+e)^3/a/f,1],
[csc(f*x+e)^6/(a+b*tan(f*x+e)^2),x,4,-(a-b)^2*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/f-(a-b)^2*cot(f*x+e)/a^3/f-1/3*(2*a-b)*cot(f*x+e)^3/a^2/f-1/5*cot(f*x+e)^5/a/f,1],
[sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x,5,-1/2*a*sqrt(b)*(3*a+4*b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(9/2)/f-a*(a+2*b)*cos(f*x+e)/(a-b)^4/f+2/3*a*cos(f*x+e)^3/(a-b)^3/f-1/5*cos(f*x+e)^5/(a-b)^2/f-1/2*a^2*b*sec(f*x+e)/(a-b)^4/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x,5,-1/2*sqrt(b)*(3*a+2*b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(7/2)/f-(a+b)*cos(f*x+e)/(a-b)^3/f+1/3*cos(f*x+e)^3/(a-b)^2/f-1/2*a*b*sec(f*x+e)/(a-b)^3/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)/(a+b*tan(f*x+e)^2)^2,x,4,-3/2*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(5/2)/f-3/2*cos(f*x+e)/(a-b)^2/f+1/2*cos(f*x+e)/(a-b)/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)/(a+b*tan(f*x+e)^2)^2,x,5,-1/2*(3*a-2*b)*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^2/(a-b)^(3/2)/f-arctanh(cos(f*x+e))/a^2/f-1/2*b*sec(f*x+e)/a/(a-b)/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x,6,-1/2*(3*a-4*b)*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^3/sqrt(a-b)/f-1/2*(a-4*b)*arctanh(cos(f*x+e))/a^3/f-1/2*cot(f*x+e)*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)-b*sec(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x,7,-3/2*(a-2*b)*sqrt(a-b)*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^4/f-3/8*(a^2-8*a*b+8*b^2)*arctanh(cos(f*x+e))/a^4/f-1/8*(5*a-6*b)*cot(f*x+e)*csc(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2)-1/4*cot(f*x+e)^3*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)-3/8*(3*a-4*b)*b*sec(f*x+e)/a^3/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x,7,3/8*(a^2+6*a*b+b^2)*x/(a-b)^4-3/2*sqrt(a)*sqrt(b)*(a+b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^4/f-1/8*(5*a+b)*cos(f*x+e)*sin(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)+1/4*cos(f*x+e)^3*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)-3/8*b*(3*a+b)*tan(f*x+e)/(a-b)^3/f/(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x,6,1/2*(a+3*b)*x/(a-b)^3-1/2*sqrt(b)*(3*a+b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)^3/f-1/2*cos(f*x+e)*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)-b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^2,x,5,x/(a-b)^2-1/2*(3*a-b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/(a-b)^2/f-1/2*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x,4,-3/2*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/f-3/2*cot(f*x+e)/a^2/f+1/2*cot(f*x+e)/a/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x,5,-1/2*(3*a-5*b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/f-(a-2*b)*cot(f*x+e)/a^3/f-1/3*cot(f*x+e)^3/a^2/f-1/2*(a-b)*b*tan(f*x+e)/a^3/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x,5,-1/2*(3*a-7*b)*(a-b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(9/2)/f-(a-3*b)*(a-b)*cot(f*x+e)/a^4/f-2/3*(a-b)*cot(f*x+e)^3/a^3/f-1/5*cot(f*x+e)^5/a^2/f-1/2*(a-b)^2*b*tan(f*x+e)/a^4/f/(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x,6,-1/8*sqrt(b)*(15*a^2+40*a*b+8*b^2)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(11/2)/f-(a^2+4*a*b+b^2)*cos(f*x+e)/(a-b)^5/f+1/3*(2*a+b)*cos(f*x+e)^3/(a-b)^4/f-1/5*cos(f*x+e)^5/(a-b)^3/f-1/4*a^2*b*sec(f*x+e)/(a-b)^4/f/(a-b+b*sec(f*x+e)^2)^2-1/8*a*b*(7*a+8*b)*sec(f*x+e)/(a-b)^5/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x,6,-5/8*sqrt(b)*(3*a+4*b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(9/2)/f-(a+2*b)*cos(f*x+e)/(a-b)^4/f+1/3*cos(f*x+e)^3/(a-b)^3/f-1/4*a*b*sec(f*x+e)/(a-b)^3/f/(a-b+b*sec(f*x+e)^2)^2-1/8*b*(7*a+4*b)*sec(f*x+e)/(a-b)^4/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)/(a+b*tan(f*x+e)^2)^3,x,5,-15/8*sqrt(b)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/(a-b)^(7/2)/f-15/8*cos(f*x+e)/(a-b)^3/f+1/4*cos(f*x+e)/(a-b)/f/(a-b+b*sec(f*x+e)^2)^2+5/8*cos(f*x+e)/(a-b)^2/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)/(a+b*tan(f*x+e)^2)^3,x,6,-1/8*sqrt(b)*(15*a^2-20*a*b+8*b^2)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^3/(a-b)^(5/2)/f-arctanh(cos(f*x+e))/a^3/f-1/4*b*sec(f*x+e)/a/(a-b)/f/(a-b+b*sec(f*x+e)^2)^2-1/8*(7*a-4*b)*b*sec(f*x+e)/a^2/(a-b)^2/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x,7,-1/8*sqrt(b)*(15*a^2-40*a*b+24*b^2)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^4/(a-b)^(3/2)/f-1/2*(a-6*b)*arctanh(cos(f*x+e))/a^4/f-1/2*cot(f*x+e)*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)^2-3/4*b*sec(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2)^2-1/8*(11*a-12*b)*b*sec(f*x+e)/a^3/(a-b)/f/(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x,8,-3/8*sqrt(b)*(5*a^2-20*a*b+16*b^2)*arctan(sqrt(b)*sec(f*x+e)/sqrt(a-b))/a^5/sqrt(a-b)/f-3/8*(a^2-12*a*b+16*b^2)*arctanh(cos(f*x+e))/a^5/f-1/8*(5*a-8*b)*cot(f*x+e)*csc(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2)^2-1/4*cot(f*x+e)^3*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)^2-1/8*(7*a-12*b)*b*sec(f*x+e)/a^3/f/(a-b+b*sec(f*x+e)^2)^2-3/2*(a-2*b)*b*sec(f*x+e)/a^4/f/(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x,8,3/8*(a^2+10*a*b+5*b^2)*x/(a-b)^5-3/8*sqrt(b)*(5*a^2+10*a*b+b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)^5/f-1/8*(5*a+3*b)*cos(f*x+e)*sin(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)^2+1/4*cos(f*x+e)^3*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*b*(7*a+5*b)*tan(f*x+e)/(a-b)^3/f/(a+b*tan(f*x+e)^2)^2-3/2*b*(a+b)*tan(f*x+e)/(a-b)^4/f/(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x,7,1/2*(a+5*b)*x/(a-b)^4-1/8*sqrt(b)*(15*a^2+10*a*b-b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/(a-b)^4/f-1/2*cos(f*x+e)*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^2-3/4*b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)^2-1/8*b*(11*a+b)*tan(f*x+e)/a/(a-b)^3/f/(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^3,x,6,x/(a-b)^3-1/8*sqrt(b)*(15*a^2-10*a*b+3*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/(a-b)^3/f-1/4*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*(7*a-3*b)*b*tan(f*x+e)/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x,5,-15/8*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/f-15/8*cot(f*x+e)/a^3/f+1/4*cot(f*x+e)/a/f/(a+b*tan(f*x+e)^2)^2+5/8*cot(f*x+e)/a^2/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x,6,-5/8*(3*a-7*b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(9/2)/f-(a-3*b)*cot(f*x+e)/a^4/f-1/3*cot(f*x+e)^3/a^3/f-1/4*(a-b)*b*tan(f*x+e)/a^3/f/(a+b*tan(f*x+e)^2)^2-1/8*(7*a-11*b)*b*tan(f*x+e)/a^4/f/(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x,6,-1/8*sqrt(b)*(15*a^2-70*a*b+63*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(11/2)/f-(a^2-6*a*b+6*b^2)*cot(f*x+e)/a^5/f-1/3*(2*a-3*b)*cot(f*x+e)^3/a^4/f-1/5*cot(f*x+e)^5/a^3/f-1/4*(a-b)^2*b*tan(f*x+e)/a^4/f/(a+b*tan(f*x+e)^2)^2-1/8*(7*a-15*b)*(a-b)*b*tan(f*x+e)/a^5/f/(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f-cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f+2/15*(5*a-4*b)*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(3/2)/(a-b)^2/f-1/5*cos(f*x+e)^5*(a-b+b*sec(f*x+e)^2)^(3/2)/(a-b)/f,1],
[sin(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2),x,5,sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f-cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f+1/3*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(3/2)/(a-b)/f,1],
[sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2),x,4,sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f-cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f,1],
[csc(f*x+e)*sqrt(a+b*tan(f*x+e)^2),x,6,-sqrt(a)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f,1],
[csc(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2),x,7,-1/2*(a+b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/sqrt(a)/f+sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f-1/2*cot(f*x+e)*csc(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f,1],
[csc(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2),x,8,-1/8*(3*a^2+6*a*b-b^2)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(3/2)/f+sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f-1/8*(3*a+b)*cot(f*x+e)*csc(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/a/f-1/4*cot(f*x+e)*csc(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/f,1],
[sin(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2),x,8,1/8*(3*a^2-12*a*b+8*b^2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f+sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/8*(3*a-4*b)*cos(f*x+e)*sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/(a-b)/f-1/4*cos(f*x+e)*sin(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f,1],
[sin(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2),x,7,1/2*(a-2*b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f+sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/2*cos(f*x+e)*sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f,1],
[csc(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2),x,4,sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[csc(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2),x,5,sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-1/3*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2)/a/f,1],
[csc(f*x+e)^6*sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-2/15*(5*a-b)*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2)/a^2/f-1/5*cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2)/a/f,1],
[sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x,7,1/2*(3*a-7*b)*sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+1/2*(3*a-7*b)*b*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)/f-1/3*(3*a-7*b)*cos(f*x+e)*(a-b+b*sec(f*x+e)^2)^(3/2)/(a-b)/f+2/3*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(5/2)/(a-b)/f-1/5*cos(f*x+e)^5*(a-b+b*sec(f*x+e)^2)^(5/2)/(a-b)/f,1],
[sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x,6,1/2*(3*a-5*b)*sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+1/2*(3*a-5*b)*b*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)/f-1/3*(3*a-5*b)*cos(f*x+e)*(a-b+b*sec(f*x+e)^2)^(3/2)/(a-b)/f+1/3*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(5/2)/(a-b)/f,1],
[sin(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x,5,3/2*(a-b)*sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+3/2*b*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f-cos(f*x+e)*(a-b+b*sec(f*x+e)^2)^(3/2)/f,1],
[csc(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x,7,-a^(3/2)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+1/2*(3*a-b)*sqrt(b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+1/2*b*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f,1],
[csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x,8,-1/2*sqrt(a)*(a+3*b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+1/2*sqrt(b)*(3*a+b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+b*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f-1/2*cot(f*x+e)*csc(f*x+e)*(a-b+b*sec(f*x+e)^2)^(3/2)/f,1],
[csc(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x,9,-3/8*(a^2+6*a*b+b^2)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/sqrt(a)/f+3/2*sqrt(b)*(a+b)*arctanh(sqrt(b)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/f+3/8*(a+3*b)*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f-3/8*(a+b)*csc(f*x+e)^2*sec(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/f-1/4*cot(f*x+e)*csc(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(3/2)/f,1],
[sin(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x,9,3/8*(a^2-8*a*b+8*b^2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f+3/2*(a-2*b)*sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-3/8*(a-4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f+3/8*(a-2*b)*sin(f*x+e)^2*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-1/4*cos(f*x+e)*sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2)/f,1],
[sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x,8,1/2*(a-4*b)*sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*(3*a-4*b)*sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+b*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-1/2*cos(f*x+e)*sin(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/f,1],
[(a+b*tan(f*x+e)^2)^(3/2),x,7,(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*(3*a-2*b)*sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*b*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x,5,3/2*a*sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+3/2*b*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/f,1],
[csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x,6,1/2*sqrt(b)*(3*a+2*b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*b*(3*a+2*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f-1/3*(3*a+2*b)*cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/a/f-1/3*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(5/2)/a/f,1],
[csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x,7,1/2*sqrt(b)*(3*a+4*b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*b*(3*a+4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f-1/3*(3*a+4*b)*cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2)/a/f-2/3*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(5/2)/a/f-1/5*cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(5/2)/a/f,1],
[sin(f*x+e)^5/sqrt(a+b*tan(f*x+e)^2),x,4,-1/15*(15*a^2-10*a*b+3*b^2)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^3/f+2/15*(5*a-3*b)*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^2/f-1/5*cos(f*x+e)^5*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)/f,1],
[sin(f*x+e)^3/sqrt(a+b*tan(f*x+e)^2),x,3,-1/3*(3*a-b)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^2/f+1/3*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)/f,1],
[sin(f*x+e)/sqrt(a+b*tan(f*x+e)^2),x,2,-cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)/f,1],
[csc(f*x+e)/sqrt(a+b*tan(f*x+e)^2),x,3,-arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/sqrt(a)/f,1],
[csc(f*x+e)^3/sqrt(a+b*tan(f*x+e)^2),x,5,-1/2*(a-b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(3/2)/f-1/2*cot(f*x+e)*csc(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/a/f,1],
[csc(f*x+e)^5/sqrt(a+b*tan(f*x+e)^2),x,6,-3/8*(a-b)^2*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(5/2)/f-1/8*(5*a-3*b)*cot(f*x+e)*csc(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/a^2/f-1/4*cot(f*x+e)^3*csc(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/a/f,1],
[sin(f*x+e)^4/sqrt(a+b*tan(f*x+e)^2),x,6,3/8*a^2*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/8*(5*a-2*b)*cos(f*x+e)*sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/(a-b)^2/f+1/4*cos(f*x+e)^3*sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/(a-b)/f,1],
[sin(f*x+e)^2/sqrt(a+b*tan(f*x+e)^2),x,5,1/2*a*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-1/2*cos(f*x+e)*sin(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/(a-b)/f,1],
[1/sqrt(a+b*tan(f*x+e)^2),x,3,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f,1],
[csc(f*x+e)^2/sqrt(a+b*tan(f*x+e)^2),x,2,-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[csc(f*x+e)^4/sqrt(a+b*tan(f*x+e)^2),x,3,-1/3*(3*a-2*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^2/f-1/3*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[csc(f*x+e)^6/sqrt(a+b*tan(f*x+e)^2),x,4,-1/15*(15*a^2-20*a*b+8*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^3/f-2/15*(5*a-2*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^2/f-1/5*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x,5,-a^2*b*sec(f*x+e)/(a-b)^4/f/sqrt(a-b+b*sec(f*x+e)^2)-1/15*(15*a^2+20*a*b-2*b^2)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^4/f+1/15*(10*a-b)*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^3/f-1/5*cos(f*x+e)^5*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^2/f,1],
[sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x,4,-a*b*sec(f*x+e)/(a-b)^3/f/sqrt(a-b+b*sec(f*x+e)^2)-1/3*(3*a+2*b)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^3/f+1/3*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^2/f,1],
[sin(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x,3,-cos(f*x+e)/(a-b)/f/sqrt(a-b+b*sec(f*x+e)^2)-2*b*sec(f*x+e)/(a-b)^2/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x,4,-arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(3/2)/f-b*sec(f*x+e)/a/(a-b)/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x,6,-1/2*(a-3*b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(5/2)/f-1/2*cot(f*x+e)*csc(f*x+e)/a/f/sqrt(a-b+b*sec(f*x+e)^2)-3/2*b*sec(f*x+e)/a^2/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x,7,-3/8*(a-5*b)*(a-b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(7/2)/f-5/8*(a-b)*cot(f*x+e)*csc(f*x+e)/a^2/f/sqrt(a-b+b*sec(f*x+e)^2)-1/4*cot(f*x+e)^3*csc(f*x+e)/a/f/sqrt(a-b+b*sec(f*x+e)^2)-1/8*(13*a-15*b)*b*sec(f*x+e)/a^3/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x,7,3/8*a*(a+4*b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(7/2)/f-5/8*a*cos(f*x+e)*sin(f*x+e)/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2)+1/4*cos(f*x+e)^3*sin(f*x+e)/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)-1/8*b*(13*a+2*b)*tan(f*x+e)/(a-b)^3/f/sqrt(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x,6,1/2*(a+2*b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/2*cos(f*x+e)*sin(f*x+e)/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)-3/2*b*tan(f*x+e)/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^(3/2),x,4,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-b*tan(f*x+e)/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x,3,-cot(f*x+e)/a/f/sqrt(a+b*tan(f*x+e)^2)-2*b*tan(f*x+e)/a^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x,4,-(a-b)*b*tan(f*x+e)/a^3/f/sqrt(a+b*tan(f*x+e)^2)-1/3*(3*a-5*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^3/f-1/3*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^2/f,1],
[csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x,5,-(a-b)^2*b*tan(f*x+e)/a^4/f/sqrt(a+b*tan(f*x+e)^2)-1/15*(15*a^2-50*a*b+33*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^4/f-1/15*(10*a-9*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^3/f-1/5*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a^2/f,1],
[sin(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x,6,-1/3*a^2*b*sec(f*x+e)/(a-b)^4/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/3*a*b*(5*a+6*b)*sec(f*x+e)/(a-b)^5/f/sqrt(a-b+b*sec(f*x+e)^2)-1/15*(15*a^2+50*a*b+8*b^2)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^5/f+2/15*(5*a+2*b)*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^4/f-1/5*cos(f*x+e)^5*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^3/f,1],
[sin(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x,5,-1/3*a*b*sec(f*x+e)/(a-b)^3/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/3*b*(5*a+3*b)*sec(f*x+e)/(a-b)^4/f/sqrt(a-b+b*sec(f*x+e)^2)-1/3*(3*a+5*b)*cos(f*x+e)*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^4/f+1/3*cos(f*x+e)^3*sqrt(a-b+b*sec(f*x+e)^2)/(a-b)^3/f,1],
[sin(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x,4,-cos(f*x+e)/(a-b)/f/(a-b+b*sec(f*x+e)^2)^(3/2)-4/3*b*sec(f*x+e)/(a-b)^2/f/(a-b+b*sec(f*x+e)^2)^(3/2)-8/3*b*sec(f*x+e)/(a-b)^3/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x,6,-arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(5/2)/f-1/3*b*sec(f*x+e)/a/(a-b)/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/3*(5*a-3*b)*b*sec(f*x+e)/a^2/(a-b)^2/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x,7,-1/2*(a-5*b)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(7/2)/f-1/2*cot(f*x+e)*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)^(3/2)-5/6*b*sec(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/6*(13*a-15*b)*b*sec(f*x+e)/a^3/(a-b)/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[csc(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x,8,-1/8*(3*a^2-30*a*b+35*b^2)*arctanh(sqrt(a)*sec(f*x+e)/sqrt(a-b+b*sec(f*x+e)^2))/a^(9/2)/f-1/8*(5*a-7*b)*cot(f*x+e)*csc(f*x+e)/a^2/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/4*cot(f*x+e)^3*csc(f*x+e)/a/f/(a-b+b*sec(f*x+e)^2)^(3/2)-1/24*(23*a-35*b)*b*sec(f*x+e)/a^3/f/(a-b+b*sec(f*x+e)^2)^(3/2)-5/24*(11*a-21*b)*b*sec(f*x+e)/a^4/f/sqrt(a-b+b*sec(f*x+e)^2),1],
[sin(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x,8,1/8*(3*a^2+24*a*b+8*b^2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(9/2)/f-1/8*(5*a+2*b)*cos(f*x+e)*sin(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)^(3/2)+1/4*cos(f*x+e)^3*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/24*b*(23*a+12*b)*tan(f*x+e)/(a-b)^3/f/(a+b*tan(f*x+e)^2)^(3/2)-5/24*b*(11*a+10*b)*tan(f*x+e)/(a-b)^4/f/sqrt(a+b*tan(f*x+e)^2),1],
[sin(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x,7,1/2*(a+4*b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(7/2)/f-1/2*cos(f*x+e)*sin(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-5/6*b*tan(f*x+e)/(a-b)^2/f/(a+b*tan(f*x+e)^2)^(3/2)-1/6*b*(13*a+2*b)*tan(f*x+e)/a/(a-b)^3/f/sqrt(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^(5/2),x,6,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(5*a-2*b)*b*tan(f*x+e)/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x,4,-cot(f*x+e)/a/f/(a+b*tan(f*x+e)^2)^(3/2)-4/3*b*tan(f*x+e)/a^2/f/(a+b*tan(f*x+e)^2)^(3/2)-8/3*b*tan(f*x+e)/a^3/f/sqrt(a+b*tan(f*x+e)^2),1],
[csc(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x,5,-1/3*(a-b)*b*tan(f*x+e)/a^3/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(5*a-8*b)*b*tan(f*x+e)/a^4/f/sqrt(a+b*tan(f*x+e)^2)-1/3*(3*a-8*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^4/f-1/3*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^3/f,1],
[csc(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x,6,-1/3*(a-b)^2*b*tan(f*x+e)/a^4/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(5*a-11*b)*(a-b)*b*tan(f*x+e)/a^5/f/sqrt(a+b*tan(f*x+e)^2)-1/15*(15*a^2-80*a*b+73*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^5/f-2/15*(5*a-7*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^4/f-1/5*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a^3/f,1],
[(d*sin(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,3,(cos(f*x+e)^2)^(1/2+p)*hypergeom([1/2+p, 1/2+1/2*m+p],[3/2+1/2*m+p],sin(f*x+e)^2)*(d*sin(f*x+e))^m*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1+m+2*p),1],
[(d*sin(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,4,AppellF1(1/2+1/2*m,1+1/2*m,-p,3/2+1/2*m,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(sec(f*x+e)^2)^(1/2*m)*(d*sin(f*x+e))^m*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(1+m)/(((a+b*tan(f*x+e)^2)/a)^p),1],
[sin(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x,5,1/15*(-2*b*p+10*a-7*b)*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(p+1)/(a-b)^2/f-1/5*cos(f*x+e)^5*(a-b+b*sec(f*x+e)^2)^(p+1)/(a-b)/f-1/15*(15*a^2-20*a*b*(p+1)+4*b^2*(p^2+3*p+2))*cos(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*sec(f*x+e)^2/(a-b))*(a-b+b*sec(f*x+e)^2)^p/(a-b)^2/f/(((a-b+b*sec(f*x+e)^2)/(a-b))^p),1],
[sin(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x,4,1/3*cos(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^(p+1)/(a-b)/f-1/3*(3*a-2*b*(p+1))*cos(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*sec(f*x+e)^2/(a-b))*(a-b+b*sec(f*x+e)^2)^p/(a-b)/f/(((a-b+b*sec(f*x+e)^2)/(a-b))^p),1],
[sin(f*x+e)*(a+b*tan(f*x+e)^2)^p,x,3,-cos(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*sec(f*x+e)^2/(a-b))*(a-b+b*sec(f*x+e)^2)^p/f/(((a-b+b*sec(f*x+e)^2)/(a-b))^p),1],
[csc(f*x+e)*(a+b*tan(f*x+e)^2)^p,x,3,-AppellF1(1/2,1,-p,3/2,sec(f*x+e)^2,-b*sec(f*x+e)^2/(a-b))*sec(f*x+e)*(a-b+b*sec(f*x+e)^2)^p/f/(((a-b+b*sec(f*x+e)^2)/(a-b))^p),1],
[csc(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x,3,1/3*AppellF1(3/2,2,-p,5/2,sec(f*x+e)^2,-b*sec(f*x+e)^2/(a-b))*sec(f*x+e)^3*(a-b+b*sec(f*x+e)^2)^p/f/(((a-b+b*sec(f*x+e)^2)/(a-b))^p),1],
[sin(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x,3,1/3*AppellF1(3/2,2,-p,5/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(a+b*tan(f*x+e)^2)^p,x,3,AppellF1(1/2,1,-p,3/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[csc(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x,3,-cot(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*tan(f*x+e)^2/a)*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[csc(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x,4,-1/3*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(p+1)/a/f-1/3*(3*a-b*(1-2*p))*cot(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*tan(f*x+e)^2/a)*(a+b*tan(f*x+e)^2)^p/a/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[csc(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x,5,-1/15*(10*a-b*(3-2*p))*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(p+1)/a^2/f-1/5*cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(p+1)/a/f-1/15*(15*a^2-b*(10*a-b*(3-2*p))*(1-2*p))*cot(f*x+e)*hypergeom([-1/2, -p],[1/2],-b*tan(f*x+e)^2/a)*(a+b*tan(f*x+e)^2)^p/a^2/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(d*sin(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,3,(cos(f*x+e)^2)^(1/2*n*p+1/2)*hypergeom([1/2*n*p+1/2, 1/2*n*p+1/2*m+1/2],[1/2*n*p+1/2*m+3/2],sin(f*x+e)^2)*(d*sin(f*x+e))^m*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+m+1),1],
[sin(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([2, 1/2*n*p+3/2],[1/2*n*p+5/2],-tan(f*x+e)^2)*tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(n*p+3),1],
[(b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[csc(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,3,-cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+1),1],
[csc(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+1)-cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+3),1],
[csc(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+1)-2*cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+3)-cot(f*x+e)^5*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+5),1],
[sin(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,3,(cos(f*x+e)^2)^(1/2*n*p+1/2)*hypergeom([1/2*n*p+1/2, 1/2*n*p+2],[1/2*n*p+3],sin(f*x+e)^2)*sin(f*x+e)^3*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+4),1],
[sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,3,(cos(f*x+e)^2)^(1/2*n*p+1/2)*hypergeom([1/2*n*p+1/2, 1/2*n*p+1],[1/2*n*p+2],sin(f*x+e)^2)*sin(f*x+e)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+2),1],
[csc(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,3,(cos(f*x+e)^2)^(1/2*n*p+1/2)*hypergeom([1/2*n*p, 1/2*n*p+1/2],[1/2*n*p+1],sin(f*x+e)^2)*sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/n/p,1],
[csc(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,3,-(cos(f*x+e)^2)^(1/2*n*p+1/2)*csc(f*x+e)^2*hypergeom([1/2*n*p-1, 1/2*n*p+1/2],[1/2*n*p],sin(f*x+e)^2)*sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+2),1],
[(d*sin(f*x+e))^m*(a+b*tan(f*x+e)^n)^p,x,0,Defer(Int)((d*sin(f*x+e))^m*(a+b*tan(f*x+e)^n)^p,x),0],
[(d*cos(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,3,(d*cos(f*x+e))^m*(cos(f*x+e)^2)^(1/2-1/2*m+p)*hypergeom([1/2+p, 1/2-1/2*m+p],[3/2+p],sin(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1+2*p),1],
[(d*cos(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,4,AppellF1(1/2,1+1/2*m,-p,3/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(d*cos(f*x+e))^m*(sec(f*x+e)^2)^(1/2*m)*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(d*cos(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,3,(d*cos(f*x+e))^m*(cos(f*x+e)^2)^(1/2*n*p-1/2*m+1/2)*hypergeom([1/2*n*p+1/2, 1/2*n*p-1/2*m+1/2],[1/2*n*p+3/2],sin(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[(d*cos(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x,1,(d*cos(f*x+e))^m*(sec(f*x+e)/d)^m*Defer(Int)((a+b*(c*tan(f*x+e))^n)^p/((sec(f*x+e)/d)^m),x),0],
[(a+a*tan(d*x+c)^2)^4,x,4,a^4*tan(d*x+c)/d+a^4*tan(d*x+c)^3/d+3/5*a^4*tan(d*x+c)^5/d+1/7*a^4*tan(d*x+c)^7/d,1],
[(a+a*tan(d*x+c)^2)^3,x,4,a^3*tan(d*x+c)/d+2/3*a^3*tan(d*x+c)^3/d+1/5*a^3*tan(d*x+c)^5/d,1],
[(a+a*tan(d*x+c)^2)^2,x,4,a^2*tan(d*x+c)/d+1/3*a^2*tan(d*x+c)^3/d,1],
[1/(a+a*tan(d*x+c)^2),x,4,1/2*x/a+1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[1/(a+a*tan(d*x+c)^2)^2,x,5,3/8*x/a^2+3/8*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],
[1/(a+a*tan(d*x+c)^2)^3,x,6,5/16*x/a^3+5/16*cos(d*x+c)*sin(d*x+c)/a^3/d+5/24*cos(d*x+c)^3*sin(d*x+c)/a^3/d+1/6*cos(d*x+c)^5*sin(d*x+c)/a^3/d,1],
[tan(f*x+e)^5*(a+b*tan(f*x+e)^2),x,4,-(a-b)*ln(cos(f*x+e))/f-1/2*(a-b)*tan(f*x+e)^2/f+1/4*(a-b)*tan(f*x+e)^4/f+1/6*b*tan(f*x+e)^6/f,1],
[tan(f*x+e)^3*(a+b*tan(f*x+e)^2),x,3,(a-b)*ln(cos(f*x+e))/f+1/2*(a-b)*tan(f*x+e)^2/f+1/4*b*tan(f*x+e)^4/f,1],
[tan(f*x+e)*(a+b*tan(f*x+e)^2),x,2,-(a-b)*ln(cos(f*x+e))/f+1/2*b*tan(f*x+e)^2/f,1],
[cot(f*x+e)*(a+b*tan(f*x+e)^2),x,3,-b*ln(cos(f*x+e))/f+a*ln(sin(f*x+e))/f,1],
[cot(f*x+e)^3*(a+b*tan(f*x+e)^2),x,3,-1/2*a*cot(f*x+e)^2/f-(a-b)*ln(sin(f*x+e))/f,1],
[cot(f*x+e)^5*(a+b*tan(f*x+e)^2),x,4,1/2*(a-b)*cot(f*x+e)^2/f-1/4*a*cot(f*x+e)^4/f+(a-b)*ln(sin(f*x+e))/f,1],
[tan(f*x+e)^6*(a+b*tan(f*x+e)^2),x,5,-(a-b)*x+(a-b)*tan(f*x+e)/f-1/3*(a-b)*tan(f*x+e)^3/f+1/5*(a-b)*tan(f*x+e)^5/f+1/7*b*tan(f*x+e)^7/f,1],
[tan(f*x+e)^4*(a+b*tan(f*x+e)^2),x,4,(a-b)*x-(a-b)*tan(f*x+e)/f+1/3*(a-b)*tan(f*x+e)^3/f+1/5*b*tan(f*x+e)^5/f,1],
[tan(f*x+e)^2*(a+b*tan(f*x+e)^2),x,3,-(a-b)*x+(a-b)*tan(f*x+e)/f+1/3*b*tan(f*x+e)^3/f,1],
[a+b*tan(f*x+e)^2,x,3,a*x-b*x+b*tan(f*x+e)/f,1],
[cot(f*x+e)^2*(a+b*tan(f*x+e)^2),x,2,-(a-b)*x-a*cot(f*x+e)/f,1],
[cot(f*x+e)^4*(a+b*tan(f*x+e)^2),x,4,(a-b)*x+(a-b)*cot(f*x+e)/f-1/3*a*cot(f*x+e)^3/f,1],
[cot(f*x+e)^6*(a+b*tan(f*x+e)^2),x,5,-(a-b)*x-(a-b)*cot(f*x+e)/f+1/3*(a-b)*cot(f*x+e)^3/f-1/5*a*cot(f*x+e)^5/f,1],
[tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*ln(cos(f*x+e))/f-1/2*(a-b)^2*tan(f*x+e)^2/f+1/4*(a-b)^2*tan(f*x+e)^4/f+1/6*(2*a-b)*b*tan(f*x+e)^6/f+1/8*b^2*tan(f*x+e)^8/f,1],
[tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*ln(cos(f*x+e))/f+1/2*(a-b)^2*tan(f*x+e)^2/f+1/4*(2*a-b)*b*tan(f*x+e)^4/f+1/6*b^2*tan(f*x+e)^6/f,1],
[tan(f*x+e)*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*ln(cos(f*x+e))/f+1/2*(a-b)*b*tan(f*x+e)^2/f+1/4*(a+b*tan(f*x+e)^2)^2/f,1],
[cot(f*x+e)*(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*ln(cos(f*x+e))/f+a^2*ln(tan(f*x+e))/f+1/2*b^2*tan(f*x+e)^2/f,1],
[cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^2,x,4,-1/2*a^2*cot(f*x+e)^2/f-(a-b)^2*ln(cos(f*x+e))/f-a*(a-2*b)*ln(tan(f*x+e))/f,1],
[cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^2,x,4,1/2*a*(a-2*b)*cot(f*x+e)^2/f-1/4*a^2*cot(f*x+e)^4/f+(a-b)^2*ln(cos(f*x+e))/f+(a-b)^2*ln(tan(f*x+e))/f,1],
[tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*x+(a-b)^2*tan(f*x+e)/f-1/3*(a-b)^2*tan(f*x+e)^3/f+1/5*(a-b)^2*tan(f*x+e)^5/f+1/7*(2*a-b)*b*tan(f*x+e)^7/f+1/9*b^2*tan(f*x+e)^9/f,1],
[tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*x-(a-b)^2*tan(f*x+e)/f+1/3*(a-b)^2*tan(f*x+e)^3/f+1/5*(2*a-b)*b*tan(f*x+e)^5/f+1/7*b^2*tan(f*x+e)^7/f,1],
[tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*x+(a-b)^2*tan(f*x+e)/f+1/3*(2*a-b)*b*tan(f*x+e)^3/f+1/5*b^2*tan(f*x+e)^5/f,1],
[(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*x+(2*a-b)*b*tan(f*x+e)/f+1/3*b^2*tan(f*x+e)^3/f,1],
[cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*x-a^2*cot(f*x+e)/f+b^2*tan(f*x+e)/f,1],
[cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^2,x,4,(a-b)^2*x+a*(a-2*b)*cot(f*x+e)/f-1/3*a^2*cot(f*x+e)^3/f,1],
[cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^2,x,4,-(a-b)^2*x-(a-b)^2*cot(f*x+e)/f+1/3*a*(a-2*b)*cot(f*x+e)^3/f-1/5*a^2*cot(f*x+e)^5/f,1],
[tan(f*x+e)^5/(a+b*tan(f*x+e)^2),x,4,-ln(cos(f*x+e))/(a-b)/f-1/2*a^2*ln(a+b*tan(f*x+e)^2)/(a-b)/b^2/f+1/2*tan(f*x+e)^2/b/f,1],
[tan(f*x+e)^3/(a+b*tan(f*x+e)^2),x,4,ln(cos(f*x+e))/(a-b)/f+1/2*a*ln(a+b*tan(f*x+e)^2)/(a-b)/b/f,1],
[tan(f*x+e)/(a+b*tan(f*x+e)^2),x,5,-1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)/f,1],
[cot(f*x+e)/(a+b*tan(f*x+e)^2),x,4,ln(cos(f*x+e))/(a-b)/f+ln(tan(f*x+e))/a/f+1/2*b*ln(a+b*tan(f*x+e)^2)/a/(a-b)/f,1],
[cot(f*x+e)^3/(a+b*tan(f*x+e)^2),x,4,-1/2*cot(f*x+e)^2/a/f-ln(cos(f*x+e))/(a-b)/f-(a+b)*ln(tan(f*x+e))/a^2/f-1/2*b^2*ln(a+b*tan(f*x+e)^2)/a^2/(a-b)/f,1],
[cot(f*x+e)^5/(a+b*tan(f*x+e)^2),x,4,1/2*(a+b)*cot(f*x+e)^2/a^2/f-1/4*cot(f*x+e)^4/a/f+ln(cos(f*x+e))/(a-b)/f+(a^2+a*b+b^2)*ln(tan(f*x+e))/a^3/f+1/2*b^3*ln(a+b*tan(f*x+e)^2)/a^3/(a-b)/f,1],
[tan(f*x+e)^6/(a+b*tan(f*x+e)^2),x,6,-x/(a-b)+a^(5/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)/b^(5/2)/f-(a+b)*tan(f*x+e)/b^2/f+1/3*tan(f*x+e)^3/b/f,1],
[tan(f*x+e)^4/(a+b*tan(f*x+e)^2),x,5,x/(a-b)-a^(3/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)/b^(3/2)/f+tan(f*x+e)/b/f,1],
[tan(f*x+e)^2/(a+b*tan(f*x+e)^2),x,4,-x/(a-b)+sqrt(a)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)/sqrt(b)/f,1],
[1/(a+b*tan(f*x+e)^2),x,3,x/(a-b)-sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)/f,1],
[cot(f*x+e)^2/(a+b*tan(f*x+e)^2),x,5,-x/(a-b)+b^(3/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/(a-b)/f-cot(f*x+e)/a/f,1],
[cot(f*x+e)^4/(a+b*tan(f*x+e)^2),x,6,x/(a-b)-b^(5/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/(a-b)/f+(a+b)*cot(f*x+e)/a^2/f-1/3*cot(f*x+e)^3/a/f,1],
[cot(f*x+e)^6/(a+b*tan(f*x+e)^2),x,7,-x/(a-b)+b^(7/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/(a-b)/f-(a^2+a*b+b^2)*cot(f*x+e)/a^3/f+1/3*(a+b)*cot(f*x+e)^3/a^2/f-1/5*cot(f*x+e)^5/a/f,1],
[tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x,4,-ln(cos(f*x+e))/(a-b)^2/f+1/2*a*(a-2*b)*ln(a+b*tan(f*x+e)^2)/(a-b)^2/b^2/f+1/2*a^2/(a-b)/b^2/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x,4,1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)^2/f-1/2*a/(a-b)/b/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)/(a+b*tan(f*x+e)^2)^2,x,4,-1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)^2/f+1/2/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)/(a+b*tan(f*x+e)^2)^2,x,4,ln(cos(f*x+e))/(a-b)^2/f+ln(tan(f*x+e))/a^2/f+1/2*(2*a-b)*b*ln(a+b*tan(f*x+e)^2)/a^2/(a-b)^2/f-1/2*b/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^2,x,4,-1/2*cot(f*x+e)^2/a^2/f-ln(cos(f*x+e))/(a-b)^2/f-(a+2*b)*ln(tan(f*x+e))/a^3/f-1/2*(3*a-2*b)*b^2*ln(a+b*tan(f*x+e)^2)/a^3/(a-b)^2/f+1/2*b^2/a^2/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^2,x,4,1/2*(a+2*b)*cot(f*x+e)^2/a^3/f-1/4*cot(f*x+e)^4/a^2/f+ln(cos(f*x+e))/(a-b)^2/f+(a^2+2*a*b+3*b^2)*ln(tan(f*x+e))/a^4/f+1/2*(4*a-3*b)*b^3*ln(a+b*tan(f*x+e)^2)/a^4/(a-b)^2/f-1/2*b^3/a^3/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x,6,-x/(a-b)^2-1/2*a^(3/2)*(3*a-5*b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^2/b^(5/2)/f+1/2*(3*a-2*b)*tan(f*x+e)/(a-b)/b^2/f-1/2*a*tan(f*x+e)^3/(a-b)/b/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x,5,x/(a-b)^2+1/2*sqrt(a)*(a-3*b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^2/b^(3/2)/f-1/2*a*tan(f*x+e)/(a-b)/b/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x,5,-x/(a-b)^2+1/2*(a+b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)^2/sqrt(b)/f+1/2*tan(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^2,x,5,x/(a-b)^2-1/2*(3*a-b)*sqrt(b)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/(a-b)^2/f-1/2*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^2,x,6,-x/(a-b)^2+1/2*(5*a-3*b)*b^(3/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/(a-b)^2/f-1/2*(2*a-3*b)*cot(f*x+e)/a^2/(a-b)/f-1/2*b*cot(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^2,x,7,x/(a-b)^2-1/2*(7*a-5*b)*b^(5/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/(a-b)^2/f+1/2*(2*a^2+2*a*b-5*b^2)*cot(f*x+e)/a^3/(a-b)/f-1/6*(2*a-5*b)*cot(f*x+e)^3/a^2/(a-b)/f-1/2*b*cot(f*x+e)^3/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^2,x,8,-x/(a-b)^2+1/2*(9*a-7*b)*b^(7/2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(9/2)/(a-b)^2/f-1/2*(2*a^3+2*a^2*b+2*a*b^2-7*b^3)*cot(f*x+e)/a^4/(a-b)/f+1/6*(2*a^2+2*a*b-7*b^2)*cot(f*x+e)^3/a^3/(a-b)/f-1/10*(2*a-7*b)*cot(f*x+e)^5/a^2/(a-b)/f-1/2*b*cot(f*x+e)^5/a/(a-b)/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x,4,-1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)^3/f+1/4*a^2/(a-b)/b^2/f/(a+b*tan(f*x+e)^2)^2-1/2*a*(a-2*b)/(a-b)^2/b^2/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x,4,1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)^3/f-1/4*a/(a-b)/b/f/(a+b*tan(f*x+e)^2)^2-1/2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)/(a+b*tan(f*x+e)^2)^3,x,4,-1/2*ln(a*cos(f*x+e)^2+b*sin(f*x+e)^2)/(a-b)^3/f+1/4/(a-b)/f/(a+b*tan(f*x+e)^2)^2+1/2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)/(a+b*tan(f*x+e)^2)^3,x,4,ln(cos(f*x+e))/(a-b)^3/f+ln(tan(f*x+e))/a^3/f+1/2*b*(3*a^2-3*a*b+b^2)*ln(a+b*tan(f*x+e)^2)/a^3/(a-b)^3/f-1/4*b/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/2*(2*a-b)*b/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^3,x,4,-1/2*cot(f*x+e)^2/a^3/f-ln(cos(f*x+e))/(a-b)^3/f-(a+3*b)*ln(tan(f*x+e))/a^4/f-1/2*b^2*(6*a^2-8*a*b+3*b^2)*ln(a+b*tan(f*x+e)^2)/a^4/(a-b)^3/f+1/4*b^2/a^2/(a-b)/f/(a+b*tan(f*x+e)^2)^2+1/2*(3*a-2*b)*b^2/a^3/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^3,x,4,1/2*(a+3*b)*cot(f*x+e)^2/a^4/f-1/4*cot(f*x+e)^4/a^3/f+ln(cos(f*x+e))/(a-b)^3/f+(a^2+3*a*b+6*b^2)*ln(tan(f*x+e))/a^5/f+1/2*b^3*(10*a^2-15*a*b+6*b^2)*ln(a+b*tan(f*x+e)^2)/a^5/(a-b)^3/f-1/4*b^3/a^3/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/2*(4*a-3*b)*b^3/a^4/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x,6,-x/(a-b)^3+1/8*sqrt(a)*(3*a^2-10*a*b+15*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/(a-b)^3/b^(5/2)/f-1/4*a*tan(f*x+e)^3/(a-b)/b/f/(a+b*tan(f*x+e)^2)^2-1/8*a*(3*a-7*b)*tan(f*x+e)/(a-b)^2/b^2/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x,6,x/(a-b)^3+1/8*(a^2-6*a*b-3*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/sqrt(a)/(a-b)^3/b^(3/2)/f-1/4*a*tan(f*x+e)/(a-b)/b/f/(a+b*tan(f*x+e)^2)^2+1/8*(a-5*b)*tan(f*x+e)/(a-b)^2/b/f/(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x,6,-x/(a-b)^3+1/8*(3*a^2+6*a*b-b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(3/2)/(a-b)^3/sqrt(b)/f+1/4*tan(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^2+1/8*(3*a+b)*tan(f*x+e)/a/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^3,x,6,x/(a-b)^3-1/8*sqrt(b)*(15*a^2-10*a*b+3*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(5/2)/(a-b)^3/f-1/4*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*(7*a-3*b)*b*tan(f*x+e)/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^3,x,7,-x/(a-b)^3+1/8*b^(3/2)*(35*a^2-42*a*b+15*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(7/2)/(a-b)^3/f-1/8*(8*a^2-27*a*b+15*b^2)*cot(f*x+e)/a^3/(a-b)^2/f-1/4*b*cot(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*(9*a-5*b)*b*cot(f*x+e)/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^3,x,8,x/(a-b)^3-1/8*b^(5/2)*(63*a^2-90*a*b+35*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(9/2)/(a-b)^3/f+1/8*(8*a^3+8*a^2*b-55*a*b^2+35*b^3)*cot(f*x+e)/a^4/(a-b)^2/f-1/24*(8*a^2-55*a*b+35*b^2)*cot(f*x+e)^3/a^3/(a-b)^2/f-1/4*b*cot(f*x+e)^3/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*(11*a-7*b)*b*cot(f*x+e)^3/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^3,x,9,-x/(a-b)^3+1/8*b^(7/2)*(99*a^2-154*a*b+63*b^2)*arctan(sqrt(b)*tan(f*x+e)/sqrt(a))/a^(11/2)/(a-b)^3/f-1/8*(8*a^4+8*a^3*b+8*a^2*b^2-91*a*b^3+63*b^4)*cot(f*x+e)/a^5/(a-b)^2/f+1/24*(8*a^3+8*a^2*b-91*a*b^2+63*b^3)*cot(f*x+e)^3/a^4/(a-b)^2/f-1/40*(8*a^2-91*a*b+63*b^2)*cot(f*x+e)^5/a^3/(a-b)^2/f-1/4*b*cot(f*x+e)^5/a/(a-b)/f/(a+b*tan(f*x+e)^2)^2-1/8*(13*a-9*b)*b*cot(f*x+e)^5/a^2/(a-b)^2/f/(a+b*tan(f*x+e)^2),1],
[(a+b*tan(d*x+c)^2)^4,x,4,(a-b)^4*x+(2*a-b)*b*(2*a^2-2*a*b+b^2)*tan(d*x+c)/d+1/3*b^2*(6*a^2-4*a*b+b^2)*tan(d*x+c)^3/d+1/5*(4*a-b)*b^3*tan(d*x+c)^5/d+1/7*b^4*tan(d*x+c)^7/d,1],
[(a+b*tan(d*x+c)^2)^3,x,4,(a-b)^3*x+b*(3*a^2-3*a*b+b^2)*tan(d*x+c)/d+1/3*(3*a-b)*b^2*tan(d*x+c)^3/d+1/5*b^3*tan(d*x+c)^5/d,1],
[(a+b*tan(d*x+c)^2)^2,x,4,(a-b)^2*x+(2*a-b)*b*tan(d*x+c)/d+1/3*b^2*tan(d*x+c)^3/d,1],
[a+b*tan(d*x+c)^2,x,3,a*x-b*x+b*tan(d*x+c)/d,1],
[1/(a+b*tan(d*x+c)^2),x,3,x/(a-b)-sqrt(b)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/(a-b)/d,1],
[1/(a+b*tan(d*x+c)^2)^2,x,5,x/(a-b)^2-1/2*(3*a-b)*sqrt(b)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^2/d-1/2*b*tan(d*x+c)/a/(a-b)/d/(a+b*tan(d*x+c)^2),1],
[1/(a+b*tan(d*x+c)^2)^3,x,6,x/(a-b)^3-1/8*sqrt(b)*(15*a^2-10*a*b+3*b^2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(5/2)/(a-b)^3/d-1/4*b*tan(d*x+c)/a/(a-b)/d/(a+b*tan(d*x+c)^2)^2-1/8*(7*a-3*b)*b*tan(d*x+c)/a^2/(a-b)^2/d/(a+b*tan(d*x+c)^2),1],
[tan(x)^4*sqrt(a+a*tan(x)^2),x,5,3/8*arctanh(sin(x))*cos(x)*sqrt(a*sec(x)^2)-3/8*sqrt(a*sec(x)^2)*tan(x)+1/4*sqrt(a*sec(x)^2)*tan(x)^3,1],
[tan(x)^3*sqrt(a+a*tan(x)^2),x,4,-sqrt(a*sec(x)^2)+1/3*(a*sec(x)^2)^(3/2)/a,1],
[tan(x)^2*sqrt(a+a*tan(x)^2),x,4,-1/2*arctanh(sin(x))*cos(x)*sqrt(a*sec(x)^2)+1/2*sqrt(a*sec(x)^2)*tan(x),1],
[tan(x)*sqrt(a+a*tan(x)^2),x,3,sqrt(a*sec(x)^2),1],
[cot(x)*sqrt(a+a*tan(x)^2),x,4,-sqrt(a)*arctanh(sqrt(a*sec(x)^2)/sqrt(a)),1],
[cot(x)^2*sqrt(a+a*tan(x)^2),x,4,-cot(x)*sqrt(a*sec(x)^2),1],
[cot(x)^3*sqrt(a+a*tan(x)^2),x,5,1/2*sqrt(a)*arctanh(sqrt(a*sec(x)^2)/sqrt(a))-1/2*cot(x)^2*sqrt(a*sec(x)^2),1],
[cot(x)^4*sqrt(a+a*tan(x)^2),x,4,cot(x)*sqrt(a*sec(x)^2)-1/3*cot(x)*csc(x)^2*sqrt(a*sec(x)^2),1],
[sqrt(a+a*tan(d*x+c)^2),x,4,sqrt(a)*arctanh(sqrt(a)*tan(d*x+c)/sqrt(a*sec(d*x+c)^2))/d,1],
[tan(x)^3*(a+a*tan(x)^2)^(3/2),x,4,-1/3*(a*sec(x)^2)^(3/2)+1/5*(a*sec(x)^2)^(5/2)/a,1],
[tan(x)^2*(a+a*tan(x)^2)^(3/2),x,5,-1/8*a*arctanh(sin(x))*cos(x)*sqrt(a*sec(x)^2)-1/8*a*sqrt(a*sec(x)^2)*tan(x)+1/4*a*sec(x)^2*sqrt(a*sec(x)^2)*tan(x),1],
[tan(x)*(a+a*tan(x)^2)^(3/2),x,3,1/3*(a*sec(x)^2)^(3/2),1],
[cot(x)*(a+a*tan(x)^2)^(3/2),x,5,-a^(3/2)*arctanh(sqrt(a*sec(x)^2)/sqrt(a))+a*sqrt(a*sec(x)^2),1],
[cot(x)^2*(a+a*tan(x)^2)^(3/2),x,5,a*arctanh(sin(x))*cos(x)*sqrt(a*sec(x)^2)-a*cot(x)*sqrt(a*sec(x)^2),1],
[(a+a*tan(d*x+c)^2)^(3/2),x,5,1/2*a^(3/2)*arctanh(sqrt(a)*tan(d*x+c)/sqrt(a*sec(d*x+c)^2))/d+1/2*a*sqrt(a*sec(d*x+c)^2)*tan(d*x+c)/d,1],
[(a+a*tan(d*x+c)^2)^(5/2),x,6,3/8*a^(5/2)*arctanh(sqrt(a)*tan(d*x+c)/sqrt(a*sec(d*x+c)^2))/d+3/8*a^2*sqrt(a*sec(d*x+c)^2)*tan(d*x+c)/d+1/4*a*(a*sec(d*x+c)^2)^(3/2)*tan(d*x+c)/d,1],
[tan(x)^3/sqrt(a+a*tan(x)^2),x,4,1/sqrt(a*sec(x)^2)+sqrt(a*sec(x)^2)/a,1],
[tan(x)^2/sqrt(a+a*tan(x)^2),x,5,arctanh(sin(x))*sec(x)/sqrt(a*sec(x)^2)-tan(x)/sqrt(a*sec(x)^2),1],
[tan(x)/sqrt(a+a*tan(x)^2),x,3,-1/sqrt(a*sec(x)^2),1],
[cot(x)/sqrt(a+a*tan(x)^2),x,5,-arctanh(sqrt(a*sec(x)^2)/sqrt(a))/sqrt(a)+1/sqrt(a*sec(x)^2),1],
[cot(x)^2/sqrt(a+a*tan(x)^2),x,5,-csc(x)*sec(x)/sqrt(a*sec(x)^2)-tan(x)/sqrt(a*sec(x)^2),1],
[tan(x)^3/(a+a*tan(x)^2)^(3/2),x,4,1/3/(a*sec(x)^2)^(3/2)-1/a/sqrt(a*sec(x)^2),1],
[tan(x)^2/(a+a*tan(x)^2)^(3/2),x,4,1/3*sin(x)^2*tan(x)/a/sqrt(a*sec(x)^2),1],
[tan(x)/(a+a*tan(x)^2)^(3/2),x,3,-1/3/(a*sec(x)^2)^(3/2),1],
[cot(x)/(a+a*tan(x)^2)^(3/2),x,6,-arctanh(sqrt(a*sec(x)^2)/sqrt(a))/a^(3/2)+1/3/(a*sec(x)^2)^(3/2)+1/a/sqrt(a*sec(x)^2),1],
[cot(x)^2/(a+a*tan(x)^2)^(3/2),x,5,-csc(x)*sec(x)/a/sqrt(a*sec(x)^2)-2*tan(x)/a/sqrt(a*sec(x)^2)+1/3*sin(x)^2*tan(x)/a/sqrt(a*sec(x)^2),1],
[1/sqrt(a+a*tan(d*x+c)^2),x,3,tan(d*x+c)/d/sqrt(a*sec(d*x+c)^2),1],
[1/(a+a*tan(d*x+c)^2)^(3/2),x,4,1/3*tan(d*x+c)/d/(a*sec(d*x+c)^2)^(3/2)+2/3*tan(d*x+c)/a/d/sqrt(a*sec(d*x+c)^2),1],
[1/(a+a*tan(d*x+c)^2)^(5/2),x,5,1/5*tan(d*x+c)/d/(a*sec(d*x+c)^2)^(5/2)+4/15*tan(d*x+c)/a/d/(a*sec(d*x+c)^2)^(3/2)+8/15*tan(d*x+c)/a^2/d/sqrt(a*sec(d*x+c)^2),1],
[1/(a+a*tan(d*x+c)^2)^(7/2),x,6,1/7*tan(d*x+c)/d/(a*sec(d*x+c)^2)^(7/2)+6/35*tan(d*x+c)/a/d/(a*sec(d*x+c)^2)^(5/2)+8/35*tan(d*x+c)/a^2/d/(a*sec(d*x+c)^2)^(3/2)+16/35*tan(d*x+c)/a^3/d/sqrt(a*sec(d*x+c)^2),1],
[(1+tan(x)^2)^(3/2),x,4,1/2*arcsinh(tan(x))+1/2*sqrt(sec(x)^2)*tan(x),1],
[sqrt(1+tan(x)^2),x,3,arcsinh(tan(x)),1],
[1/sqrt(1+tan(x)^2),x,3,tan(x)/sqrt(sec(x)^2),1],
[(-1-tan(x)^2)^(3/2),x,5,1/2*arctan(tan(x)/sqrt(-sec(x)^2))-1/2*sqrt(-sec(x)^2)*tan(x),1],
[sqrt(-1-tan(x)^2),x,4,-arctan(tan(x)/sqrt(-sec(x)^2)),1],
[1/sqrt(-1-tan(x)^2),x,3,tan(x)/sqrt(-sec(x)^2),1],
[tan(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2),x,7,-sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+sqrt(a+b*tan(f*x+e)^2)/f-1/3*(a+b)*(a+b*tan(f*x+e)^2)^(3/2)/b^2/f+1/5*(a+b*tan(f*x+e)^2)^(5/2)/b^2/f,1],
[tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f-sqrt(a+b*tan(f*x+e)^2)/f+1/3*(a+b*tan(f*x+e)^2)^(3/2)/b/f,1],
[tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2),x,5,-sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2),x,7,-sqrt(a)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/f+sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f,1],
[cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2),x,8,1/2*(2*a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/sqrt(a)/f-sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f-1/2*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2),x,9,-1/8*(8*a^2-4*a*b-b^2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(3/2)/f+sqrt(a-b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+1/8*(4*a-b)*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/a/f-1/4*cot(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^6*sqrt(a+b*tan(f*x+e)^2),x,9,-sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/16*(a^3+2*a^2*b+8*a*b^2-16*b^3)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(5/2)/f-1/16*(a-2*b)*(a+4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b^2/f+1/24*(a-6*b)*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/b/f+1/6*tan(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2),x,8,sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/8*(a^2+4*a*b-8*b^2)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(3/2)/f+1/8*(a-4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b/f+1/4*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2),x,7,-sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*(a-2*b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(b)/f+1/2*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f,1],
[cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2),x,5,-sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2),x,6,sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/3*(3*a-b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f-1/3*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^6*sqrt(a+b*tan(f*x+e)^2),x,7,-sqrt(a-b)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/15*(15*a^2-5*a*b-2*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^2/f+1/15*(5*a-b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a/f-1/5*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x,8,-(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+(a-b)*sqrt(a+b*tan(f*x+e)^2)/f+1/3*(a+b*tan(f*x+e)^2)^(3/2)/f-1/5*(a+b)*(a+b*tan(f*x+e)^2)^(5/2)/b^2/f+1/7*(a+b*tan(f*x+e)^2)^(7/2)/b^2/f,1],
[tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x,7,(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f-(a-b)*sqrt(a+b*tan(f*x+e)^2)/f-1/3*(a+b*tan(f*x+e)^2)^(3/2)/f+1/5*(a+b*tan(f*x+e)^2)^(5/2)/b/f,1],
[tan(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x,6,-(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+(a-b)*sqrt(a+b*tan(f*x+e)^2)/f+1/3*(a+b*tan(f*x+e)^2)^(3/2)/f,1],
[cot(f*x+e)*(a+b*tan(f*x+e)^2)^(3/2),x,8,-a^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/f+(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+b*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^(3/2),x,8,1/2*sqrt(a)*(2*a-3*b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/f-(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f-1/2*a*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^(3/2),x,9,-1/8*(8*a^2-12*a*b+3*b^2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/sqrt(a)/f+(a-b)^(3/2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/f+1/8*(4*a-5*b)*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/f-1/4*a*cot(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x,10,-(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/128*(3*a^4+8*a^3*b+48*a^2*b^2-192*a*b^3+128*b^4)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(5/2)/f-1/128*(3*a^3+8*a^2*b-80*a*b^2+64*b^3)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b^2/f+1/192*(3*a^2-56*a*b+48*b^2)*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/b/f+1/48*(9*a-8*b)*tan(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/f+1/8*b*tan(f*x+e)^7*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x,9,(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/16*(a^3+6*a^2*b-24*a*b^2+16*b^3)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(3/2)/f+1/16*(a^2-10*a*b+8*b^2)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b/f+1/24*(7*a-6*b)*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f+1/6*b*tan(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/f,1],
[tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x,8,-(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/8*(3*a^2-12*a*b+8*b^2)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(b)/f+1/8*(5*a-4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f+1/4*b*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f,1],
[(a+b*tan(f*x+e)^2)^(3/2),x,7,(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*(3*a-2*b)*sqrt(b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/2*b*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(3/2),x,7,-(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+b^(3/2)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-a*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(3/2),x,6,(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f+1/3*(3*a-4*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/f-1/3*a*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f,1],
[cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^(3/2),x,7,-(a-b)^(3/2)*arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/f-1/15*(15*a^2-20*a*b+3*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f+1/15*(5*a-6*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/f-1/5*a*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/f,1],
[(a+b*tan(d*x+c)^2)^(5/2),x,8,(a-b)^(5/2)*arctan(sqrt(a-b)*tan(d*x+c)/sqrt(a+b*tan(d*x+c)^2))/d+1/8*sqrt(b)*(15*a^2-20*a*b+8*b^2)*arctanh(sqrt(b)*tan(d*x+c)/sqrt(a+b*tan(d*x+c)^2))/d+1/8*(7*a-4*b)*b*tan(d*x+c)*sqrt(a+b*tan(d*x+c)^2)/d+1/4*b*tan(d*x+c)*(a+b*tan(d*x+c)^2)^(3/2)/d,1],
[tan(f*x+e)^5/sqrt(a+b*tan(f*x+e)^2),x,6,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f-(a+b)*sqrt(a+b*tan(f*x+e)^2)/b^2/f+1/3*(a+b*tan(f*x+e)^2)^(3/2)/b^2/f,1],
[tan(f*x+e)^3/sqrt(a+b*tan(f*x+e)^2),x,5,arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f+sqrt(a+b*tan(f*x+e)^2)/b/f,1],
[tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2),x,4,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f,1],
[cot(f*x+e)/sqrt(a+b*tan(f*x+e)^2),x,7,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/sqrt(a)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f,1],
[cot(f*x+e)^3/sqrt(a+b*tan(f*x+e)^2),x,8,1/2*(2*a+b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(3/2)/f-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f-1/2*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[cot(f*x+e)^5/sqrt(a+b*tan(f*x+e)^2),x,9,-1/8*(8*a^2+4*a*b+3*b^2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(5/2)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/sqrt(a-b)/f+1/8*(4*a+3*b)*cot(f*x+e)^2*sqrt(a+b*tan(f*x+e)^2)/a^2/f-1/4*cot(f*x+e)^4*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[tan(f*x+e)^6/sqrt(a+b*tan(f*x+e)^2),x,8,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f+1/8*(3*a^2+4*a*b+8*b^2)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(5/2)/f-1/8*(3*a+4*b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b^2/f+1/4*tan(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/b/f,1],
[tan(f*x+e)^4/sqrt(a+b*tan(f*x+e)^2),x,7,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f-1/2*(a+2*b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(3/2)/f+1/2*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/b/f,1],
[tan(f*x+e)^2/sqrt(a+b*tan(f*x+e)^2),x,6,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f+arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(b)/f,1],
[1/sqrt(a+b*tan(f*x+e)^2),x,3,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f,1],
[cot(f*x+e)^2/sqrt(a+b*tan(f*x+e)^2),x,5,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f-cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[cot(f*x+e)^4/sqrt(a+b*tan(f*x+e)^2),x,6,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f+1/3*(3*a+2*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^2/f-1/3*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[cot(f*x+e)^6/sqrt(a+b*tan(f*x+e)^2),x,7,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/sqrt(a-b)/f-1/15*(15*a^2+10*a*b+8*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^3/f+1/15*(5*a+4*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^2/f-1/5*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a/f,1],
[tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x,6,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f+a^2/(a-b)/b^2/f/sqrt(a+b*tan(f*x+e)^2)+sqrt(a+b*tan(f*x+e)^2)/b^2/f,1],
[tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x,5,arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f-a/(a-b)/b/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x,5,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f+1/(a-b)/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)/(a+b*tan(f*x+e)^2)^(3/2),x,8,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(3/2)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f-b/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(3/2),x,9,1/2*(2*a+3*b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(5/2)/f-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f-1/2*(a-3*b)*b/a^2/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)-1/2*cot(f*x+e)^2/a/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(3/2),x,10,-1/8*(8*a^2+12*a*b+15*b^2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(7/2)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(3/2)/f+1/8*b*(4*a^2+3*a*b-15*b^2)/a^3/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)+1/8*(4*a+5*b)*cot(f*x+e)^2/a^2/f/sqrt(a+b*tan(f*x+e)^2)-1/4*cot(f*x+e)^4/a/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x,8,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-1/2*(3*a+2*b)*arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(5/2)/f-a*tan(f*x+e)^3/(a-b)/b/f/sqrt(a+b*tan(f*x+e)^2)+1/2*(3*a-b)*tan(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/(a-b)/b^2/f,1],
[tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x,7,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f+arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(3/2)/f-a*tan(f*x+e)/(a-b)/b/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x,4,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f+tan(f*x+e)/(a-b)/f/sqrt(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^(3/2),x,4,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-b*tan(f*x+e)/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(3/2),x,6,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-b*cot(f*x+e)/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)-(a-2*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^2/(a-b)/f,1],
[cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(3/2),x,7,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-b*cot(f*x+e)^3/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)+1/3*(3*a-4*b)*(a+2*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^3/(a-b)/f-1/3*(a-4*b)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^2/(a-b)/f,1],
[cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(3/2),x,8,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(3/2)/f-b*cot(f*x+e)^5/a/(a-b)/f/sqrt(a+b*tan(f*x+e)^2)-1/15*(15*a^3+10*a^2*b+8*a*b^2-48*b^3)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^4/(a-b)/f+1/15*(5*a^2+4*a*b-24*b^2)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^3/(a-b)/f-1/5*(a-6*b)*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a^2/(a-b)/f,1],
[tan(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x,6,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f+1/3*a^2/(a-b)/b^2/f/(a+b*tan(f*x+e)^2)^(3/2)-a*(a-2*b)/(a-b)^2/b^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x,6,arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f-1/3*a/(a-b)/b/f/(a+b*tan(f*x+e)^2)^(3/2)-1/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x,6,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f+1/3/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+1/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)/(a+b*tan(f*x+e)^2)^(5/2),x,9,-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(5/2)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f-1/3*b/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-(2*a-b)*b/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^3/(a+b*tan(f*x+e)^2)^(5/2),x,10,1/2*(2*a+5*b)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(7/2)/f-arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f-1/6*(3*a-5*b)*b/a^2/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/2*cot(f*x+e)^2/a/f/(a+b*tan(f*x+e)^2)^(3/2)-1/2*b*(a^2-8*a*b+5*b^2)/a^3/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^5/(a+b*tan(f*x+e)^2)^(5/2),x,11,-1/8*(8*a^2+20*a*b+35*b^2)*arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a))/a^(9/2)/f+arctanh(sqrt(a+b*tan(f*x+e)^2)/sqrt(a-b))/(a-b)^(5/2)/f+1/24*b*(12*a^2+15*a*b-35*b^2)/a^3/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+1/8*(4*a+7*b)*cot(f*x+e)^2/a^2/f/(a+b*tan(f*x+e)^2)^(3/2)-1/4*cot(f*x+e)^4/a/f/(a+b*tan(f*x+e)^2)^(3/2)+1/8*b*(4*a^3+3*a^2*b-50*a*b^2+35*b^3)/a^4/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x,8,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f+arctanh(sqrt(b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/b^(5/2)/f-1/3*a*tan(f*x+e)^3/(a-b)/b/f/(a+b*tan(f*x+e)^2)^(3/2)-a*(a-2*b)*tan(f*x+e)/(a-b)^2/b^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x,6,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*a*tan(f*x+e)/(a-b)/b/f/(a+b*tan(f*x+e)^2)^(3/2)+1/3*(a-4*b)*tan(f*x+e)/(a-b)^2/b/f/sqrt(a+b*tan(f*x+e)^2),1],
[tan(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x,6,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f+1/3*tan(f*x+e)/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)+1/3*(2*a+b)*tan(f*x+e)/a/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[1/(a+b*tan(f*x+e)^2)^(5/2),x,6,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*b*tan(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(5*a-2*b)*b*tan(f*x+e)/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2),1],
[cot(f*x+e)^2/(a+b*tan(f*x+e)^2)^(5/2),x,7,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*b*cot(f*x+e)/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(7*a-4*b)*b*cot(f*x+e)/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2)-1/3*(a-4*b)*(3*a-2*b)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^3/(a-b)^2/f,1],
[cot(f*x+e)^4/(a+b*tan(f*x+e)^2)^(5/2),x,8,arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*b*cot(f*x+e)^3/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-(3*a-2*b)*b*cot(f*x+e)^3/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2)+1/3*(a-2*b)*(3*a^2+8*a*b-8*b^2)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^4/(a-b)^2/f-1/3*(a^2-12*a*b+8*b^2)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^3/(a-b)^2/f,1],
[cot(f*x+e)^6/(a+b*tan(f*x+e)^2)^(5/2),x,9,-arctan(sqrt(a-b)*tan(f*x+e)/sqrt(a+b*tan(f*x+e)^2))/(a-b)^(5/2)/f-1/3*b*cot(f*x+e)^5/a/(a-b)/f/(a+b*tan(f*x+e)^2)^(3/2)-1/3*(11*a-8*b)*b*cot(f*x+e)^5/a^2/(a-b)^2/f/sqrt(a+b*tan(f*x+e)^2)-1/15*(15*a^4+10*a^3*b+8*a^2*b^2-176*a*b^3+128*b^4)*cot(f*x+e)*sqrt(a+b*tan(f*x+e)^2)/a^5/(a-b)^2/f+1/15*(5*a^3+4*a^2*b-88*a*b^2+64*b^3)*cot(f*x+e)^3*sqrt(a+b*tan(f*x+e)^2)/a^4/(a-b)^2/f-1/5*(a^2-22*a*b+16*b^2)*cot(f*x+e)^5*sqrt(a+b*tan(f*x+e)^2)/a^3/(a-b)^2/f,1],
[(d*tan(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,4,hypergeom([1, 1/2+1/2*m+p],[3/2+1/2*m+p],-tan(f*x+e)^2)*tan(f*x+e)*(d*tan(f*x+e))^m*(b*tan(f*x+e)^2)^p/f/(1+m+2*p),1],
[(d*tan(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,3,AppellF1(1/2+1/2*m,1,-p,3/2+1/2*m,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(d*tan(f*x+e))^(1+m)*(a+b*tan(f*x+e)^2)^p/d/f/(1+m)/(((a+b*tan(f*x+e)^2)/a)^p),1],
[tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x,5,-1/2*(a+b)*(a+b*tan(f*x+e)^2)^(p+1)/b^2/f/(p+1)-1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1)+1/2*(a+b*tan(f*x+e)^2)^(2+p)/b^2/f/(2+p),1],
[tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x,4,1/2*(a+b*tan(f*x+e)^2)^(p+1)/b/f/(p+1)+1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1),1],
[tan(f*x+e)*(a+b*tan(f*x+e)^2)^p,x,3,-1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1),1],
[cot(f*x+e)*(a+b*tan(f*x+e)^2)^p,x,5,-1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/a)*(a+b*tan(f*x+e)^2)^(p+1)/a/f/(p+1)+1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1),1],
[cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^p,x,6,-1/2*cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(p+1)/a/f+1/2*(-b*p+a)*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/a)*(a+b*tan(f*x+e)^2)^(p+1)/a^2/f/(p+1)-1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1),1],
[cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^p,x,7,1/4*(-b*p+2*a+b)*cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^(p+1)/a^2/f-1/4*cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^(p+1)/a/f-1/4*(2*a^2-2*a*b*p-b^2*(1-p)*p)*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/a)*(a+b*tan(f*x+e)^2)^(p+1)/a^3/f/(p+1)+1/2*hypergeom([1, p+1],[2+p],(a+b*tan(f*x+e)^2)/(a-b))*(a+b*tan(f*x+e)^2)^(p+1)/(a-b)/f/(p+1),1],
[tan(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x,3,1/7*AppellF1(7/2,1,-p,9/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)^7*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[tan(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x,3,1/5*AppellF1(5/2,1,-p,7/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)^5*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[tan(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x,3,1/3*AppellF1(3/2,1,-p,5/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)^3*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(a+b*tan(f*x+e)^2)^p,x,3,AppellF1(1/2,1,-p,3/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[cot(f*x+e)^2*(a+b*tan(f*x+e)^2)^p,x,3,-AppellF1(-1/2,1,-p,1/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*cot(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[cot(f*x+e)^4*(a+b*tan(f*x+e)^2)^p,x,3,-1/3*AppellF1(-3/2,1,-p,-1/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*cot(f*x+e)^3*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[cot(f*x+e)^6*(a+b*tan(f*x+e)^2)^p,x,3,-1/5*AppellF1(-5/2,1,-p,-3/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*cot(f*x+e)^5*(a+b*tan(f*x+e)^2)^p/f/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(a+b*tan(d*x+c)^3)^4,x,6,(a^4-6*a^2*b^2+b^4)*x+4*a*b*(a^2-b^2)*ln(cos(d*x+c))/d+b^2*(6*a^2-b^2)*tan(d*x+c)/d+2*a*b*(a^2-b^2)*tan(d*x+c)^2/d-1/3*b^2*(6*a^2-b^2)*tan(d*x+c)^3/d+a*b^3*tan(d*x+c)^4/d+1/5*b^2*(6*a^2-b^2)*tan(d*x+c)^5/d-2/3*a*b^3*tan(d*x+c)^6/d+1/7*b^4*tan(d*x+c)^7/d+1/2*a*b^3*tan(d*x+c)^8/d-1/9*b^4*tan(d*x+c)^9/d+1/11*b^4*tan(d*x+c)^11/d,1],
[(a+b*tan(d*x+c)^3)^3,x,6,a*(a^2-3*b^2)*x+b*(3*a^2-b^2)*ln(cos(d*x+c))/d+3*a*b^2*tan(d*x+c)/d+1/2*b*(3*a^2-b^2)*tan(d*x+c)^2/d-a*b^2*tan(d*x+c)^3/d+1/4*b^3*tan(d*x+c)^4/d+3/5*a*b^2*tan(d*x+c)^5/d-1/6*b^3*tan(d*x+c)^6/d+1/8*b^3*tan(d*x+c)^8/d,1],
[(a+b*tan(d*x+c)^3)^2,x,6,(a^2-b^2)*x+2*a*b*ln(cos(d*x+c))/d+b^2*tan(d*x+c)/d+a*b*tan(d*x+c)^2/d-1/3*b^2*tan(d*x+c)^3/d+1/5*b^2*tan(d*x+c)^5/d,1],
[a+b*tan(d*x+c)^3,x,3,a*x+b*ln(cos(d*x+c))/d+1/2*b*tan(d*x+c)^2/d,1],
[1/(a+b*tan(d*x+c)^3),x,14,a*x/(a^2+b^2)+b^(1/3)*(a^(4/3)-b^(4/3))*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c))/sqrt(3)/a^(1/3))/sqrt(3)/a^(2/3)/(a^2+b^2)/d-1/3*b*ln(a*cos(d*x+c)^3+b*sin(d*x+c)^3)/(a^2+b^2)/d+1/3*b^(1/3)*(a^(4/3)+b^(4/3))*ln(a^(1/3)+b^(1/3)*tan(d*x+c))/a^(2/3)/(a^2+b^2)/d-1/6*b^(1/3)*(a^(4/3)+b^(4/3))*ln(a^(2/3)-a^(1/3)*b^(1/3)*tan(d*x+c)+b^(2/3)*tan(d*x+c)^2)/a^(2/3)/(a^2+b^2)/d,1],
[1/(a+b*tan(d*x+c)^3)^2,x,21,(a^2-b^2)*x/(a^2+b^2)^2+b^(1/3)*(a^2-2*a^(2/3)*b^(4/3)-b^2)*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c))/sqrt(3)/a^(1/3))/sqrt(3)/a^(1/3)/(a^2+b^2)^2/d+1/3*b^(1/3)*(a^(4/3)-2*b^(4/3))*arctan((a^(1/3)-2*b^(1/3)*tan(d*x+c))/sqrt(3)/a^(1/3))/sqrt(3)/a^(5/3)/(a^2+b^2)/d-2/3*a*b*ln(a*cos(d*x+c)^3+b*sin(d*x+c)^3)/(a^2+b^2)^2/d+1/3*b^(1/3)*(a^2+2*a^(2/3)*b^(4/3)-b^2)*ln(a^(1/3)+b^(1/3)*tan(d*x+c))/a^(1/3)/(a^2+b^2)^2/d+1/9*b^(1/3)*(a^(4/3)+2*b^(4/3))*ln(a^(1/3)+b^(1/3)*tan(d*x+c))/a^(5/3)/(a^2+b^2)/d-1/6*b^(1/3)*(a^2+2*a^(2/3)*b^(4/3)-b^2)*ln(a^(2/3)-a^(1/3)*b^(1/3)*tan(d*x+c)+b^(2/3)*tan(d*x+c)^2)/a^(1/3)/(a^2+b^2)^2/d-1/18*b^(1/3)*(a^(4/3)+2*b^(4/3))*ln(a^(2/3)-a^(1/3)*b^(1/3)*tan(d*x+c)+b^(2/3)*tan(d*x+c)^2)/a^(5/3)/(a^2+b^2)/d+1/3*b*(a+tan(d*x+c)*(b-a*tan(d*x+c)))/a/(a^2+b^2)/d/(a+b*tan(d*x+c)^3),1],
[1/(1+tan(x)^3),x,7,1/2*x-1/2*ln(cos(x))+1/6*ln(1+tan(x))-1/3*ln(1-tan(x)+tan(x)^2),1],
[(a+b*tan(d*x+c)^4)^4,x,4,(a+b)^4*x-b*(2*a+b)*(2*a^2+2*a*b+b^2)*tan(d*x+c)/d+1/3*b*(2*a+b)*(2*a^2+2*a*b+b^2)*tan(d*x+c)^3/d-1/5*b^2*(6*a^2+4*a*b+b^2)*tan(d*x+c)^5/d+1/7*b^2*(6*a^2+4*a*b+b^2)*tan(d*x+c)^7/d-1/9*b^3*(4*a+b)*tan(d*x+c)^9/d+1/11*b^3*(4*a+b)*tan(d*x+c)^11/d-1/13*b^4*tan(d*x+c)^13/d+1/15*b^4*tan(d*x+c)^15/d,1],
[(a+b*tan(d*x+c)^4)^3,x,4,(a+b)^3*x-b*(3*a^2+3*a*b+b^2)*tan(d*x+c)/d+1/3*b*(3*a^2+3*a*b+b^2)*tan(d*x+c)^3/d-1/5*b^2*(3*a+b)*tan(d*x+c)^5/d+1/7*b^2*(3*a+b)*tan(d*x+c)^7/d-1/9*b^3*tan(d*x+c)^9/d+1/11*b^3*tan(d*x+c)^11/d,1],
[(a+b*tan(d*x+c)^4)^2,x,4,(a+b)^2*x-b*(2*a+b)*tan(d*x+c)/d+1/3*b*(2*a+b)*tan(d*x+c)^3/d-1/5*b^2*tan(d*x+c)^5/d+1/7*b^2*tan(d*x+c)^7/d,1],
[a+b*tan(d*x+c)^4,x,4,a*x+b*x-b*tan(d*x+c)/d+1/3*b*tan(d*x+c)^3/d,1],
[1/(a+b*tan(d*x+c)^4),x,11,x/(a+b)+1/2*(sqrt(a)-sqrt(b))*b^(1/4)*arctan(1-sqrt(2)*b^(1/4)*tan(d*x+c)/a^(1/4))/sqrt(2)/a^(3/4)/(a+b)/d-1/2*(sqrt(a)-sqrt(b))*b^(1/4)*arctan(1+sqrt(2)*b^(1/4)*tan(d*x+c)/a^(1/4))/sqrt(2)/a^(3/4)/(a+b)/d+1/2*(sqrt(a)+sqrt(b))*b^(1/4)*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x+c)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2))/sqrt(2)/a^(3/4)/(a+b)/d,1],
[1/(a+b*tan(d*x+c)^4)^2,x,12,x/(a+b)^2+1/8*b^(1/4)*(5*a+b-sqrt(b)*(7*a+3*b)/sqrt(a))*arctan(1-sqrt(2)*b^(1/4)*tan(d*x+c)/a^(1/4))/sqrt(2)/a^(5/4)/(a+b)^2/d-1/8*b^(1/4)*(5*a+b-sqrt(b)*(7*a+3*b)/sqrt(a))*arctan(1+sqrt(2)*b^(1/4)*tan(d*x+c)/a^(1/4))/sqrt(2)/a^(5/4)/(a+b)^2/d+1/8*b^(1/4)*(5*a+b+sqrt(b)*(7*a+3*b)/sqrt(a))*arctanh(sqrt(2)*a^(1/4)*b^(1/4)*tan(d*x+c)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2))/sqrt(2)/a^(5/4)/(a+b)^2/d+1/4*b*tan(d*x+c)*(1-tan(d*x+c)^2)/a/(a+b)/d/(a+b*tan(d*x+c)^4),1],
[sqrt(a+b*tan(d*x+c)^4),x,7,1/2*sqrt(a+b)*arctan(sqrt(a+b)*tan(d*x+c)/sqrt(a+b*tan(d*x+c)^4))/d+sqrt(b)*tan(d*x+c)*sqrt(a+b*tan(d*x+c)^4)/d/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)-a^(1/4)*b^(1/4)*EllipticE(sin(2*arctan(b^(1/4)*tan(d*x+c)/a^(1/4))),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(d*x+c)^2)*sqrt((a+b*tan(d*x+c)^4)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)^2)/d/sqrt(a+b*tan(d*x+c)^4)-a^(1/4)*b^(3/4)*InverseJacobiAM(2*arctan(b^(1/4)*tan(d*x+c)/a^(1/4)),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(d*x+c)^2)*sqrt((a+b*tan(d*x+c)^4)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)^2)/(sqrt(a)-sqrt(b))/d/sqrt(a+b*tan(d*x+c)^4)+1/4*(sqrt(a)+sqrt(b))*(a+b)*EllipticPi(sin(2*arctan(b^(1/4)*tan(d*x+c)/a^(1/4))),-1/4*(sqrt(a)-sqrt(b))^2/sqrt(a)/sqrt(b),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(d*x+c)^2)*sqrt((a+b*tan(d*x+c)^4)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(b))/b^(1/4)/d/sqrt(a+b*tan(d*x+c)^4),1],
[1/sqrt(a+b*tan(d*x+c)^4),x,4,1/2*arctan(sqrt(a+b)*tan(d*x+c)/sqrt(a+b*tan(d*x+c)^4))/sqrt(a+b)/d-1/2*b^(1/4)*InverseJacobiAM(2*arctan(b^(1/4)*tan(d*x+c)/a^(1/4)),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(d*x+c)^2)*sqrt((a+b*tan(d*x+c)^4)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(b))/d/sqrt(a+b*tan(d*x+c)^4)+1/4*(sqrt(a)+sqrt(b))*EllipticPi(sin(2*arctan(b^(1/4)*tan(d*x+c)/a^(1/4))),-1/4*(sqrt(a)-sqrt(b))^2/sqrt(a)/sqrt(b),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(d*x+c)^2)*sqrt((a+b*tan(d*x+c)^4)/(sqrt(a)+sqrt(b)*tan(d*x+c)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(b))/b^(1/4)/d/sqrt(a+b*tan(d*x+c)^4),1],
[tan(x)^3*sqrt(a+b*tan(x)^4),x,9,1/4*(a+2*b)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))/sqrt(b)+1/2*sqrt(a+b)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))-1/2*sqrt(a+b*tan(x)^4)+1/4*tan(x)^2*sqrt(a+b*tan(x)^4),1],
[tan(x)*sqrt(a+b*tan(x)^4),x,8,-1/2*sqrt(b)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))-1/2*sqrt(a+b)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))+1/2*sqrt(a+b*tan(x)^4),1],
[cot(x)*sqrt(a+b*tan(x)^4),x,11,1/2*sqrt(b)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))+1/2*sqrt(a+b)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))-1/2*sqrt(a)*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a)),1],
[tan(x)^2*sqrt(a+b*tan(x)^4),x,8,-1/2*sqrt(a+b)*arctan(sqrt(a+b)*tan(x)/sqrt(a+b*tan(x)^4))+1/3*tan(x)*sqrt(a+b*tan(x)^4)-sqrt(b)*tan(x)*sqrt(a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)+a^(1/4)*b^(1/4)*EllipticE(sin(2*arctan(b^(1/4)*tan(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(x)^2)*sqrt((a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)^2)/sqrt(a+b*tan(x)^4)+1/3*a^(1/4)*(a-sqrt(a)*sqrt(b)+3*b)*InverseJacobiAM(2*arctan(b^(1/4)*tan(x)/a^(1/4)),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(x)^2)*sqrt((a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)^2)/(sqrt(a)-sqrt(b))/b^(1/4)/sqrt(a+b*tan(x)^4)-1/4*(sqrt(a)+sqrt(b))*(a+b)*EllipticPi(sin(2*arctan(b^(1/4)*tan(x)/a^(1/4))),-1/4*(sqrt(a)-sqrt(b))^2/sqrt(a)/sqrt(b),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(x)^2)*sqrt((a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(b))/b^(1/4)/sqrt(a+b*tan(x)^4),1],
[tan(x)^3*(a+b*tan(x)^4)^(3/2),x,11,1/16*(3*a^2+12*a*b+8*b^2)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))/sqrt(b)+1/2*(a+b)^(3/2)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))-1/2*(a+b)*sqrt(a+b*tan(x)^4)+1/16*(3*a+4*b)*tan(x)^2*sqrt(a+b*tan(x)^4)-1/6*(a+b*tan(x)^4)^(3/2)+1/8*tan(x)^2*(a+b*tan(x)^4)^(3/2),1],
[tan(x)*(a+b*tan(x)^4)^(3/2),x,10,-1/4*sqrt(b)*(3*a+2*b)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))-1/2*(a+b)^(3/2)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))+1/2*(a+b)*sqrt(a+b*tan(x)^4)-1/4*b*tan(x)^2*sqrt(a+b*tan(x)^4)+1/6*(a+b*tan(x)^4)^(3/2),1],
[cot(x)*(a+b*tan(x)^4)^(3/2),x,13,1/4*sqrt(b)*(3*a+2*b)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))+1/2*(a+b)^(3/2)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))-1/2*a^(3/2)*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))-1/2*b*sqrt(a+b*tan(x)^4)+1/4*b*tan(x)^2*sqrt(a+b*tan(x)^4),1],
[cot(x)^3*(a+b*tan(x)^4)^(3/2),x,13,-1/2*b^(3/2)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))-1/2*(a+b)^(3/2)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))+1/2*a^(3/2)*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))+1/2*b*sqrt(a+b*tan(x)^4)-1/2*a*cot(x)^2*sqrt(a+b*tan(x)^4),1],
[cot(x)^5*(a+b*tan(x)^4)^(3/2),x,13,1/2*b^(3/2)*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))+1/2*(a+b)^(3/2)*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))-1/4*sqrt(a)*(2*a+3*b)*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))+1/2*a*cot(x)^2*sqrt(a+b*tan(x)^4)-1/4*a*cot(x)^4*sqrt(a+b*tan(x)^4),1],
[tan(x)^3/sqrt(a+b*tan(x)^4),x,7,1/2*arctanh(sqrt(b)*tan(x)^2/sqrt(a+b*tan(x)^4))/sqrt(b)+1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/sqrt(a+b),1],
[tan(x)/sqrt(a+b*tan(x)^4),x,4,-1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/sqrt(a+b),1],
[cot(x)/sqrt(a+b*tan(x)^4),x,8,1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/sqrt(a+b)-1/2*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))/sqrt(a),1],
[tan(x)^2/sqrt(a+b*tan(x)^4),x,4,-1/2*arctan(sqrt(a+b)*tan(x)/sqrt(a+b*tan(x)^4))/sqrt(a+b)+1/2*a^(1/4)*InverseJacobiAM(2*arctan(b^(1/4)*tan(x)/a^(1/4)),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(x)^2)*sqrt((a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)^2)/(sqrt(a)-sqrt(b))/b^(1/4)/sqrt(a+b*tan(x)^4)-1/4*(sqrt(a)+sqrt(b))*EllipticPi(sin(2*arctan(b^(1/4)*tan(x)/a^(1/4))),-1/4*(sqrt(a)-sqrt(b))^2/sqrt(a)/sqrt(b),sqrt(1/2))*(sqrt(a)+sqrt(b)*tan(x)^2)*sqrt((a+b*tan(x)^4)/(sqrt(a)+sqrt(b)*tan(x)^2)^2)/a^(1/4)/(sqrt(a)-sqrt(b))/b^(1/4)/sqrt(a+b*tan(x)^4),1],
[tan(x)^3/(a+b*tan(x)^4)^(3/2),x,6,1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(3/2)-1/2*(1-tan(x)^2)/(a+b)/sqrt(a+b*tan(x)^4),1],
[tan(x)/(a+b*tan(x)^4)^(3/2),x,6,-1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(3/2)+1/2*(a+b*tan(x)^2)/a/(a+b)/sqrt(a+b*tan(x)^4),1],
[cot(x)/(a+b*tan(x)^4)^(3/2),x,10,1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(3/2)-1/2*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))/a^(3/2)+1/2*b*(1-tan(x)^2)/a/(a+b)/sqrt(a+b*tan(x)^4),1],
[tan(x)^3/(a+b*tan(x)^4)^(5/2),x,7,1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(5/2)-1/6*(1-tan(x)^2)/(a+b)/(a+b*tan(x)^4)^(3/2)-1/6*(3*a-(2*a-b)*tan(x)^2)/a/(a+b)^2/sqrt(a+b*tan(x)^4),1],
[tan(x)/(a+b*tan(x)^4)^(5/2),x,7,-1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(5/2)+1/6*(a+b*tan(x)^2)/a/(a+b)/(a+b*tan(x)^4)^(3/2)+1/6*(3*a^2+b*(5*a+2*b)*tan(x)^2)/a^2/(a+b)^2/sqrt(a+b*tan(x)^4),1],
[cot(x)/(a+b*tan(x)^4)^(5/2),x,11,1/2*arctanh((a-b*tan(x)^2)/sqrt(a+b)/sqrt(a+b*tan(x)^4))/(a+b)^(5/2)-1/2*arctanh(sqrt(a+b*tan(x)^4)/sqrt(a))/a^(5/2)+1/6*b*(1-tan(x)^2)/a/(a+b)/(a+b*tan(x)^4)^(3/2)+1/6*b*(6*a+3*b-(5*a+2*b)*tan(x)^2)/a^2/(a+b)^2/sqrt(a+b*tan(x)^4),1],
[(d*tan(f*x+e))^m*(a+b*sqrt(c*tan(f*x+e)))^2,x,9,1/2*(a^2-b^2*sqrt(-c^2))*hypergeom([1, 1+m],[2+m],-c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/f/(1+m)+1/2*(a^2+b^2*sqrt(-c^2))*hypergeom([1, 1+m],[2+m],c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/f/(1+m)+4*a*b*hypergeom([1, 3/4+1/2*m],[7/4+1/2*m],-tan(f*x+e)^2)*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/f/(3+2*m),1],
[(d*tan(f*x+e))^m*(a+b*sqrt(c*tan(f*x+e))),x,7,a*hypergeom([1, 1/2+1/2*m],[3/2+1/2*m],-tan(f*x+e)^2)*tan(f*x+e)*(d*tan(f*x+e))^m/f/(1+m)+2*b*hypergeom([1, 3/4+1/2*m],[7/4+1/2*m],-tan(f*x+e)^2)*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/f/(3+2*m),1],
[(d*tan(f*x+e))^m/(a+b*sqrt(c*tan(f*x+e))),x,14,1/2*a*(a^2-b^2*sqrt(-c^2))*hypergeom([1, 1+m],[2+m],-c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/(b^4*c^2+a^4)/f/(1+m)+1/2*a*(a^2+b^2*sqrt(-c^2))*hypergeom([1, 1+m],[2+m],c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/(b^4*c^2+a^4)/f/(1+m)+b^4*c^2*hypergeom([1, 2+2*m],[3+2*m],-b*sqrt(c*tan(f*x+e))/a)*tan(f*x+e)*(d*tan(f*x+e))^m/a/(b^4*c^2+a^4)/f/(1+m)-b*(a^2-b^2*sqrt(-c^2))*hypergeom([1, 3/2+m],[5/2+m],-c*tan(f*x+e)/sqrt(-c^2))*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/(b^4*c^2+a^4)/f/(3+2*m)-b*(a^2+b^2*sqrt(-c^2))*hypergeom([1, 3/2+m],[5/2+m],c*tan(f*x+e)/sqrt(-c^2))*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/(b^4*c^2+a^4)/f/(3+2*m),1],
[(d*tan(f*x+e))^m/(a+b*sqrt(c*tan(f*x+e)))^2,x,15,1/2*(a^6-3*a^2*b^4*c^2-3*a^4*b^2*sqrt(-c^2)-b^6*(-c^2)^(3/2))*hypergeom([1, 1+m],[2+m],-c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/(b^4*c^2+a^4)^2/f/(1+m)+1/2*(a^6-3*a^2*b^4*c^2+3*a^4*b^2*sqrt(-c^2)+b^6*(-c^2)^(3/2))*hypergeom([1, 1+m],[2+m],c*tan(f*x+e)/sqrt(-c^2))*tan(f*x+e)*(d*tan(f*x+e))^m/(b^4*c^2+a^4)^2/f/(1+m)+4*a^2*b^4*c^2*hypergeom([1, 2+2*m],[3+2*m],-b*sqrt(c*tan(f*x+e))/a)*tan(f*x+e)*(d*tan(f*x+e))^m/(b^4*c^2+a^4)^2/f/(1+m)+b^4*c^2*hypergeom([2, 2+2*m],[3+2*m],-b*sqrt(c*tan(f*x+e))/a)*tan(f*x+e)*(d*tan(f*x+e))^m/a^2/(b^4*c^2+a^4)/f/(1+m)-2*a*b*(a^4-b^4*c^2-2*a^2*b^2*sqrt(-c^2))*hypergeom([1, 3/2+m],[5/2+m],-c*tan(f*x+e)/sqrt(-c^2))*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/(b^4*c^2+a^4)^2/f/(3+2*m)-2*a*b*(a^4-b^4*c^2+2*a^2*b^2*sqrt(-c^2))*hypergeom([1, 3/2+m],[5/2+m],c*tan(f*x+e)/sqrt(-c^2))*(c*tan(f*x+e))^(3/2)*(d*tan(f*x+e))^m/c/(b^4*c^2+a^4)^2/f/(3+2*m),1],
[(d*tan(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,4,hypergeom([1, 1/2*n*p+1/2*m+1/2],[1/2*n*p+1/2*m+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(d*tan(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p/f/(n*p+m+1),1],
[tan(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,4,hypergeom([1, 1/2*n*p+3/2],[1/2*n*p+5/2],-tan(f*x+e)^2)*tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(n*p+3),1],
[(b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[cot(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)*hypergeom([1, 1/2*n*p-1/2],[1/2*n*p+1/2],-tan(f*x+e)^2)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+1),1],
[cot(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)^3*hypergeom([1, 1/2*n*p-3/2],[1/2*n*p-1/2],-tan(f*x+e)^2)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+3),1],
[cot(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)^5*hypergeom([1, 1/2*n*p-5/2],[1/2*n*p-3/2],-tan(f*x+e)^2)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+5),1],
[tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,4,hypergeom([1, 1/2*n*p+2],[1/2*n*p+3],-tan(f*x+e)^2)*tan(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p/f/(n*p+4),1],
[tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,4,hypergeom([1, 1/2*n*p+1],[1/2*n*p+2],-tan(f*x+e)^2)*tan(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p/f/(n*p+2),1],
[cot(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,4,hypergeom([1, 1/2*n*p],[1/2*n*p+1],-tan(f*x+e)^2)*(b*(c*tan(f*x+e))^n)^p/f/n/p,1],
[cot(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,4,-cot(f*x+e)^2*hypergeom([1, 1/2*n*p-1],[1/2*n*p],-tan(f*x+e)^2)*(b*(c*tan(f*x+e))^n)^p/f/(-n*p+2),1],
[(d*tan(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)((d*tan(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[(d*cot(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,4,(d*cot(f*x+e))^m*hypergeom([1, 1/2-1/2*m+p],[3/2-1/2*m+p],-tan(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1-m+2*p),1],
[(d*cot(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,4,AppellF1(1/2-1/2*m,1,-p,3/2-1/2*m,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(d*cot(f*x+e))^m*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(1-m)/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(d*cot(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,4,(d*cot(f*x+e))^m*hypergeom([1, 1/2*n*p-1/2*m+1/2],[1/2*n*p-1/2*m+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p-m+1),1],
[(d*cot(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x,1,(d*cot(f*x+e))^m*(tan(f*x+e)/d)^m*Defer(Int)((a+b*(c*tan(f*x+e))^n)^p/((tan(f*x+e)/d)^m),x),0],
[sec(d*x+c)^3*(a+b*tan(d*x+c)^2),x,4,1/8*(4*a-b)*arctanh(sin(d*x+c))/d+1/8*(4*a-b)*sec(d*x+c)*tan(d*x+c)/d+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d,1],
[sec(d*x+c)*(a+b*tan(d*x+c)^2),x,3,1/2*(2*a-b)*arctanh(sin(d*x+c))/d+1/2*b*sec(d*x+c)*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*tan(d*x+c)^2),x,3,b*arctanh(sin(d*x+c))/d+(a-b)*sin(d*x+c)/d,1],
[cos(d*x+c)^3*(a+b*tan(d*x+c)^2),x,2,a*sin(d*x+c)/d-1/3*(a-b)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^5*(a+b*tan(d*x+c)^2),x,3,a*sin(d*x+c)/d-1/3*(2*a-b)*sin(d*x+c)^3/d+1/5*(a-b)*sin(d*x+c)^5/d,1],
[cos(d*x+c)^7*(a+b*tan(d*x+c)^2),x,3,a*sin(d*x+c)/d-1/3*(3*a-b)*sin(d*x+c)^3/d+1/5*(3*a-2*b)*sin(d*x+c)^5/d-1/7*(a-b)*sin(d*x+c)^7/d,1],
[sec(d*x+c)^6*(a+b*tan(d*x+c)^2),x,3,a*tan(d*x+c)/d+1/3*(2*a+b)*tan(d*x+c)^3/d+1/5*(a+2*b)*tan(d*x+c)^5/d+1/7*b*tan(d*x+c)^7/d,1],
[sec(d*x+c)^4*(a+b*tan(d*x+c)^2),x,3,a*tan(d*x+c)/d+1/3*(a+b)*tan(d*x+c)^3/d+1/5*b*tan(d*x+c)^5/d,1],
[sec(d*x+c)^2*(a+b*tan(d*x+c)^2),x,2,a*tan(d*x+c)/d+1/3*b*tan(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+b*tan(d*x+c)^2),x,3,1/2*(a+b)*x+1/2*(a-b)*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)^4*(a+b*tan(d*x+c)^2),x,4,1/8*(3*a+b)*x+1/8*(3*a+b)*cos(d*x+c)*sin(d*x+c)/d+1/4*(a-b)*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^6*(a+b*tan(d*x+c)^2),x,5,1/16*(5*a+b)*x+1/16*(5*a+b)*cos(d*x+c)*sin(d*x+c)/d+1/24*(5*a+b)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*(a-b)*cos(d*x+c)^5*sin(d*x+c)/d,1],
[sec(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x,5,1/16*(8*a^2-4*a*b+b^2)*arctanh(sin(d*x+c))/d+1/16*(8*a^2-4*a*b+b^2)*sec(d*x+c)*tan(d*x+c)/d+1/24*(12*a-7*b)*b*sec(d*x+c)^3*tan(d*x+c)/d+1/6*b^2*sec(d*x+c)^5*tan(d*x+c)/d,1],
[sec(d*x+c)*(a+b*tan(d*x+c)^2)^2,x,4,1/8*(8*a^2-8*a*b+3*b^2)*arctanh(sin(d*x+c))/d+1/8*(8*a-5*b)*b*sec(d*x+c)*tan(d*x+c)/d+1/4*b^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*tan(d*x+c)^2)^2,x,4,1/2*(4*a-3*b)*b*arctanh(sin(d*x+c))/d+(a-b)^2*sin(d*x+c)/d+1/2*b^2*sec(d*x+c)*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(a+b*tan(d*x+c)^2)^2,x,4,b^2*arctanh(sin(d*x+c))/d+(a^2-b^2)*sin(d*x+c)/d-1/3*(a-b)^2*sin(d*x+c)^3/d,1],
[cos(d*x+c)^5*(a+b*tan(d*x+c)^2)^2,x,3,a^2*sin(d*x+c)/d-2/3*a*(a-b)*sin(d*x+c)^3/d+1/5*(a-b)^2*sin(d*x+c)^5/d,1],
[cos(d*x+c)^7*(a+b*tan(d*x+c)^2)^2,x,3,a^2*sin(d*x+c)/d-1/3*a*(3*a-2*b)*sin(d*x+c)^3/d+1/5*(a-b)*(3*a-b)*sin(d*x+c)^5/d-1/7*(a-b)^2*sin(d*x+c)^7/d,1],
[cos(d*x+c)^9*(a+b*tan(d*x+c)^2)^2,x,3,a^2*sin(d*x+c)/d-2/3*a*(2*a-b)*sin(d*x+c)^3/d+1/5*(6*a^2-6*a*b+b^2)*sin(d*x+c)^5/d-2/7*(a-b)*(2*a-b)*sin(d*x+c)^7/d+1/9*(a-b)^2*sin(d*x+c)^9/d,1],
[sec(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x,3,a^2*tan(d*x+c)/d+2/3*a*(a+b)*tan(d*x+c)^3/d+1/5*(a^2+4*a*b+b^2)*tan(d*x+c)^5/d+2/7*b*(a+b)*tan(d*x+c)^7/d+1/9*b^2*tan(d*x+c)^9/d,1],
[sec(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x,3,a^2*tan(d*x+c)/d+1/3*a*(a+2*b)*tan(d*x+c)^3/d+1/5*b*(2*a+b)*tan(d*x+c)^5/d+1/7*b^2*tan(d*x+c)^7/d,1],
[sec(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x,3,a^2*tan(d*x+c)/d+2/3*a*b*tan(d*x+c)^3/d+1/5*b^2*tan(d*x+c)^5/d,1],
[cos(d*x+c)^2*(a+b*tan(d*x+c)^2)^2,x,4,1/2*(a-b)*(a+3*b)*x+1/2*(a-b)^2*cos(d*x+c)*sin(d*x+c)/d+b^2*tan(d*x+c)/d,1],
[cos(d*x+c)^4*(a+b*tan(d*x+c)^2)^2,x,4,1/8*(3*a^2+2*a*b+3*b^2)*x+1/8*(a-b)*(3*a+5*b)*cos(d*x+c)*sin(d*x+c)/d+1/4*(a-b)^2*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^6*(a+b*tan(d*x+c)^2)^2,x,5,1/16*(5*a^2+2*a*b+b^2)*x+1/16*(5*a^2+2*a*b+b^2)*cos(d*x+c)*sin(d*x+c)/d+1/24*(a-b)*(5*a+7*b)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*(a-b)^2*cos(d*x+c)^5*sin(d*x+c)/d,1],
[sec(d*x+c)^5/(a+b*tan(d*x+c)^2),x,5,-1/2*(2*a-3*b)*arctanh(sin(d*x+c))/b^2/d+(a-b)^(3/2)*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/b^2/d+1/2*sec(d*x+c)*tan(d*x+c)/b/d,1],
[sec(d*x+c)^3/(a+b*tan(d*x+c)^2),x,4,arctanh(sin(d*x+c))/b/d-sqrt(a-b)*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/b/d,1],
[sec(d*x+c)/(a+b*tan(d*x+c)^2),x,2,arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/sqrt(a-b)/d,1],
[cos(d*x+c)/(a+b*tan(d*x+c)^2),x,3,-b*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/(a-b)^(3/2)/d+sin(d*x+c)/(a-b)/d,1],
[cos(d*x+c)^3/(a+b*tan(d*x+c)^2),x,4,b^2*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/(a-b)^(5/2)/d+(a-2*b)*sin(d*x+c)/(a-b)^2/d-1/3*sin(d*x+c)^3/(a-b)/d,1],
[cos(d*x+c)^5/(a+b*tan(d*x+c)^2),x,4,-b^3*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/sqrt(a)/(a-b)^(7/2)/d+(a^2-3*a*b+3*b^2)*sin(d*x+c)/(a-b)^3/d-1/3*(2*a-3*b)*sin(d*x+c)^3/(a-b)^2/d+1/5*sin(d*x+c)^5/(a-b)/d,1],
[sec(d*x+c)^8/(a+b*tan(d*x+c)^2),x,4,-(a-b)^3*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/b^(7/2)/d+(a^2-3*a*b+3*b^2)*tan(d*x+c)/b^3/d-1/3*(a-3*b)*tan(d*x+c)^3/b^2/d+1/5*tan(d*x+c)^5/b/d,1],
[sec(d*x+c)^6/(a+b*tan(d*x+c)^2),x,4,(a-b)^2*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/b^(5/2)/d-(a-2*b)*tan(d*x+c)/b^2/d+1/3*tan(d*x+c)^3/b/d,1],
[sec(d*x+c)^4/(a+b*tan(d*x+c)^2),x,3,-(a-b)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/b^(3/2)/d+tan(d*x+c)/b/d,1],
[sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x,2,arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/sqrt(b)/d,1],
[cos(d*x+c)^2/(a+b*tan(d*x+c)^2),x,5,1/2*(a-3*b)*x/(a-b)^2+b^(3/2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/(a-b)^2/d+1/2*cos(d*x+c)*sin(d*x+c)/(a-b)/d,1],
[cos(d*x+c)^4/(a+b*tan(d*x+c)^2),x,6,1/8*(3*a^2-10*a*b+15*b^2)*x/(a-b)^3-b^(5/2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/sqrt(a)/(a-b)^3/d+1/8*(3*a-7*b)*cos(d*x+c)*sin(d*x+c)/(a-b)^2/d+1/4*cos(d*x+c)^3*sin(d*x+c)/(a-b)/d,1],
[sec(d*x+c)^7/(a+b*tan(d*x+c)^2)^2,x,6,-1/2*(4*a-5*b)*arctanh(sin(d*x+c))/b^3/d+1/2*(a-b)^(3/2)*(4*a+b)*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/b^3/d+1/2*(a-b)*(2*a-b)*sin(d*x+c)/a/b^2/d/(a-(a-b)*sin(d*x+c)^2)+1/2*sec(d*x+c)*tan(d*x+c)/b/d/(a-(a-b)*sin(d*x+c)^2),1],
[sec(d*x+c)^5/(a+b*tan(d*x+c)^2)^2,x,5,arctanh(sin(d*x+c))/b^2/d-1/2*sqrt(a-b)*(2*a+b)*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/b^2/d-1/2*(a-b)*sin(d*x+c)/a/b/d/(a-(a-b)*sin(d*x+c)^2),1],
[sec(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x,3,1/2*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/sqrt(a-b)/d+1/2*sin(d*x+c)/a/d/(a-(a-b)*sin(d*x+c)^2),1],
[sec(d*x+c)/(a+b*tan(d*x+c)^2)^2,x,3,1/2*(2*a-b)*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^(3/2)/d-1/2*b*sin(d*x+c)/a/(a-b)/d/(a-(a-b)*sin(d*x+c)^2),1],
[cos(d*x+c)/(a+b*tan(d*x+c)^2)^2,x,4,-1/2*(4*a-b)*b*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^(5/2)/d+sin(d*x+c)/(a-b)^2/d+1/2*b^2*sin(d*x+c)/a/(a-b)^2/d/(a-(a-b)*sin(d*x+c)^2),1],
[cos(d*x+c)^3/(a+b*tan(d*x+c)^2)^2,x,5,1/2*(6*a-b)*b^2*arctanh(sqrt(a-b)*sin(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^(7/2)/d+(a-3*b)*sin(d*x+c)/(a-b)^3/d-1/3*sin(d*x+c)^3/(a-b)^2/d-1/2*b^3*sin(d*x+c)/a/(a-b)^3/d/(a-(a-b)*sin(d*x+c)^2),1],
[sec(d*x+c)^8/(a+b*tan(d*x+c)^2)^2,x,5,1/2*(a-b)^2*(5*a+b)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/b^(7/2)/d-(2*a-3*b)*tan(d*x+c)/b^3/d+1/3*tan(d*x+c)^3/b^2/d-1/2*(a-b)^3*tan(d*x+c)/a/b^3/d/(a+b*tan(d*x+c)^2),1],
[sec(d*x+c)^6/(a+b*tan(d*x+c)^2)^2,x,4,-1/2*(3*a^2-2*a*b-b^2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/b^(5/2)/d+tan(d*x+c)/b^2/d+1/2*(a-b)^2*tan(d*x+c)/a/b^2/d/(a+b*tan(d*x+c)^2),1],
[sec(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x,3,1/2*(a+b)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/b^(3/2)/d-1/2*(a-b)*tan(d*x+c)/a/b/d/(a+b*tan(d*x+c)^2),1],
[sec(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x,3,1/2*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/sqrt(b)/d+1/2*tan(d*x+c)/a/d/(a+b*tan(d*x+c)^2),1],
[cos(d*x+c)^2/(a+b*tan(d*x+c)^2)^2,x,6,1/2*(a-5*b)*x/(a-b)^3+1/2*(5*a-b)*b^(3/2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^3/d+1/2*cos(d*x+c)*sin(d*x+c)/(a-b)/d/(a+b*tan(d*x+c)^2)+1/2*b*(a+b)*tan(d*x+c)/a/(a-b)^2/d/(a+b*tan(d*x+c)^2),1],
[cos(d*x+c)^4/(a+b*tan(d*x+c)^2)^2,x,7,1/8*(3*a^2-14*a*b+35*b^2)*x/(a-b)^4-1/2*(7*a-b)*b^(5/2)*arctan(sqrt(b)*tan(d*x+c)/sqrt(a))/a^(3/2)/(a-b)^4/d+3/8*(a-3*b)*cos(d*x+c)*sin(d*x+c)/(a-b)^2/d/(a+b*tan(d*x+c)^2)+1/4*cos(d*x+c)^3*sin(d*x+c)/(a-b)/d/(a+b*tan(d*x+c)^2)+1/8*(a-4*b)*b*(3*a+b)*tan(d*x+c)/a/(a-b)^3/d/(a+b*tan(d*x+c)^2),1],
[(d*sec(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,2,(cos(f*x+e)^2)^(1/2+1/2*m+p)*hypergeom([1/2+p, 1/2+1/2*m+p],[3/2+p],sin(f*x+e)^2)*(d*sec(f*x+e))^m*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1+2*p),1],
[(d*sec(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,3,AppellF1(1/2,1-1/2*m,-p,3/2,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(d*sec(f*x+e))^m*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/((sec(f*x+e)^2)^(1/2*m))/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(d*sec(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,2,(cos(f*x+e)^2)^(1/2*n*p+1/2*m+1/2)*hypergeom([1/2*n*p+1/2, 1/2*n*p+1/2*m+1/2],[1/2*n*p+3/2],sin(f*x+e)^2)*(d*sec(f*x+e))^m*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[sec(f*x+e)^6*(b*(c*tan(f*x+e))^n)^p,x,4,tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1)+2*tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(n*p+3)+tan(f*x+e)^5*(b*(c*tan(f*x+e))^n)^p/f/(n*p+5),1],
[sec(f*x+e)^4*(b*(c*tan(f*x+e))^n)^p,x,4,tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1)+tan(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p/f/(n*p+3),1],
[sec(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,3,tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[(b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([1, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[cos(f*x+e)^2*(b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([2, 1/2*n*p+1/2],[1/2*n*p+3/2],-tan(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[sec(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,2,(cos(f*x+e)^2)^(1/2*n*p+2)*hypergeom([1/2*n*p+1/2, 1/2*n*p+2],[1/2*n*p+3/2],sin(f*x+e)^2)*sec(f*x+e)^3*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[sec(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,2,(cos(f*x+e)^2)^(1/2*n*p+1)*hypergeom([1/2*n*p+1/2, 1/2*n*p+1],[1/2*n*p+3/2],sin(f*x+e)^2)*sec(f*x+e)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[cos(f*x+e)*(b*(c*tan(f*x+e))^n)^p,x,2,(cos(f*x+e)^2)^(1/2*n*p)*hypergeom([1/2*n*p, 1/2*n*p+1/2],[1/2*n*p+3/2],sin(f*x+e)^2)*sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[cos(f*x+e)^3*(b*(c*tan(f*x+e))^n)^p,x,2,(cos(f*x+e)^2)^(1/2*n*p)*hypergeom([1/2*n*p-1, 1/2*n*p+1/2],[1/2*n*p+3/2],sin(f*x+e)^2)*sin(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p+1),1],
[(d*sec(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)((d*sec(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[sec(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)(sec(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[sec(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)(sec(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[cos(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)(cos(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[cos(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)(cos(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[sec(f*x+e)^6*(a+b*(c*tan(f*x+e))^n)^p,x,9,hypergeom([1/n, -p],[1+1/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p)+2/3*hypergeom([3/n, -p],[(3+n)/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p)+1/5*hypergeom([5/n, -p],[(5+n)/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)^5*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p),1],
[sec(f*x+e)^4*(a+b*(c*tan(f*x+e))^n)^p,x,7,hypergeom([1/n, -p],[1+1/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p)+1/3*hypergeom([3/n, -p],[(3+n)/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)^3*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p),1],
[sec(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x,3,hypergeom([1/n, -p],[1+1/n],-b*(c*tan(f*x+e))^n/a)*tan(f*x+e)*(a+b*(c*tan(f*x+e))^n)^p/f/(((a+b*(c*tan(f*x+e))^n)/a)^p),1],
[(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)((a+b*(c*tan(f*x+e))^n)^p,x),0],
[cos(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x,0,Defer(Int)(cos(f*x+e)^2*(a+b*(c*tan(f*x+e))^n)^p,x),0],
[(d*csc(f*x+e))^m*(b*tan(f*x+e)^2)^p,x,4,(cos(f*x+e)^2)^(1/2+p)*(d*csc(f*x+e))^m*hypergeom([1/2+p, 1/2-1/2*m+p],[3/2-1/2*m+p],sin(f*x+e)^2)*tan(f*x+e)*(b*tan(f*x+e)^2)^p/f/(1-m+2*p),1],
[(d*csc(f*x+e))^m*(a+b*tan(f*x+e)^2)^p,x,5,AppellF1(1/2-1/2*m,1-1/2*m,-p,3/2-1/2*m,-tan(f*x+e)^2,-b*tan(f*x+e)^2/a)*(d*csc(f*x+e))^m*tan(f*x+e)*(a+b*tan(f*x+e)^2)^p/f/(1-m)/((sec(f*x+e)^2)^(1/2*m))/(((a+b*tan(f*x+e)^2)/a)^p),1],
[(d*csc(f*x+e))^m*(b*(c*tan(f*x+e))^n)^p,x,4,(cos(f*x+e)^2)^(1/2*n*p+1/2)*(d*csc(f*x+e))^m*hypergeom([1/2*n*p+1/2, 1/2*n*p-1/2*m+1/2],[1/2*n*p-1/2*m+3/2],sin(f*x+e)^2)*tan(f*x+e)*(b*(c*tan(f*x+e))^n)^p/f/(n*p-m+1),1],
[(d*csc(f*x+e))^m*(a+b*(c*tan(f*x+e))^n)^p,x,1,(d*csc(f*x+e))^m*(sin(f*x+e)/d)^m*Defer(Int)((a+b*(c*tan(f*x+e))^n)^p/((sin(f*x+e)/d)^m),x),0]]: