1,0,0,361,8.248000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{3} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x)","F"
2,0,0,265,7.543000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{2} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x)","F"
3,0,0,179,5.395000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right) \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x)","F"
4,0,0,190,1.973000," ","int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n} \left(A +B \sin \left(f x +e \right)\right)}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x)","F"
5,0,0,259,11.460000," ","int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n} \left(A +B \sin \left(f x +e \right)\right)}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","F"
6,0,0,340,11.615000," ","int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n} \left(A +B \sin \left(f x +e \right)\right)}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","F"
7,0,0,326,1.087000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x)","F"
8,0,0,221,1.051000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x)","F"
9,0,0,131,1.055000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \sqrt{a +a \sin \left(f x +e \right)}\, \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)),x)","F"
10,0,0,138,0.895000," ","int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n} \left(A +B \sin \left(f x +e \right)\right)}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","F"
11,0,0,204,0.893000," ","int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n} \left(A +B \sin \left(f x +e \right)\right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x)","F"
12,0,0,193,6.039000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
13,0,0,106,5.908000," ","int((d*sin(f*x+e))^n*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m,x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(a -a \sin \left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sin(f*x+e))^n*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m,x)","F"
14,0,0,37,4.153000," ","int(sin(d*x+c)^n*(a+a*sin(d*x+c))^(-2-n)*(-1-n-(-2-n)*sin(d*x+c)),x)","\int \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{-2-n} \left(-1-n -\left(-2-n \right) \sin \left(d x +c \right)\right)\, dx"," ",0,"int(sin(d*x+c)^n*(a+a*sin(d*x+c))^(-2-n)*(-1-n-(-2-n)*sin(d*x+c)),x)","F"
15,0,0,35,1.659000," ","int(sin(d*x+c)^(-2-m)*(a+a*sin(d*x+c))^m*(1+m-m*sin(d*x+c)),x)","\int \left(\sin^{-2-m}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m} \left(1+m -m \sin \left(d x +c \right)\right)\, dx"," ",0,"int(sin(d*x+c)^(-2-m)*(a+a*sin(d*x+c))^m*(1+m-m*sin(d*x+c)),x)","F"
16,1,493,148,0.372000," ","int(sin(f*x+e)^2*(A+B*sin(f*x+e))/(a+b*sin(f*x+e))^2,x)","-\frac{2 B}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,b^{2}}-\frac{4 B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{3}}+\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f b \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 a^{2} A}{f b \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} B}{f \,b^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) A}{f \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) A}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{4 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) B}{f \,b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) B}{f b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/f/b^2*B/(1+tan(1/2*f*x+1/2*e)^2)+2/f/b^2*A*arctan(tan(1/2*f*x+1/2*e))-4/f/b^3*B*arctan(tan(1/2*f*x+1/2*e))*a+2/f*a/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*tan(1/2*f*x+1/2*e)*A-2/f*a^2/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*tan(1/2*f*x+1/2*e)*B+2/f*a^2/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*A-2/f*a^3/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/(a^2-b^2)*B-2/f*a^3/b^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*A+4/f*a/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*A+4/f*a^4/b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*B-6/f*a^2/b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*B","B"
17,1,342,170,0.586000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x)","\frac{-\frac{A \,c^{4} a \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-3 A \,c^{4} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 A \,c^{4} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 A \,c^{4} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+3 A \,c^{4} a \cos \left(f x +e \right)+B \,c^{4} a \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{3 B \,c^{4} a \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+2 B \,c^{4} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 B \,c^{4} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-3 B \,c^{4} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+A \,c^{4} a \left(f x +e \right)-B \,c^{4} a \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-1/5*A*c^4*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-3*A*c^4*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/3*A*c^4*a*(2+sin(f*x+e)^2)*cos(f*x+e)+2*A*c^4*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*A*c^4*a*cos(f*x+e)+B*c^4*a*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+3/5*B*c^4*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*B*c^4*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/3*B*c^4*a*(2+sin(f*x+e)^2)*cos(f*x+e)-3*B*c^4*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+A*c^4*a*(f*x+e)-B*c^4*a*cos(f*x+e))","B"
18,1,208,132,0.485000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","\frac{-A \,c^{3} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 A \,c^{3} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 A \,c^{3} a \cos \left(f x +e \right)+\frac{B \,c^{3} a \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+2 B \,c^{3} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-2 B \,c^{3} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+A \,c^{3} a \left(f x +e \right)-B \,c^{3} a \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-A*c^3*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/3*A*c^3*a*(2+sin(f*x+e)^2)*cos(f*x+e)+2*A*c^3*a*cos(f*x+e)+1/5*B*c^3*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*B*c^3*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*B*c^3*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+A*c^3*a*(f*x+e)-B*c^3*a*cos(f*x+e))","A"
19,1,185,89,0.391000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","\frac{-\frac{A \,c^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-A \,c^{2} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+A \,c^{2} a \cos \left(f x +e \right)+B \,c^{2} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{B \,c^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-B \,c^{2} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+A \,c^{2} a \left(f x +e \right)-B \,c^{2} a \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-1/3*A*c^2*a*(2+sin(f*x+e)^2)*cos(f*x+e)-A*c^2*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+A*c^2*a*cos(f*x+e)+B*c^2*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/3*B*c^2*a*(2+sin(f*x+e)^2)*cos(f*x+e)-B*c^2*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+A*c^2*a*(f*x+e)-B*c^2*a*cos(f*x+e))","B"
20,1,74,43,0.287000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\frac{\frac{B a c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-A a c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B a c \cos \left(f x +e \right)+A a c \left(f x +e \right)}{f}"," ",0,"1/f*(1/3*B*a*c*(2+sin(f*x+e)^2)*cos(f*x+e)-A*a*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a*c*cos(f*x+e)+A*a*c*(f*x+e))","A"
21,1,113,56,0.407000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","-\frac{4 a A}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{4 a B}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}+\frac{2 a B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{2 a \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c}-\frac{4 a \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c}"," ",0,"-4/f*a/c/(tan(1/2*f*x+1/2*e)-1)*A-4/f*a/c/(tan(1/2*f*x+1/2*e)-1)*B+2/f*a/c*B/(1+tan(1/2*f*x+1/2*e)^2)-2/f*a/c*arctan(tan(1/2*f*x+1/2*e))*A-4/f*a/c*arctan(tan(1/2*f*x+1/2*e))*B","A"
22,1,160,68,0.438000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","-\frac{2 a A}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}+\frac{2 a B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{8 a A}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8 a B}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{4 a A}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{4 a B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{2 a B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{2} f}"," ",0,"-2*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)*A+2*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)*B-8/3*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*A-8/3*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*B-4*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*A-4*a/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*B+2*a/c^2/f*B*arctan(tan(1/2*f*x+1/2*e))","B"
23,1,115,98,0.481000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","\frac{2 a \left(-\frac{14 A +10 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8 A +8 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{16 A +16 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{6 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{3}}"," ",0,"2/f*a/c^3*(-1/3*(14*A+10*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/5*(8*A+8*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/4*(16*A+16*B)/(tan(1/2*f*x+1/2*e)-1)^4-A/(tan(1/2*f*x+1/2*e)-1)-1/2*(6*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2)","A"
24,1,159,134,0.467000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","\frac{2 a \left(-\frac{28 A +14 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{68 A +60 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{16 A +16 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{8 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{48 A +48 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{56 A +40 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}\right)}{f \,c^{4}}"," ",0,"2/f*a/c^4*(-1/3*(28*A+14*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/5*(68*A+60*B)/(tan(1/2*f*x+1/2*e)-1)^5-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(16*A+16*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/2*(8*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/6*(48*A+48*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(56*A+40*B)/(tan(1/2*f*x+1/2*e)-1)^4)","A"
25,1,203,166,0.513000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x)","\frac{2 a \left(-\frac{46 A +18 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{128 A +128 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{236 A +168 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{32 A +32 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{10 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{248 A +232 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{296 A +248 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{128 A +72 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}\right)}{f \,c^{5}}"," ",0,"2/f*a/c^5*(-1/3*(46*A+18*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/8*(128*A+128*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/5*(236*A+168*B)/(tan(1/2*f*x+1/2*e)-1)^5-A/(tan(1/2*f*x+1/2*e)-1)-1/9*(32*A+32*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/2*(10*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/7*(248*A+232*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(296*A+248*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(128*A+72*B)/(tan(1/2*f*x+1/2*e)-1)^4)","A"
26,1,569,215,0.670000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x)","\frac{a^{2} A \,c^{5} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{B \,a^{2} c^{5} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 a^{2} A \,c^{5} \cos \left(f x +e \right)+a^{2} A \,c^{5} \left(f x +e \right)-B \,a^{2} c^{5} \cos \left(f x +e \right)-3 B \,a^{2} c^{5} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{a^{2} A \,c^{5} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}+3 a^{2} A \,c^{5} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{a^{2} A \,c^{5} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-5 a^{2} A \,c^{5} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{5 a^{2} A \,c^{5} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-B \,a^{2} c^{5} \left(-\frac{\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)}{8}+\frac{35 f x}{128}+\frac{35 e}{128}\right)-\frac{3 B \,a^{2} c^{5} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-B \,a^{2} c^{5} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+B \,a^{2} c^{5} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)+5 B \,a^{2} c^{5} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(a^2*A*c^5*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*B*a^2*c^5*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^2*A*c^5*cos(f*x+e)+a^2*A*c^5*(f*x+e)-B*a^2*c^5*cos(f*x+e)-3*B*a^2*c^5*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+1/7*a^2*A*c^5*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)+3*a^2*A*c^5*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/5*a^2*A*c^5*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-5*a^2*A*c^5*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-5/3*a^2*A*c^5*(2+sin(f*x+e)^2)*cos(f*x+e)-B*a^2*c^5*(-1/8*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/128*f*x+35/128*e)-3/7*B*a^2*c^5*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-B*a^2*c^5*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+B*a^2*c^5*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+5*B*a^2*c^5*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e))","B"
27,1,463,177,0.574000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x)","\frac{a^{2} A \,c^{4} \left(f x +e \right)+4 B \,a^{2} c^{4} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{B \,a^{2} c^{4} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 a^{2} A \,c^{4} \cos \left(f x +e \right)-2 B \,a^{2} c^{4} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{4 a^{2} A \,c^{4} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-\frac{B \,a^{2} c^{4} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-2 B \,a^{2} c^{4} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{B \,a^{2} c^{4} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-a^{2} A \,c^{4} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+a^{2} A \,c^{4} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{2 a^{2} A \,c^{4} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-a^{2} A \,c^{4} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c^{4} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*A*c^4*(f*x+e)+4*B*a^2*c^4*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/3*B*a^2*c^4*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a^2*A*c^4*cos(f*x+e)-2*B*a^2*c^4*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4/3*a^2*A*c^4*(2+sin(f*x+e)^2)*cos(f*x+e)-1/7*B*a^2*c^4*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-2*B*a^2*c^4*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+1/5*B*a^2*c^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-a^2*A*c^4*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+a^2*A*c^4*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+2/5*a^2*A*c^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-a^2*A*c^4*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c^4*cos(f*x+e))","B"
28,1,365,137,0.571000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","\frac{\frac{a^{2} A \,c^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+a^{2} A \,c^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 a^{2} A \,c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a^{2} A \,c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c^{3} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{B \,a^{2} c^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+2 B \,a^{2} c^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{2 B \,a^{2} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} A \,c^{3} \cos \left(f x +e \right)-B \,a^{2} c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{2} A \,c^{3} \left(f x +e \right)-B \,a^{2} c^{3} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(1/5*a^2*A*c^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*A*c^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/3*a^2*A*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a^2*A*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/5*B*a^2*c^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*B*a^2*c^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2/3*B*a^2*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*A*c^3*cos(f*x+e)-B*a^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*A*c^3*(f*x+e)-B*a^2*c^3*cos(f*x+e))","B"
29,1,166,81,0.480000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","\frac{-\frac{B \,a^{2} c^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+a^{2} A \,c^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{2 B \,a^{2} c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a^{2} A \,c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c^{2} \cos \left(f x +e \right)+a^{2} A \,c^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/5*B*a^2*c^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*A*c^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2/3*B*a^2*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a^2*A*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c^2*cos(f*x+e)+a^2*A*c^2*(f*x+e))","B"
30,1,186,90,0.388000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\frac{\frac{a^{2} A c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-a^{2} A c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{B \,a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-a^{2} A c \cos \left(f x +e \right)+B \,a^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{2} A c \left(f x +e \right)-B \,a^{2} c \cos \left(f x +e \right)}{f}"," ",0,"1/f*(1/3*a^2*A*c*(2+sin(f*x+e)^2)*cos(f*x+e)-a^2*A*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+1/3*B*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)-a^2*A*c*cos(f*x+e)+B*a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*A*c*(f*x+e)-B*a^2*c*cos(f*x+e))","B"
31,1,299,111,0.431000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","-\frac{8 a^{2} A}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{8 a^{2} B}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{a^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{a^{2} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 a^{2} A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 a^{2} B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{9 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c}-\frac{6 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c}"," ",0,"-8/f*a^2/c/(tan(1/2*f*x+1/2*e)-1)*A-8/f*a^2/c/(tan(1/2*f*x+1/2*e)-1)*B-1/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3*B+2/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*A+6/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*B+1/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)+2/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*A+6/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)^2*B-9/f*a^2/c*arctan(tan(1/2*f*x+1/2*e))*B-6/f*a^2/c*arctan(tan(1/2*f*x+1/2*e))*A","B"
32,1,198,105,0.460000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","-\frac{16 a^{2} A}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16 a^{2} B}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8 a^{2} A}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{8 a^{2} B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{8 a^{2} B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2 a^{2} B}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{c^{2} f}+\frac{8 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{c^{2} f}"," ",0,"-16/3*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*A-16/3*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*B-8*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*A-8*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*B+8*a^2/c^2/f*B/(tan(1/2*f*x+1/2*e)-1)-2*a^2/c^2/f*B/(1+tan(1/2*f*x+1/2*e)^2)+2*a^2/c^2/f*arctan(tan(1/2*f*x+1/2*e))*A+8*a^2/c^2/f*arctan(tan(1/2*f*x+1/2*e))*B","A"
33,1,249,108,0.505000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","-\frac{2 a^{2} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2 a^{2} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{32 a^{2} A}{5 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{32 a^{2} B}{5 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{16 a^{2} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{32 a^{2} B}{3 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16 a^{2} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{16 a^{2} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{8 a^{2} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 a^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{3} f}"," ",0,"-2*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)*A-2*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)*B-32/5*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^5*A-32/5*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^5*B-16*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^3*A-32/3*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^3*B-16*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^4*A-16*a^2/c^3/f/(tan(1/2*f*x+1/2*e)-1)^4*B-8*a^2/c^3/f*A/(tan(1/2*f*x+1/2*e)-1)^2-2*a^2/c^3/f*B*arctan(tan(1/2*f*x+1/2*e))","B"
34,1,161,71,0.474000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","\frac{2 a^{2} \left(-\frac{128 A +112 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{96 A +64 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{96 A +96 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{42 A +18 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{32 A +32 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{10 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{4}}"," ",0,"2/f*a^2/c^4*(-1/5*(128*A+112*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/4*(96*A+64*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/6*(96*A+96*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/3*(42*A+18*B)/(tan(1/2*f*x+1/2*e)-1)^3-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(32*A+32*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/2*(10*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2)","B"
35,1,205,109,0.526000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x)","\frac{2 a^{2} \left(-\frac{404 A +276 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{64 A +64 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{64 A +22 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{480 A +448 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{12 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{200 A +104 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{544 A +448 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{256 A +256 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}\right)}{f \,c^{5}}"," ",0,"2/f*a^2/c^5*(-1/5*(404*A+276*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/9*(64*A+64*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/3*(64*A+22*B)/(tan(1/2*f*x+1/2*e)-1)^3-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(480*A+448*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/2*(12*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/4*(200*A+104*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/6*(544*A+448*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/8*(256*A+256*B)/(tan(1/2*f*x+1/2*e)-1)^8)","A"
36,1,249,148,0.513000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x)","\frac{2 a^{2} \left(-\frac{932 A +528 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{128 A +128 B}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{1536 A +1472 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{352 A +152 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{640 A +640 B}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{90 A +26 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2304 A +2048 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{2376 A +1896 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{1752 A +1208 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{14 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{6}}"," ",0,"2/f*a^2/c^6*(-1/5*(932*A+528*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/11*(128*A+128*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/9*(1536*A+1472*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/4*(352*A+152*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/10*(640*A+640*B)/(tan(1/2*f*x+1/2*e)-1)^10-1/3*(90*A+26*B)/(tan(1/2*f*x+1/2*e)-1)^3-A/(tan(1/2*f*x+1/2*e)-1)-1/8*(2304*A+2048*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/7*(2376*A+1896*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(1752*A+1208*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/2*(14*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2)","A"
37,1,293,187,0.573000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x)","\frac{2 a^{2} \left(-\frac{10896 A +9360 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{1816 A +884 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{4480 A +4352 B}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{1536 A +1536 B}{12 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{12}}-\frac{560 A +208 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{16 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{120 A +30 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{7744 A +5368 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{256 A +256 B}{13 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{13}}-\frac{8320 A +7680 B}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{4320 A +2568 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{10560 A +8256 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}\right)}{f \,c^{7}}"," ",0,"2/f*a^2/c^7*(-1/9*(10896*A+9360*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/5*(1816*A+884*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/11*(4480*A+4352*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/12*(1536*A+1536*B)/(tan(1/2*f*x+1/2*e)-1)^12-1/4*(560*A+208*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/2*(16*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/3*(120*A+30*B)/(tan(1/2*f*x+1/2*e)-1)^3-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(7744*A+5368*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/13*(256*A+256*B)/(tan(1/2*f*x+1/2*e)-1)^13-1/10*(8320*A+7680*B)/(tan(1/2*f*x+1/2*e)-1)^10-1/6*(4320*A+2568*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/8*(10560*A+8256*B)/(tan(1/2*f*x+1/2*e)-1)^8)","A"
38,1,651,249,0.853000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^6,x)","\frac{a^{3} A \,c^{6} \left(f x +e \right)-B \,a^{3} c^{6} \cos \left(f x +e \right)-\frac{8 a^{3} A \,c^{6} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+8 B \,a^{3} c^{6} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+3 a^{3} A \,c^{6} \cos \left(f x +e \right)+\frac{6 B \,a^{3} c^{6} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+B \,a^{3} c^{6} \left(-\frac{\left(\sin^{9}\left(f x +e \right)+\frac{9 \left(\sin^{7}\left(f x +e \right)\right)}{8}+\frac{21 \left(\sin^{5}\left(f x +e \right)\right)}{16}+\frac{105 \left(\sin^{3}\left(f x +e \right)\right)}{64}+\frac{315 \sin \left(f x +e \right)}{128}\right) \cos \left(f x +e \right)}{10}+\frac{63 f x}{256}+\frac{63 e}{256}\right)+\frac{B \,a^{3} c^{6} \left(\frac{128}{35}+\sin^{8}\left(f x +e \right)+\frac{8 \left(\sin^{6}\left(f x +e \right)\right)}{7}+\frac{48 \left(\sin^{4}\left(f x +e \right)\right)}{35}+\frac{64 \left(\sin^{2}\left(f x +e \right)\right)}{35}\right) \cos \left(f x +e \right)}{3}-\frac{8 B \,a^{3} c^{6} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-6 B \,a^{3} c^{6} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{a^{3} A \,c^{6} \left(\frac{128}{35}+\sin^{8}\left(f x +e \right)+\frac{8 \left(\sin^{6}\left(f x +e \right)\right)}{7}+\frac{48 \left(\sin^{4}\left(f x +e \right)\right)}{35}+\frac{64 \left(\sin^{2}\left(f x +e \right)\right)}{35}\right) \cos \left(f x +e \right)}{9}-3 a^{3} A \,c^{6} \left(-\frac{\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)}{8}+\frac{35 f x}{128}+\frac{35 e}{128}\right)+8 a^{3} A \,c^{6} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{6 a^{3} A \,c^{6} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-6 a^{3} A \,c^{6} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-3 B \,a^{3} c^{6} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(a^3*A*c^6*(f*x+e)-B*a^3*c^6*cos(f*x+e)-8/3*a^3*A*c^6*(2+sin(f*x+e)^2)*cos(f*x+e)+8*B*a^3*c^6*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3*a^3*A*c^6*cos(f*x+e)+6/5*B*a^3*c^6*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+B*a^3*c^6*(-1/10*(sin(f*x+e)^9+9/8*sin(f*x+e)^7+21/16*sin(f*x+e)^5+105/64*sin(f*x+e)^3+315/128*sin(f*x+e))*cos(f*x+e)+63/256*f*x+63/256*e)+1/3*B*a^3*c^6*(128/35+sin(f*x+e)^8+8/7*sin(f*x+e)^6+48/35*sin(f*x+e)^4+64/35*sin(f*x+e)^2)*cos(f*x+e)-8/7*B*a^3*c^6*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-6*B*a^3*c^6*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/9*a^3*A*c^6*(128/35+sin(f*x+e)^8+8/7*sin(f*x+e)^6+48/35*sin(f*x+e)^4+64/35*sin(f*x+e)^2)*cos(f*x+e)-3*a^3*A*c^6*(-1/8*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/128*f*x+35/128*e)+8*a^3*A*c^6*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+6/5*a^3*A*c^6*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-6*a^3*A*c^6*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3*B*a^3*c^6*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
39,1,611,208,0.763000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x)","\frac{a^{3} A \,c^{5} \left(f x +e \right)-a^{3} A \,c^{5} \left(-\frac{\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)}{8}+\frac{35 f x}{128}+\frac{35 e}{128}\right)-\frac{2 a^{3} A \,c^{5} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}+2 a^{3} A \,c^{5} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{6 a^{3} A \,c^{5} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+\frac{B \,a^{3} c^{5} \left(\frac{128}{35}+\sin^{8}\left(f x +e \right)+\frac{8 \left(\sin^{6}\left(f x +e \right)\right)}{7}+\frac{48 \left(\sin^{4}\left(f x +e \right)\right)}{35}+\frac{64 \left(\sin^{2}\left(f x +e \right)\right)}{35}\right) \cos \left(f x +e \right)}{9}+2 B \,a^{3} c^{5} \left(-\frac{\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)}{8}+\frac{35 f x}{128}+\frac{35 e}{128}\right)-\frac{2 B \,a^{3} c^{5} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-6 B \,a^{3} c^{5} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-B \,a^{3} c^{5} \cos \left(f x +e \right)-2 a^{3} A \,c^{5} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+6 B \,a^{3} c^{5} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-2 a^{3} A \,c^{5} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{2 B \,a^{3} c^{5} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 a^{3} A \,c^{5} \cos \left(f x +e \right)-2 B \,a^{3} c^{5} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(a^3*A*c^5*(f*x+e)-a^3*A*c^5*(-1/8*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/128*f*x+35/128*e)-2/7*a^3*A*c^5*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)+2*a^3*A*c^5*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+6/5*a^3*A*c^5*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+1/9*B*a^3*c^5*(128/35+sin(f*x+e)^8+8/7*sin(f*x+e)^6+48/35*sin(f*x+e)^4+64/35*sin(f*x+e)^2)*cos(f*x+e)+2*B*a^3*c^5*(-1/8*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/128*f*x+35/128*e)-2/7*B*a^3*c^5*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-6*B*a^3*c^5*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-B*a^3*c^5*cos(f*x+e)-2*a^3*A*c^5*(2+sin(f*x+e)^2)*cos(f*x+e)+6*B*a^3*c^5*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*a^3*A*c^5*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2/3*B*a^3*c^5*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a^3*A*c^5*cos(f*x+e)-2*B*a^3*c^5*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
40,1,568,169,0.674000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x)","\frac{a^{3} A \,c^{4} \left(f x +e \right)+B \,a^{3} c^{4} \left(-\frac{\left(\sin^{7}\left(f x +e \right)+\frac{7 \left(\sin^{5}\left(f x +e \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(f x +e \right)\right)}{24}+\frac{35 \sin \left(f x +e \right)}{16}\right) \cos \left(f x +e \right)}{8}+\frac{35 f x}{128}+\frac{35 e}{128}\right)+\frac{B \,a^{3} c^{4} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-3 B \,a^{3} c^{4} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{3 B \,a^{3} c^{4} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-a^{3} A \,c^{4} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+\frac{3 a^{3} A \,c^{4} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+3 a^{3} A \,c^{4} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{a^{3} A \,c^{4} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}+a^{3} A \,c^{4} \cos \left(f x +e \right)-B \,a^{3} c^{4} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{3} A \,c^{4} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B \,a^{3} c^{4} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-3 a^{3} A \,c^{4} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+B \,a^{3} c^{4} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-B \,a^{3} c^{4} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(a^3*A*c^4*(f*x+e)+B*a^3*c^4*(-1/8*(sin(f*x+e)^7+7/6*sin(f*x+e)^5+35/24*sin(f*x+e)^3+35/16*sin(f*x+e))*cos(f*x+e)+35/128*f*x+35/128*e)+1/7*B*a^3*c^4*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-3*B*a^3*c^4*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-3/5*B*a^3*c^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-a^3*A*c^4*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+3/5*a^3*A*c^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*a^3*A*c^4*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/7*a^3*A*c^4*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)+a^3*A*c^4*cos(f*x+e)-B*a^3*c^4*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*A*c^4*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^3*c^4*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3*a^3*A*c^4*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+B*a^3*c^4*(2+sin(f*x+e)^2)*cos(f*x+e)-B*a^3*c^4*cos(f*x+e))","B"
41,1,263,107,0.666000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","\frac{\frac{B \,a^{3} c^{3} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}-a^{3} A \,c^{3} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{3 B \,a^{3} c^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+3 a^{3} A \,c^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+B \,a^{3} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 a^{3} A \,c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{3} c^{3} \cos \left(f x +e \right)+a^{3} A \,c^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(1/7*B*a^3*c^3*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)-a^3*A*c^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-3/5*B*a^3*c^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*a^3*A*c^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+B*a^3*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)-3*a^3*A*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^3*c^3*cos(f*x+e)+a^3*A*c^3*(f*x+e))","B"
42,1,364,128,0.576000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","\frac{-\frac{a^{3} A \,c^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+a^{3} A \,c^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{2 a^{3} A \,c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+B \,a^{3} c^{2} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-\frac{B \,a^{3} c^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-2 B \,a^{3} c^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-2 a^{3} A \,c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+\frac{2 B \,a^{3} c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-a^{3} A \,c^{2} \cos \left(f x +e \right)+B \,a^{3} c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{3} A \,c^{2} \left(f x +e \right)-B \,a^{3} c^{2} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-1/5*a^3*A*c^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^3*A*c^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2/3*a^3*A*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)+B*a^3*c^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-1/5*B*a^3*c^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-2*B*a^3*c^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*a^3*A*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2/3*B*a^3*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)-a^3*A*c^2*cos(f*x+e)+B*a^3*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*A*c^2*(f*x+e)-B*a^3*c^2*cos(f*x+e))","B"
43,1,208,130,0.481000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\frac{-a^{3} A c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+\frac{2 a^{3} A c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+\frac{B \,a^{3} c \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-2 B \,a^{3} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-2 a^{3} A c \cos \left(f x +e \right)+2 B \,a^{3} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{3} A c \left(f x +e \right)-B \,a^{3} c \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-a^3*A*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2/3*a^3*A*c*(2+sin(f*x+e)^2)*cos(f*x+e)+1/5*B*a^3*c*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-2*B*a^3*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*a^3*A*c*cos(f*x+e)+2*B*a^3*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*A*c*(f*x+e)-B*a^3*c*cos(f*x+e))","A"
44,1,449,150,0.443000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","-\frac{16 a^{3} A}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{16 a^{3} B}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 a^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{14 a^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{16 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{32 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{4 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 a^{3} A}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{46 a^{3} B}{3 f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{15 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f c}-\frac{20 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f c}"," ",0,"-16/f*a^3/c/(tan(1/2*f*x+1/2*e)-1)*A-16/f*a^3/c/(tan(1/2*f*x+1/2*e)-1)*B-1/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A-4/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B+8/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*A+14/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*B+16/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*A+32/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*B+1/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A+4/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B+8/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*A+46/3/f*a^3/c/(1+tan(1/2*f*x+1/2*e)^2)^3*B-15/f*a^3/c*arctan(tan(1/2*f*x+1/2*e))*A-20/f*a^3/c*arctan(tan(1/2*f*x+1/2*e))*B","B"
45,1,399,153,0.470000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","\frac{8 a^{3} A}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}+\frac{24 a^{3} B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{32 a^{3} A}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{32 a^{3} B}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16 a^{3} A}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{16 a^{3} B}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{a^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{10 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{a^{3} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{3} A}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{10 a^{3} B}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{25 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{c^{2} f}+\frac{10 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{c^{2} f}"," ",0,"8*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)*A+24*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)*B-32/3*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*A-32/3*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3*B-16*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*A-16*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2*B+a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3*B-2*a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*A-10*a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*B-a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)-2*a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A-10*a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B+25*a^3/c^2/f*arctan(tan(1/2*f*x+1/2*e))*B+10*a^3/c^2/f*arctan(tan(1/2*f*x+1/2*e))*A","B"
46,1,323,147,0.509000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","-\frac{4 a^{3} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{12 a^{3} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{8 a^{3} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{8 a^{3} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{64 a^{3} A}{5 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{64 a^{3} B}{5 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{80 a^{3} A}{3 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16 a^{3} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{32 a^{3} A}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{32 a^{3} B}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}+\frac{2 a^{3} B}{c^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{c^{3} f}-\frac{12 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{c^{3} f}"," ",0,"-4*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)*A-12*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)*B-8*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^2*A+8*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^2*B-64/5*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^5*A-64/5*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^5*B-80/3*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^3*A-16*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^3*B-32*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^4*A-32*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^4*B+2*a^3/c^3/f*B/(1+tan(1/2*f*x+1/2*e)^2)-2*a^3/c^3/f*arctan(tan(1/2*f*x+1/2*e))*A-12*a^3/c^3/f*arctan(tan(1/2*f*x+1/2*e))*B","B"
47,1,374,145,0.485000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","-\frac{2 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}+\frac{2 a^{3} B}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{12 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{4 a^{3} B}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{40 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{40 a^{3} B}{3 c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{128 a^{3} A}{7 c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{128 a^{3} B}{7 c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{80 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{48 a^{3} B}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{64 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{64 a^{3} B}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{96 a^{3} A}{c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{416 a^{3} B}{5 c^{4} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}+\frac{2 a^{3} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{4} f}"," ",0,"-2*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)*A+2*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)*B-12*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^2*A-4*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^2*B-40*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^3*A-40/3*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^3*B-128/7*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^7*A-128/7*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^7*B-80*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^4*A-48*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^4*B-64*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^6*A-64*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^6*B-96*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^5*A-416/5*a^3/c^4/f/(tan(1/2*f*x+1/2*e)-1)^5*B+2*a^3/c^4/f*B*arctan(tan(1/2*f*x+1/2*e))","B"
48,1,205,73,0.527000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x)","\frac{2 a^{3} \left(-\frac{992 A +800 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{304 A +144 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{928 A +864 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{86 A +26 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{512 A +512 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{14 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{680 A +440 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{128 A +128 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}\right)}{f \,c^{5}}"," ",0,"2/f*a^3/c^5*(-1/6*(992*A+800*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(304*A+144*B)/(tan(1/2*f*x+1/2*e)-1)^4-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(928*A+864*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/3*(86*A+26*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/8*(512*A+512*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/2*(14*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/5*(680*A+440*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/9*(128*A+128*B)/(tan(1/2*f*x+1/2*e)-1)^9)","B"
49,1,249,112,0.519000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x)","\frac{2 a^{3} \left(-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{504 A +200 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{4352 A +3840 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{4272 A +3344 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{116 A +30 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{1280 A +1280 B}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{2960 A +1968 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{1460 A +780 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{16 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{256 A +256 B}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{3008 A +2880 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}\right)}{f \,c^{6}}"," ",0,"2/f*a^3/c^6*(-A/(tan(1/2*f*x+1/2*e)-1)-1/4*(504*A+200*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/8*(4352*A+3840*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/7*(4272*A+3344*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/3*(116*A+30*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/10*(1280*A+1280*B)/(tan(1/2*f*x+1/2*e)-1)^10-1/6*(2960*A+1968*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/5*(1460*A+780*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/2*(16*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/11*(256*A+256*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/9*(3008*A+2880*B)/(tan(1/2*f*x+1/2*e)-1)^9)","B"
50,1,293,148,0.571000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x)","\frac{2 a^{3} \left(-\frac{16000 A +14720 B}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{512 A +512 B}{13 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{13}}-\frac{6888 A +3928 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{150 A +34 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{13112 A +8840 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{3072 A +3072 B}{12 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{12}}-\frac{2700 A +1240 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{18816 A +14464 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{768 A +264 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{8832 A +8576 B}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{18 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{20256 A +17248 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}\right)}{f \,c^{7}}"," ",0,"2/f*a^3/c^7*(-1/10*(16000*A+14720*B)/(tan(1/2*f*x+1/2*e)-1)^10-1/13*(512*A+512*B)/(tan(1/2*f*x+1/2*e)-1)^13-1/6*(6888*A+3928*B)/(tan(1/2*f*x+1/2*e)-1)^6-A/(tan(1/2*f*x+1/2*e)-1)-1/3*(150*A+34*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/7*(13112*A+8840*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/12*(3072*A+3072*B)/(tan(1/2*f*x+1/2*e)-1)^12-1/5*(2700*A+1240*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/8*(18816*A+14464*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/4*(768*A+264*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/11*(8832*A+8576*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/2*(18*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/9*(20256*A+17248*B)/(tan(1/2*f*x+1/2*e)-1)^9)","A"
51,1,337,187,0.576000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^8,x)","\frac{2 a^{3} \left(-\frac{4536 A +1836 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{20 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{81344 A +72512 B}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{24320 A +23808 B}{13 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{13}}-\frac{1104 A +336 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{32288 A +19176 B}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{1024 A +1024 B}{15 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{15}}-\frac{13824 A +6936 B}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{7168 A +7168 B}{14 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{14}}-\frac{58816 A +40000 B}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{52736 A +49664 B}{12 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{12}}-\frac{188 A +38 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{84112 A +63856 B}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{94144 A +78144 B}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}\right)}{f \,c^{8}}"," ",0,"2/f*a^3/c^8*(-1/5*(4536*A+1836*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/2*(20*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/11*(81344*A+72512*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/13*(24320*A+23808*B)/(tan(1/2*f*x+1/2*e)-1)^13-1/4*(1104*A+336*B)/(tan(1/2*f*x+1/2*e)-1)^4-A/(tan(1/2*f*x+1/2*e)-1)-1/7*(32288*A+19176*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/15*(1024*A+1024*B)/(tan(1/2*f*x+1/2*e)-1)^15-1/6*(13824*A+6936*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/14*(7168*A+7168*B)/(tan(1/2*f*x+1/2*e)-1)^14-1/8*(58816*A+40000*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/12*(52736*A+49664*B)/(tan(1/2*f*x+1/2*e)-1)^12-1/3*(188*A+38*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/9*(84112*A+63856*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/10*(94144*A+78144*B)/(tan(1/2*f*x+1/2*e)-1)^10)","A"
52,1,678,182,0.429000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x)","-\frac{5 c^{4} \left(\tan^{7}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{47 c^{4} \left(\tan^{7}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{22 c^{4} \left(\tan^{6}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{30 c^{4} \left(\tan^{6}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{5 c^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{55 c^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{70 c^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{110 c^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{5 c^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{55 c^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{214 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{3 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{350 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{3 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{5 c^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{47 c^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{4 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{70 c^{4} A}{3 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{110 c^{4} B}{3 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{35 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a}+\frac{175 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 f a}-\frac{32 c^{4} A}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{32 c^{4} B}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-5/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^7*A+47/4/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^7*B-22/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^6*A+30/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^6*B-5/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^5*A+55/4/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^5*B-70/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^4*A+110/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^4*B+5/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^3*A-55/4/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^3*B-214/3/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^2*A+350/3/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^2*B+5/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)*A-47/4/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)*B-70/3/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*A+110/3/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^4*B-35/f*c^4/a*arctan(tan(1/2*f*x+1/2*e))*A+175/4/f*c^4/a*arctan(tan(1/2*f*x+1/2*e))*B-32/f*c^4/a/(tan(1/2*f*x+1/2*e)+1)*A+32/f*c^4/a/(tan(1/2*f*x+1/2*e)+1)*B","B"
53,1,449,151,0.410000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x)","-\frac{c^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{4 c^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 c^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{14 c^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{16 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{32 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{c^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 c^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 c^{3} A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{46 c^{3} B}{3 f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{15 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a}+\frac{20 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a}-\frac{16 c^{3} A}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{16 c^{3} B}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-1/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A+4/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B-8/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*A+14/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*B-16/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*A+32/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*B+1/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A-4/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B-8/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*A+46/3/f*c^3/a/(1+tan(1/2*f*x+1/2*e)^2)^3*B-15/f*c^3/a*arctan(tan(1/2*f*x+1/2*e))*A+20/f*c^3/a*arctan(tan(1/2*f*x+1/2*e))*B-16/f*c^3/a/(tan(1/2*f*x+1/2*e)+1)*A+16/f*c^3/a/(tan(1/2*f*x+1/2*e)+1)*B","B"
54,1,299,112,0.396000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x)","\frac{c^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{c^{2} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 c^{2} A}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 c^{2} B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{9 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a}-\frac{6 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a}-\frac{8 c^{2} A}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 c^{2} B}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"1/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3*B-2/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*A+6/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*B-1/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)-2/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*A+6/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)^2*B+9/f*c^2/a*arctan(tan(1/2*f*x+1/2*e))*B-6/f*c^2/a*arctan(tan(1/2*f*x+1/2*e))*A-8/f*c^2/a/(tan(1/2*f*x+1/2*e)+1)*A+8/f*c^2/a/(tan(1/2*f*x+1/2*e)+1)*B","B"
55,1,113,57,0.379000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\frac{2 c B}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{2 c \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f a}+\frac{4 c \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f a}-\frac{4 c A}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c B}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2/f*c/a*B/(1+tan(1/2*f*x+1/2*e)^2)-2/f*c/a*arctan(tan(1/2*f*x+1/2*e))*A+4/f*c/a*arctan(tan(1/2*f*x+1/2*e))*B-4/f*c/a/(tan(1/2*f*x+1/2*e)+1)*A+4/f*c/a/(tan(1/2*f*x+1/2*e)+1)*B","A"
56,1,57,35,0.369000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\frac{-\frac{2 \left(\frac{A}{2}+\frac{B}{2}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{A}{2}-\frac{B}{2}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{a c f}"," ",0,"2/f/c/a*(-(1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)-1)-(1/2*A-1/2*B)/(tan(1/2*f*x+1/2*e)+1))","A"
57,1,93,59,0.448000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","\frac{-\frac{2 \left(A +B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{A +B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{3 A}{4}+\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{A}{4}-\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f a \,c^{2}}"," ",0,"2/f/a/c^2*(-1/3*(A+B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(A+B)/(tan(1/2*f*x+1/2*e)-1)^2-(3/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)-1)-(1/4*A-1/4*B)/(tan(1/2*f*x+1/2*e)+1))","A"
58,1,145,96,0.546000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","\frac{-\frac{2 \left(2 A +2 B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{4 A +4 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{\frac{5 A}{2}+\frac{3 B}{2}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{7 A}{8}+\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{9 A}{2}+\frac{7 B}{2}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2 \left(\frac{A}{8}-\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f a \,c^{3}}"," ",0,"2/f/a/c^3*(-1/5*(2*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/4*(4*A+4*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/2*(5/2*A+3/2*B)/(tan(1/2*f*x+1/2*e)-1)^2-(7/8*A+1/8*B)/(tan(1/2*f*x+1/2*e)-1)-1/3*(9/2*A+7/2*B)/(tan(1/2*f*x+1/2*e)-1)^3-(1/8*A-1/8*B)/(tan(1/2*f*x+1/2*e)+1))","A"
59,1,189,134,0.490000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{2 \left(4 A +4 B \right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{12 A +12 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{18 A +14 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{2 \left(19 A +17 B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 \left(\frac{15 A}{16}+\frac{B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{\frac{17 A}{4}+\frac{7 B}{4}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{45 A}{4}+\frac{27 B}{4}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2 \left(\frac{A}{16}-\frac{B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f a \,c^{4}}"," ",0,"2/f/a/c^4*(-1/7*(4*A+4*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(12*A+12*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(18*A+14*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/5*(19*A+17*B)/(tan(1/2*f*x+1/2*e)-1)^5-(15/16*A+1/16*B)/(tan(1/2*f*x+1/2*e)-1)-1/2*(17/4*A+7/4*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/3*(45/4*A+27/4*B)/(tan(1/2*f*x+1/2*e)-1)^3-(1/16*A-1/16*B)/(tan(1/2*f*x+1/2*e)+1))","A"
60,1,778,228,0.515000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x)","\frac{7 c^{5} \left(\tan^{7}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{95 c^{5} \left(\tan^{7}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{46 c^{5} \left(\tan^{6}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{98 c^{5} \left(\tan^{6}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{7 c^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{103 c^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{142 c^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{322 c^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{7 c^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{103 c^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{430 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{994 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{7 c^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{95 c^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{4 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{142 c^{5} A}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}-\frac{322 c^{5} B}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{4}}+\frac{105 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f}-\frac{735 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{4 a^{2} f}+\frac{64 c^{5} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{64 c^{5} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{96 c^{5} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{160 c^{5} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{128 c^{5} A}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{128 c^{5} B}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^7*A-95/4*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^7*B+46*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^6*A-98*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^6*B+7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^5*A-103/4*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^5*B+142*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^4*A-322*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^4*B-7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^3*A+103/4*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^3*B+430/3*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^2*A-994/3*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)^2*B-7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)*A+95/4*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*tan(1/2*f*x+1/2*e)*B+142/3*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*A-322/3*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^4*B+105*c^5/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A-735/4*c^5/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B+64*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A-64*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B+96*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A-160*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B-128/3*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A+128/3*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
61,1,549,172,0.464000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x)","\frac{c^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 c^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{12 c^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{34 c^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{24 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{72 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{c^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 c^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{12 c^{4} A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{106 c^{4} B}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{35 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f}-\frac{70 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f}+\frac{32 c^{4} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{32 c^{4} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{32 c^{4} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{64 c^{4} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{64 c^{4} A}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{64 c^{4} B}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A-6*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B+12*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*A-34*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*B+24*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*A-72*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*B-c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A+6*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B+12*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A-106/3*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B+35*c^4/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A-70*c^4/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B+32*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A-32*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B+32*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A-64*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B-64/3*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A+64/3*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
62,1,399,152,0.453000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x)","-\frac{c^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{10 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{c^{3} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 c^{3} A}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{10 c^{3} B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{25 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f}+\frac{10 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f}+\frac{16 c^{3} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c^{3} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8 c^{3} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{24 c^{3} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{32 c^{3} A}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{32 c^{3} B}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3*B+2*c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*A-10*c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*B+c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)+2*c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A-10*c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B-25*c^3/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B+10*c^3/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A+16*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A-16*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B+8*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A-24*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B-32/3*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A+32/3*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
63,1,198,104,0.426000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x)","-\frac{2 c^{2} B}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{2} f}-\frac{8 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{2} f}+\frac{8 c^{2} A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 c^{2} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c^{2} A}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c^{2} B}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 c^{2} B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2*c^2/a^2/f*B/(1+tan(1/2*f*x+1/2*e)^2)+2*c^2/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A-8*c^2/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B+8*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A-8*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B-16/3*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A+16/3*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B-8*c^2/a^2/f*B/(tan(1/2*f*x+1/2*e)+1)","A"
64,1,160,68,0.415000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","-\frac{2 c B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}+\frac{4 c A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 c A}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 c B}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{8 c A}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 c B}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-2*c/a^2/f*B*arctan(tan(1/2*f*x+1/2*e))+4*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A-4*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B-2*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A-2*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B-8/3*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A+8/3*c/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
65,1,97,58,0.444000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x)","\frac{-\frac{2 \left(\frac{A}{4}+\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{-A +B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(A -B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{3 A}{4}-\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{a^{2} c f}"," ",0,"2/f/a^2/c*(-(1/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)-1)-1/2*(-A+B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(A-B)/(tan(1/2*f*x+1/2*e)+1)^3-(3/4*A-1/4*B)/(tan(1/2*f*x+1/2*e)+1))","A"
66,1,145,58,0.352000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x)","\frac{-\frac{2 \left(\frac{A}{2}+\frac{B}{2}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{\frac{A}{2}+\frac{B}{2}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{A}{2}+\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{-\frac{A}{2}+\frac{B}{2}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{A}{2}-\frac{B}{2}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{A}{2}-\frac{B}{4}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2} c^{2}}"," ",0,"2/f/a^2/c^2*(-1/3*(1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)-1)^2-(1/2*A+1/4*B)/(tan(1/2*f*x+1/2*e)-1)-1/2*(-1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(1/2*A-1/2*B)/(tan(1/2*f*x+1/2*e)+1)^3-(1/2*A-1/4*B)/(tan(1/2*f*x+1/2*e)+1))","B"
67,1,183,87,0.498000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x)","\frac{-\frac{2 \left(A +B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{\frac{3 A}{2}+B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{5 A}{2}+2 B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2 \left(\frac{11 A}{16}+\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{-\frac{A}{4}+\frac{B}{4}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{A}{4}-\frac{B}{4}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{5 A}{16}-\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2} c^{3}}"," ",0,"2/f/a^2/c^3*(-1/5*(A+B)/(tan(1/2*f*x+1/2*e)-1)^5-1/4*(2*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/2*(3/2*A+B)/(tan(1/2*f*x+1/2*e)-1)^2-1/3*(5/2*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^3-(11/16*A+3/16*B)/(tan(1/2*f*x+1/2*e)-1)-1/2*(-1/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(1/4*A-1/4*B)/(tan(1/2*f*x+1/2*e)+1)^3-(5/16*A-3/16*B)/(tan(1/2*f*x+1/2*e)+1))","B"
68,1,233,127,0.502000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{2 \left(2 A +2 B \right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{6 A +6 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{10 A +8 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{2 \left(10 A +9 B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 \left(\frac{13 A}{16}+\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{\frac{23 A}{8}+\frac{11 B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{55 A}{8}+\frac{35 B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{-\frac{A}{8}+\frac{B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{A}{8}-\frac{B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{3 A}{16}-\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2} c^{4}}"," ",0,"2/f/a^2/c^4*(-1/7*(2*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(6*A+6*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(10*A+8*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/5*(10*A+9*B)/(tan(1/2*f*x+1/2*e)-1)^5-(13/16*A+1/8*B)/(tan(1/2*f*x+1/2*e)-1)-1/2*(23/8*A+11/8*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/3*(55/8*A+35/8*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(-1/8*A+1/8*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(1/8*A-1/8*B)/(tan(1/2*f*x+1/2*e)+1)^3-(3/16*A-1/8*B)/(tan(1/2*f*x+1/2*e)+1))","A"
69,1,277,165,0.533000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x)","\frac{-\frac{2 \left(4 A +4 B \right)}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{16 A +16 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{2 \left(34 A +32 B \right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{46 A +40 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{\frac{9 A}{2}+\frac{13 B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{57 A}{64}+\frac{5 B}{64}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{\frac{59 A}{2}+\frac{39 B}{2}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{2 \left(\frac{57 A}{4}+\frac{59 B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2 \left(\frac{175 A}{4}+\frac{135 B}{4}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{-\frac{A}{16}+\frac{B}{16}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{A}{16}-\frac{B}{16}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{7 A}{64}-\frac{5 B}{64}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2} c^{5}}"," ",0,"2/f/a^2/c^5*(-1/9*(4*A+4*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/8*(16*A+16*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/7*(34*A+32*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(46*A+40*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/2*(9/2*A+13/8*B)/(tan(1/2*f*x+1/2*e)-1)^2-(57/64*A+5/64*B)/(tan(1/2*f*x+1/2*e)-1)-1/4*(59/2*A+39/2*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/3*(57/4*A+59/8*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/5*(175/4*A+135/4*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/2*(-1/16*A+1/16*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(1/16*A-1/16*B)/(tan(1/2*f*x+1/2*e)+1)^3-(7/64*A-5/64*B)/(tan(1/2*f*x+1/2*e)+1))","A"
70,1,649,231,0.521000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x)","-\frac{c^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 c^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{16 c^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{62 c^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{32 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{128 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{c^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 c^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{16 c^{5} A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{190 c^{5} B}{3 a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{63 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f}+\frac{168 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f}+\frac{128 c^{5} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{128 c^{5} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{32 c^{5} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{96 c^{5} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{64 c^{5} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{160 c^{5} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{64 c^{5} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{64 c^{5} B}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{256 c^{5} A}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{256 c^{5} B}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}"," ",0,"-c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A+8*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B-16*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*A+62*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*B-32*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*A+128*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*B+c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A-8*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B-16*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A+190/3*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B-63*c^5/a^3/f*arctan(tan(1/2*f*x+1/2*e))*A+168*c^5/a^3/f*arctan(tan(1/2*f*x+1/2*e))*B+128*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A-128*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B-32*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A+96*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B-64*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A+160*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B-64*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A+64/3*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B-256/5*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A+256/5*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B","B"
71,1,474,189,0.495000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x)","\frac{c^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{14 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{c^{4} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 c^{4} A}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{14 c^{4} B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{49 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f}-\frac{14 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f}+\frac{64 c^{4} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{64 c^{4} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{16 c^{4} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{48 c^{4} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{128 c^{4} A}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{128 c^{4} B}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{128 c^{4} A}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{64 c^{4} B}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{32 c^{4} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3*B-2*c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*A+14*c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*B-c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)-2*c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A+14*c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B+49*c^4/a^3/f*arctan(tan(1/2*f*x+1/2*e))*B-14*c^4/a^3/f*arctan(tan(1/2*f*x+1/2*e))*A+64*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A-64*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B-16*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A+48*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B-128/5*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A+128/5*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B-128/3*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A+64/3*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B+32*c^4/a^3/f*B/(tan(1/2*f*x+1/2*e)+1)^2","B"
72,1,323,147,0.481000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x)","\frac{2 c^{3} B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{2 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{a^{3} f}+\frac{12 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{a^{3} f}+\frac{32 c^{3} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{32 c^{3} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{8 c^{3} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8 c^{3} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c^{3} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{12 c^{3} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{64 c^{3} A}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{64 c^{3} B}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{80 c^{3} A}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c^{3} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"2*c^3/a^3/f*B/(1+tan(1/2*f*x+1/2*e)^2)-2*c^3/a^3/f*arctan(tan(1/2*f*x+1/2*e))*A+12*c^3/a^3/f*arctan(tan(1/2*f*x+1/2*e))*B+32*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A-32*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B+8*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A+8*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B-4*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A+12*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B-64/5*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A+64/5*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B-80/3*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A+16*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
73,1,249,106,0.467000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x)","\frac{2 c^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}+\frac{16 c^{2} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{16 c^{2} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 c^{2} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 c^{2} B}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{32 c^{2} A}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{32 c^{2} B}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16 c^{2} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{32 c^{2} B}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 c^{2} A}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"2*c^2/a^3/f*B*arctan(tan(1/2*f*x+1/2*e))+16*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A-16*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B-2*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A+2*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B-32/5*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A+32/5*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B-16*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A+32/3*c^2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B+8*c^2/a^3/f*A/(tan(1/2*f*x+1/2*e)+1)^2","B"
74,1,115,97,0.453000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\frac{2 c \left(-\frac{-16 A +16 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 A -8 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{14 A -10 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{-6 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{f \,a^{3}}"," ",0,"2/f*c/a^3*(-1/4*(-16*A+16*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(8*A-8*B)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(14*A-10*B)/(tan(1/2*f*x+1/2*e)+1)^3-1/2*(-6*A+2*B)/(tan(1/2*f*x+1/2*e)+1)^2-A/(tan(1/2*f*x+1/2*e)+1))","A"
75,1,145,96,0.515000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x)","\frac{-\frac{2 \left(\frac{A}{8}+\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{-4 A +4 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(2 A -2 B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{-\frac{5 A}{2}+\frac{3 B}{2}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{7 A}{8}-\frac{B}{8}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{2 \left(\frac{9 A}{2}-\frac{7 B}{2}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}}{a^{3} c f}"," ",0,"2/f/a^3/c*(-(1/8*A+1/8*B)/(tan(1/2*f*x+1/2*e)-1)-1/4*(-4*A+4*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(2*A-2*B)/(tan(1/2*f*x+1/2*e)+1)^5-1/2*(-5/2*A+3/2*B)/(tan(1/2*f*x+1/2*e)+1)^2-(7/8*A-1/8*B)/(tan(1/2*f*x+1/2*e)+1)-1/3*(9/2*A-7/2*B)/(tan(1/2*f*x+1/2*e)+1)^3)","A"
76,1,185,84,0.463000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x)","\frac{-\frac{2 \left(\frac{A}{4}+\frac{B}{4}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{\frac{A}{4}+\frac{B}{4}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{5 A}{16}+\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{-2 A +2 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(A -B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{-\frac{3 A}{2}+B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{5 A}{2}-2 B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{11 A}{16}-\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3} c^{2}}"," ",0,"2/f/a^3/c^2*(-1/3*(1/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(1/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)-1)^2-(5/16*A+3/16*B)/(tan(1/2*f*x+1/2*e)-1)-1/4*(-2*A+2*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(A-B)/(tan(1/2*f*x+1/2*e)+1)^5-1/2*(-3/2*A+B)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(5/2*A-2*B)/(tan(1/2*f*x+1/2*e)+1)^3-(11/16*A-3/16*B)/(tan(1/2*f*x+1/2*e)+1))","B"
77,1,227,78,0.421000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x)","\frac{-\frac{A +B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{2 \left(\frac{A}{2}+\frac{B}{2}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{\frac{7 A}{8}+\frac{5 B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{A}{2}+\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{11 A}{8}+\frac{9 B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{-A +B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{-\frac{7 A}{8}+\frac{5 B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(\frac{A}{2}-\frac{B}{2}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(\frac{A}{2}-\frac{3 B}{16}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{2 \left(\frac{11 A}{8}-\frac{9 B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}}{f \,a^{3} c^{3}}"," ",0,"2/f/a^3/c^3*(-1/4*(A+B)/(tan(1/2*f*x+1/2*e)-1)^4-1/5*(1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/2*(7/8*A+5/8*B)/(tan(1/2*f*x+1/2*e)-1)^2-(1/2*A+3/16*B)/(tan(1/2*f*x+1/2*e)-1)-1/3*(11/8*A+9/8*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/4*(-A+B)/(tan(1/2*f*x+1/2*e)+1)^4-1/2*(-7/8*A+5/8*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/5*(1/2*A-1/2*B)/(tan(1/2*f*x+1/2*e)+1)^5-(1/2*A-3/16*B)/(tan(1/2*f*x+1/2*e)+1)-1/3*(11/8*A-9/8*B)/(tan(1/2*f*x+1/2*e)+1)^3)","B"
78,1,271,113,0.511000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{2 \left(A +B \right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{3 A +3 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{\frac{11 A}{2}+\frac{9 B}{2}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{\frac{15 A}{8}+B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{21 A}{32}+\frac{5 B}{32}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{21 A}{4}+\frac{19 B}{4}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 \left(\frac{33 A}{8}+\frac{11 B}{4}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{-\frac{A}{2}+\frac{3 B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{-\frac{A}{2}+\frac{B}{2}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(\frac{A}{4}-\frac{B}{4}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(\frac{3 A}{4}-\frac{5 B}{8}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{11 A}{32}-\frac{5 B}{32}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3} c^{4}}"," ",0,"2/f/a^3/c^4*(-1/7*(A+B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(3*A+3*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/4*(11/2*A+9/2*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/2*(15/8*A+B)/(tan(1/2*f*x+1/2*e)-1)^2-(21/32*A+5/32*B)/(tan(1/2*f*x+1/2*e)-1)-1/5*(21/4*A+19/4*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/3*(33/8*A+11/4*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(-1/2*A+3/8*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/4*(-1/2*A+1/2*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(1/4*A-1/4*B)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(3/4*A-5/8*B)/(tan(1/2*f*x+1/2*e)+1)^3-(11/32*A-5/32*B)/(tan(1/2*f*x+1/2*e)+1))","B"
79,1,321,152,0.562000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x)","\frac{-\frac{2 \left(2 A +2 B \right)}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{8 A +8 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{\frac{35 A}{2}+12 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{2 \left(\frac{35 A}{2}+\frac{33 B}{2}\right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{\frac{49 A}{2}+\frac{43 B}{2}}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{\frac{51 A}{16}+\frac{21 B}{16}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{49 A}{2}+\frac{77 B}{4}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 \left(\frac{99 A}{128}+\frac{15 B}{128}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{147 A}{16}+\frac{81 B}{16}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{-\frac{9 A}{32}+\frac{7 B}{32}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{-\frac{A}{4}+\frac{B}{4}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(\frac{A}{8}-\frac{B}{8}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(\frac{13 A}{32}-\frac{11 B}{32}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{29 A}{128}-\frac{15 B}{128}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3} c^{5}}"," ",0,"2/f/a^3/c^5*(-1/9*(2*A+2*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/8*(8*A+8*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/4*(35/2*A+12*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/7*(35/2*A+33/2*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/6*(49/2*A+43/2*B)/(tan(1/2*f*x+1/2*e)-1)^6-1/2*(51/16*A+21/16*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/5*(49/2*A+77/4*B)/(tan(1/2*f*x+1/2*e)-1)^5-(99/128*A+15/128*B)/(tan(1/2*f*x+1/2*e)-1)-1/3*(147/16*A+81/16*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(-9/32*A+7/32*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/4*(-1/4*A+1/4*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(1/8*A-1/8*B)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(13/32*A-11/32*B)/(tan(1/2*f*x+1/2*e)+1)^3-(29/128*A-15/128*B)/(tan(1/2*f*x+1/2*e)+1))","B"
80,1,365,193,0.509000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x)","\frac{-\frac{2 \left(4 A +4 B \right)}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{20 A +20 B}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{2 \left(53 A +51 B \right)}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{92 A +84 B}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{\frac{169 A}{4}+\frac{99 B}{4}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{\frac{217 A}{2}+84 B}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{2 \left(\frac{219 A}{256}+\frac{21 B}{256}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{2 \left(\frac{231 A}{2}+98 B \right)}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{\frac{303 A}{64}+\frac{99 B}{64}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{2 \left(\frac{623 A}{8}+\frac{427 B}{8}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2 \left(\frac{1095 A}{64}+\frac{507 B}{64}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{-\frac{5 A}{32}+\frac{B}{8}}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{-\frac{A}{8}+\frac{B}{8}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(\frac{A}{16}-\frac{B}{16}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(\frac{7 A}{32}-\frac{3 B}{16}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(\frac{37 A}{256}-\frac{21 B}{256}\right)}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3} c^{6}}"," ",0,"2/f/a^3/c^6*(-1/11*(4*A+4*B)/(tan(1/2*f*x+1/2*e)-1)^11-1/10*(20*A+20*B)/(tan(1/2*f*x+1/2*e)-1)^10-1/9*(53*A+51*B)/(tan(1/2*f*x+1/2*e)-1)^9-1/8*(92*A+84*B)/(tan(1/2*f*x+1/2*e)-1)^8-1/4*(169/4*A+99/4*B)/(tan(1/2*f*x+1/2*e)-1)^4-1/6*(217/2*A+84*B)/(tan(1/2*f*x+1/2*e)-1)^6-(219/256*A+21/256*B)/(tan(1/2*f*x+1/2*e)-1)-1/7*(231/2*A+98*B)/(tan(1/2*f*x+1/2*e)-1)^7-1/2*(303/64*A+99/64*B)/(tan(1/2*f*x+1/2*e)-1)^2-1/5*(623/8*A+427/8*B)/(tan(1/2*f*x+1/2*e)-1)^5-1/3*(1095/64*A+507/64*B)/(tan(1/2*f*x+1/2*e)-1)^3-1/2*(-5/32*A+1/8*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/4*(-1/8*A+1/8*B)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(1/16*A-1/16*B)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(7/32*A-3/16*B)/(tan(1/2*f*x+1/2*e)+1)^3-(37/256*A-21/256*B)/(tan(1/2*f*x+1/2*e)+1))","A"
81,1,119,178,1.301000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{4} \left(1+\sin \left(f x +e \right)\right)^{2} a \left(\left(-385 A +1435 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(3916 A -4300 B \right) \sin \left(f x +e \right)+315 B \left(\cos^{4}\left(f x +e \right)\right)+\left(1815 A -3345 B \right) \left(\cos^{2}\left(f x +e \right)\right)-5324 A +4940 B \right)}{3465 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/3465*(sin(f*x+e)-1)*c^4*(1+sin(f*x+e))^2*a*((-385*A+1435*B)*sin(f*x+e)*cos(f*x+e)^2+(3916*A-4300*B)*sin(f*x+e)+315*B*cos(f*x+e)^4+(1815*A-3345*B)*cos(f*x+e)^2-5324*A+4940*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
82,1,103,141,1.230000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{3} \left(1+\sin \left(f x +e \right)\right)^{2} a \left(-35 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-162 A +194 B \right) \sin \left(f x +e \right)+\left(-45 A +120 B \right) \left(\cos^{2}\left(f x +e \right)\right)+258 A -226 B \right)}{315 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/315*(sin(f*x+e)-1)*c^3*(1+sin(f*x+e))^2*a*(-35*B*cos(f*x+e)^2*sin(f*x+e)+(-162*A+194*B)*sin(f*x+e)+(-45*A+120*B)*cos(f*x+e)^2+258*A-226*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
83,1,81,104,1.109000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{2} \left(1+\sin \left(f x +e \right)\right)^{2} a \left(\sin \left(f x +e \right) \left(21 A -33 B \right)-15 B \left(\cos^{2}\left(f x +e \right)\right)-49 A +37 B \right)}{105 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/105*(sin(f*x+e)-1)*c^2*(1+sin(f*x+e))^2*a*(sin(f*x+e)*(21*A-33*B)-15*B*cos(f*x+e)^2-49*A+37*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
84,1,63,65,1.310000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c \left(1+\sin \left(f x +e \right)\right)^{2} a \left(3 B \sin \left(f x +e \right)+5 A -2 B \right)}{15 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*(sin(f*x+e)-1)*c*(1+sin(f*x+e))^2*a*(3*B*sin(f*x+e)+5*A-2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
85,1,159,105,1.486000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, a \left(3 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) A +3 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) B -B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}-3 A c \sqrt{c \left(1+\sin \left(f x +e \right)\right)}-3 B c \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\right)}{3 c^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*(sin(f*x+e)-1)*(c*(1+sin(f*x+e)))^(1/2)*a*(3*c^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*A+3*c^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*B-B*(c*(1+sin(f*x+e)))^(3/2)-3*A*c*(c*(1+sin(f*x+e)))^(1/2)-3*B*c*(c*(1+sin(f*x+e)))^(1/2))/c^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
86,1,227,102,1.239000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{a \left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c +5 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c -A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -4 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c}\, B \sin \left(f x +e \right)-5 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +2 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c}\, A +6 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c}\, B \right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{2 c^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/2*a/c^(5/2)*(A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c+5*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c-A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c-4*(c*(1+sin(f*x+e)))^(1/2)*c^(1/2)*B*sin(f*x+e)-5*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c+2*(c*(1+sin(f*x+e)))^(1/2)*c^(1/2)*A+6*(c*(1+sin(f*x+e)))^(1/2)*c^(1/2)*B)*(c*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
87,1,268,107,1.607000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","\frac{a \left(-2 \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2} \left(A -7 B \right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2} \left(A -7 B \right) \left(\cos^{2}\left(f x +e \right)\right)+2 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-2 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}-4 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}-14 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-18 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}+28 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{16 c^{\frac{9}{2}} \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/16*a*(-2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2*(A-7*B)-2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2*(A-7*B)*cos(f*x+e)^2+2*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-2*A*(c+c*sin(f*x+e))^(3/2)*c^(1/2)-4*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)-14*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-18*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2)+28*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2))*(c*(1+sin(f*x+e)))^(1/2)/c^(9/2)/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
88,1,352,140,1.733000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","\frac{a \left(-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4} \left(A -3 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+12 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4} \left(A -3 B \right) \sin \left(f x +e \right)+9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4} \left(A -3 B \right) \left(\cos^{2}\left(f x +e \right)\right)+24 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{7}{2}}+32 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{5}{2}}-6 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{3}{2}}-72 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{7}{2}}+32 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{5}{2}}+18 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{3}{2}}-12 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4}+36 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{192 c^{\frac{15}{2}} \left(\sin \left(f x +e \right)-1\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/192*a*(-3*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4*(A-3*B)*sin(f*x+e)*cos(f*x+e)^2+12*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4*(A-3*B)*sin(f*x+e)+9*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4*(A-3*B)*cos(f*x+e)^2+24*A*(c+c*sin(f*x+e))^(1/2)*c^(7/2)+32*A*(c+c*sin(f*x+e))^(3/2)*c^(5/2)-6*A*(c+c*sin(f*x+e))^(5/2)*c^(3/2)-72*B*(c+c*sin(f*x+e))^(1/2)*c^(7/2)+32*B*(c+c*sin(f*x+e))^(3/2)*c^(5/2)+18*B*(c+c*sin(f*x+e))^(5/2)*c^(3/2)-12*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4+36*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4)*(c*(1+sin(f*x+e)))^(1/2)/c^(15/2)/(sin(f*x+e)-1)^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
89,1,121,190,1.157000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{4} \left(1+\sin \left(f x +e \right)\right)^{3} a^{2} \left(\left(-1365 A +4935 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(11180 A -11820 B \right) \sin \left(f x +e \right)+1155 B \left(\cos^{4}\left(f x +e \right)\right)+\left(5915 A -10605 B \right) \left(\cos^{2}\left(f x +e \right)\right)-12844 A +12204 B \right)}{15015 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15015*(sin(f*x+e)-1)*c^4*(1+sin(f*x+e))^3*a^2*((-1365*A+4935*B)*sin(f*x+e)*cos(f*x+e)^2+(11180*A-11820*B)*sin(f*x+e)+1155*B*cos(f*x+e)^4+(5915*A-10605*B)*cos(f*x+e)^2-12844*A+12204*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
90,1,105,151,1.258000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{3} \left(1+\sin \left(f x +e \right)\right)^{3} a^{2} \left(-315 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-1210 A +1370 B \right) \sin \left(f x +e \right)+\left(-385 A +980 B \right) \left(\cos^{2}\left(f x +e \right)\right)+1562 A -1402 B \right)}{3465 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/3465*(sin(f*x+e)-1)*c^3*(1+sin(f*x+e))^3*a^2*(-315*B*cos(f*x+e)^2*sin(f*x+e)+(-1210*A+1370*B)*sin(f*x+e)+(-385*A+980*B)*cos(f*x+e)^2+1562*A-1402*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
91,1,83,108,1.269000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{2} \left(1+\sin \left(f x +e \right)\right)^{3} a^{2} \left(\sin \left(f x +e \right) \left(45 A -65 B \right)-35 B \left(\cos^{2}\left(f x +e \right)\right)-81 A +61 B \right)}{315 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/315*(sin(f*x+e)-1)*c^2*(1+sin(f*x+e))^3*a^2*(sin(f*x+e)*(45*A-65*B)-35*B*cos(f*x+e)^2-81*A+61*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
92,1,65,73,1.295000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c \left(1+\sin \left(f x +e \right)\right)^{3} a^{2} \left(5 B \sin \left(f x +e \right)+7 A -2 B \right)}{35 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/35*(sin(f*x+e)-1)*c*(1+sin(f*x+e))^3*a^2*(5*B*sin(f*x+e)+7*A-2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
93,1,197,142,1.489000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, a^{2} \left(-30 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) A -30 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) B +3 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}+5 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c +5 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c +30 A \,c^{2} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}+30 B \,c^{2} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\right)}{15 c^{3} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*(sin(f*x+e)-1)*(c*(1+sin(f*x+e)))^(1/2)*a^2*(-30*c^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*A-30*c^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*B+3*B*(c*(1+sin(f*x+e)))^(5/2)+5*A*(c*(1+sin(f*x+e)))^(3/2)*c+5*B*(c*(1+sin(f*x+e)))^(3/2)*c+30*A*c^2*(c*(1+sin(f*x+e)))^(1/2)+30*B*c^2*(c*(1+sin(f*x+e)))^(1/2))/c^3/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
94,1,282,157,1.465000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{a^{2} \left(\sin \left(f x +e \right) \left(9 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-6 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+21 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-18 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}-2 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}\right)-9 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+12 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}-21 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+24 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+2 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{3 c^{\frac{7}{2}} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/3*a^2*(sin(f*x+e)*(9*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-6*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+21*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-18*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2)-2*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2))-9*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+12*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)-21*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+24*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+2*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2))*(c*(1+sin(f*x+e)))^(1/2)/c^(7/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
95,1,386,152,1.599000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{a^{2} \left(3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{2}+27 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{2}-6 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{2}-16 B \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right)-54 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{2}+10 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c}+3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+26 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c}+32 B \,c^{\frac{3}{2}} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right)+27 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-12 A \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}}-60 B \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{8 c^{\frac{9}{2}} \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/8/c^(9/2)*a^2*(3*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^2+27*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^2-6*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^2-16*B*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)*sin(f*x+e)^2-54*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^2+10*A*(c*(1+sin(f*x+e)))^(3/2)*c^(1/2)+3*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2+26*B*(c*(1+sin(f*x+e)))^(3/2)*c^(1/2)+32*B*c^(3/2)*(c*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)+27*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2-12*A*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)-60*B*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2))*(c*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
96,1,354,152,1.690000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","-\frac{a^{2} \left(-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3} \left(A -11 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+12 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3} \left(A -11 B \right) \sin \left(f x +e \right)+9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3} \left(A -11 B \right) \left(\cos^{2}\left(f x +e \right)\right)+24 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}-32 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-6 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{c}-264 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}+352 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-126 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{c}-12 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}+132 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{96 c^{\frac{13}{2}} \left(\sin \left(f x +e \right)-1\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/96*a^2*(-3*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3*(A-11*B)*sin(f*x+e)*cos(f*x+e)^2+12*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3*(A-11*B)*sin(f*x+e)+9*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3*(A-11*B)*cos(f*x+e)^2+24*A*(c+c*sin(f*x+e))^(1/2)*c^(5/2)-32*A*(c+c*sin(f*x+e))^(3/2)*c^(3/2)-6*A*(c+c*sin(f*x+e))^(5/2)*c^(1/2)-264*B*(c+c*sin(f*x+e))^(1/2)*c^(5/2)+352*B*(c+c*sin(f*x+e))^(3/2)*c^(3/2)-126*B*(c+c*sin(f*x+e))^(5/2)*c^(1/2)-12*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3+132*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3)*(c*(1+sin(f*x+e)))^(1/2)/c^(13/2)/(sin(f*x+e)-1)^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
97,1,440,195,1.697000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x)","\frac{a^{2} \left(-12 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{5} \left(3 A -13 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+24 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{5} \left(3 A -13 B \right) \sin \left(f x +e \right)-3 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{5} \left(3 A -13 B \right) \left(\cos^{4}\left(f x +e \right)\right)+24 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{5} \left(3 A -13 B \right) \left(\cos^{2}\left(f x +e \right)\right)+144 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{9}{2}}-264 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{7}{2}}-132 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{5}{2}}+18 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} c^{\frac{3}{2}}-624 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{9}{2}}+1144 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{7}{2}}-452 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{5}{2}}-78 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} c^{\frac{3}{2}}-72 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{5}+312 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{5}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{1536 c^{\frac{19}{2}} \left(\sin \left(f x +e \right)-1\right)^{3} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/1536/c^(19/2)*a^2*(-12*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^5*(3*A-13*B)*sin(f*x+e)*cos(f*x+e)^2+24*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^5*(3*A-13*B)*sin(f*x+e)-3*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^5*(3*A-13*B)*cos(f*x+e)^4+24*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^5*(3*A-13*B)*cos(f*x+e)^2+144*A*(c+c*sin(f*x+e))^(1/2)*c^(9/2)-264*A*(c+c*sin(f*x+e))^(3/2)*c^(7/2)-132*A*(c+c*sin(f*x+e))^(5/2)*c^(5/2)+18*A*(c+c*sin(f*x+e))^(7/2)*c^(3/2)-624*B*(c+c*sin(f*x+e))^(1/2)*c^(9/2)+1144*B*(c+c*sin(f*x+e))^(3/2)*c^(7/2)-452*B*(c+c*sin(f*x+e))^(5/2)*c^(5/2)-78*B*(c+c*sin(f*x+e))^(7/2)*c^(3/2)-72*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^5+312*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^5)*(c*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)^3/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
98,1,121,190,1.369000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{4} \left(1+\sin \left(f x +e \right)\right)^{4} a^{3} \left(\left(-3465 A +12243 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(24780 A -25676 B \right) \sin \left(f x +e \right)+3003 B \left(\cos^{4}\left(f x +e \right)\right)+\left(14175 A -24969 B \right) \left(\cos^{2}\left(f x +e \right)\right)-26700 A +25804 B \right)}{45045 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/45045*(sin(f*x+e)-1)*c^4*(1+sin(f*x+e))^4*a^3*((-3465*A+12243*B)*sin(f*x+e)*cos(f*x+e)^2+(24780*A-25676*B)*sin(f*x+e)+3003*B*cos(f*x+e)^4+(14175*A-24969*B)*cos(f*x+e)^2-26700*A+25804*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
99,1,105,145,1.341000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{3} \left(1+\sin \left(f x +e \right)\right)^{4} a^{3} \left(-693 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-2366 A +2590 B \right) \sin \left(f x +e \right)+\left(-819 A +2016 B \right) \left(\cos^{2}\left(f x +e \right)\right)+2782 A -2558 B \right)}{9009 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/9009*(sin(f*x+e)-1)*c^3*(1+sin(f*x+e))^4*a^3*(-693*B*cos(f*x+e)^2*sin(f*x+e)+(-2366*A+2590*B)*sin(f*x+e)+(-819*A+2016*B)*cos(f*x+e)^2+2782*A-2558*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
100,1,83,112,1.290000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{2 \left(\sin \left(f x +e \right)-1\right) c^{2} \left(1+\sin \left(f x +e \right)\right)^{4} a^{3} \left(\sin \left(f x +e \right) \left(77 A -105 B \right)-63 B \left(\cos^{2}\left(f x +e \right)\right)-121 A +93 B \right)}{693 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/693*(sin(f*x+e)-1)*c^2*(1+sin(f*x+e))^4*a^3*(sin(f*x+e)*(77*A-105*B)-63*B*cos(f*x+e)^2-121*A+93*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
101,1,65,73,1.240000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) c \left(1+\sin \left(f x +e \right)\right)^{4} a^{3} \left(7 B \sin \left(f x +e \right)+9 A -2 B \right)}{63 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/63*(sin(f*x+e)-1)*c*(1+sin(f*x+e))^4*a^3*(7*B*sin(f*x+e)+9*A-2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
102,1,233,177,1.556000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(\sin \left(f x +e \right)-1\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, a^{3} \left(420 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) A +420 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) B -15 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}-21 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c -21 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c -70 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{2}-70 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{2}-420 A \,c^{3} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}-420 B \,c^{3} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\right)}{105 c^{4} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/105*(sin(f*x+e)-1)*(c*(1+sin(f*x+e)))^(1/2)*a^3*(420*c^(7/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*A+420*c^(7/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*B-15*B*(c*(1+sin(f*x+e)))^(7/2)-21*A*(c*(1+sin(f*x+e)))^(5/2)*c-21*B*(c*(1+sin(f*x+e)))^(5/2)*c-70*A*(c*(1+sin(f*x+e)))^(3/2)*c^2-70*B*(c*(1+sin(f*x+e)))^(3/2)*c^2-420*A*c^3*(c*(1+sin(f*x+e)))^(1/2)-420*B*c^3*(c*(1+sin(f*x+e)))^(1/2))/c^4/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
103,1,354,195,1.470000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{2 a^{3} \left(\sin \left(f x +e \right) \left(-60 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}-5 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-120 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}-15 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-3 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{c}+75 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}+135 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}\right)+90 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}+5 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}+150 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{5}{2}}+15 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}+3 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{c}-75 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}-135 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{15 c^{\frac{9}{2}} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*a^3*(sin(f*x+e)*(-60*A*(c+c*sin(f*x+e))^(1/2)*c^(5/2)-5*A*(c+c*sin(f*x+e))^(3/2)*c^(3/2)-120*B*(c+c*sin(f*x+e))^(1/2)*c^(5/2)-15*B*(c+c*sin(f*x+e))^(3/2)*c^(3/2)-3*B*(c+c*sin(f*x+e))^(5/2)*c^(1/2)+75*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3+135*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3)+90*A*(c+c*sin(f*x+e))^(1/2)*c^(5/2)+5*A*(c+c*sin(f*x+e))^(3/2)*c^(3/2)+150*B*(c+c*sin(f*x+e))^(1/2)*c^(5/2)+15*B*(c+c*sin(f*x+e))^(3/2)*c^(3/2)+3*B*(c+c*sin(f*x+e))^(5/2)*c^(1/2)-75*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3-135*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^3)*(c*(1+sin(f*x+e)))^(1/2)/c^(9/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
104,1,434,198,1.986000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{a^{3} \left(\sin \left(f x +e \right) \left(-90 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+48 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}-330 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+240 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+16 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}\right)+\left(-45 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+24 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}-165 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+120 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+8 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}\right) \left(\cos^{2}\left(f x +e \right)\right)+90 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-132 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+54 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}+330 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-420 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{3}{2}}+86 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{12 c^{\frac{9}{2}} \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/12/c^(9/2)*a^3*(sin(f*x+e)*(-90*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+48*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)-330*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+240*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+16*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2))+(-45*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+24*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)-165*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+120*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+8*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2))*cos(f*x+e)^2+90*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-132*A*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+54*A*(c+c*sin(f*x+e))^(3/2)*c^(1/2)+330*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-420*B*(c+c*sin(f*x+e))^(1/2)*c^(3/2)+86*B*(c+c*sin(f*x+e))^(3/2)*c^(1/2))*(c*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
105,1,524,190,1.985000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","\frac{a^{3} \left(15 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{3}\left(f x +e \right)\right) c^{3}+195 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{3}\left(f x +e \right)\right) c^{3}-45 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{3}-96 B \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{5}{2}} \left(\sin^{3}\left(f x +e \right)\right)-585 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{3}+66 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c}+45 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{3}+282 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c}+288 B \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{5}{2}} \left(\sin^{2}\left(f x +e \right)\right)+585 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{3}-160 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-15 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}-928 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-288 B \,c^{\frac{5}{2}} \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right)-195 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3}+120 A \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{5}{2}}+888 B \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{5}{2}}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{48 c^{\frac{13}{2}} \left(\sin \left(f x +e \right)-1\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/48/c^(13/2)*a^3*(15*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^3*c^3+195*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^3*c^3-45*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^3-96*B*(c*(1+sin(f*x+e)))^(1/2)*c^(5/2)*sin(f*x+e)^3-585*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^3+66*A*(c*(1+sin(f*x+e)))^(5/2)*c^(1/2)+45*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^3+282*B*(c*(1+sin(f*x+e)))^(5/2)*c^(1/2)+288*B*(c*(1+sin(f*x+e)))^(1/2)*c^(5/2)*sin(f*x+e)^2+585*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^3-160*A*(c*(1+sin(f*x+e)))^(3/2)*c^(3/2)-15*A*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^3-928*B*(c*(1+sin(f*x+e)))^(3/2)*c^(3/2)-288*B*c^(5/2)*(c*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)-195*B*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^3+120*A*(c*(1+sin(f*x+e)))^(1/2)*c^(5/2)+888*B*(c*(1+sin(f*x+e)))^(1/2)*c^(5/2))*(c*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
106,1,432,190,1.882000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x)","\frac{a^{3} \left(60 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{4} \left(A -15 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-120 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{4} \left(A -15 B \right) \sin \left(f x +e \right)+15 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{4} \left(A -15 B \right) \left(\cos^{4}\left(f x +e \right)\right)-120 \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, c^{4} \left(A -15 B \right) \left(\cos^{2}\left(f x +e \right)\right)-30 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} \sqrt{c}-292 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{3}{2}}+440 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{5}{2}}-240 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{7}{2}}-1086 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} \sqrt{c}+4380 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{3}{2}}-6600 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{5}{2}}+3600 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{7}{2}}+120 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4}-1800 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{768 c^{\frac{17}{2}} \left(\sin \left(f x +e \right)-1\right)^{3} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/768*a^3*(60*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^4*(A-15*B)*sin(f*x+e)*cos(f*x+e)^2-120*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^4*(A-15*B)*sin(f*x+e)+15*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^4*(A-15*B)*cos(f*x+e)^4-120*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^4*(A-15*B)*cos(f*x+e)^2-30*A*(c+c*sin(f*x+e))^(7/2)*c^(1/2)-292*A*(c+c*sin(f*x+e))^(5/2)*c^(3/2)+440*A*(c+c*sin(f*x+e))^(3/2)*c^(5/2)-240*A*(c+c*sin(f*x+e))^(1/2)*c^(7/2)-1086*B*(c+c*sin(f*x+e))^(7/2)*c^(1/2)+4380*B*(c+c*sin(f*x+e))^(5/2)*c^(3/2)-6600*B*(c+c*sin(f*x+e))^(3/2)*c^(5/2)+3600*B*(c+c*sin(f*x+e))^(1/2)*c^(7/2)+120*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4-1800*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^4)*(c*(1+sin(f*x+e)))^(1/2)/c^(17/2)/(sin(f*x+e)-1)^3/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
107,1,526,235,2.047000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x)","\frac{a^{3} \left(15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6} \left(3 A -17 B \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-180 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6} \left(3 A -17 B \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+240 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6} \left(3 A -17 B \right) \sin \left(f x +e \right)-75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6} \left(3 A -17 B \right) \left(\cos^{4}\left(f x +e \right)\right)+300 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6} \left(3 A -17 B \right) \left(\cos^{2}\left(f x +e \right)\right)-90 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{9}{2}} c^{\frac{3}{2}}+840 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} c^{\frac{5}{2}}+3072 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{7}{2}}-3360 A \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{9}{2}}+1440 A \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{11}{2}}+510 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{9}{2}} c^{\frac{3}{2}}+5480 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{7}{2}} c^{\frac{5}{2}}-17408 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{\frac{7}{2}}+19040 B \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c^{\frac{9}{2}}-8160 B \sqrt{c +c \sin \left(f x +e \right)}\, c^{\frac{11}{2}}-720 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6}+4080 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{15360 c^{\frac{23}{2}} \left(\sin \left(f x +e \right)-1\right)^{4} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/15360*a^3*(15*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6*(3*A-17*B)*sin(f*x+e)*cos(f*x+e)^4-180*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6*(3*A-17*B)*cos(f*x+e)^2*sin(f*x+e)+240*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6*(3*A-17*B)*sin(f*x+e)-75*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6*(3*A-17*B)*cos(f*x+e)^4+300*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6*(3*A-17*B)*cos(f*x+e)^2-90*A*(c+c*sin(f*x+e))^(9/2)*c^(3/2)+840*A*(c+c*sin(f*x+e))^(7/2)*c^(5/2)+3072*A*(c+c*sin(f*x+e))^(5/2)*c^(7/2)-3360*A*(c+c*sin(f*x+e))^(3/2)*c^(9/2)+1440*A*(c+c*sin(f*x+e))^(1/2)*c^(11/2)+510*B*(c+c*sin(f*x+e))^(9/2)*c^(3/2)+5480*B*(c+c*sin(f*x+e))^(7/2)*c^(5/2)-17408*B*(c+c*sin(f*x+e))^(5/2)*c^(7/2)+19040*B*(c+c*sin(f*x+e))^(3/2)*c^(9/2)-8160*B*(c+c*sin(f*x+e))^(1/2)*c^(11/2)-720*A*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6+4080*B*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^6)*(c*(1+sin(f*x+e)))^(1/2)/c^(23/2)/(sin(f*x+e)-1)^4/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
108,1,111,182,1.168000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e)),x)","\frac{2 c^{4} \left(\sin \left(f x +e \right)-1\right) \left(\left(-7 A +29 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(308 A -436 B \right) \sin \left(f x +e \right)+5 B \left(\cos^{4}\left(f x +e \right)\right)+\left(49 A -103 B \right) \left(\cos^{2}\left(f x +e \right)\right)+588 A -716 B \right)}{35 a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/35*c^4/a*(sin(f*x+e)-1)*((-7*A+29*B)*sin(f*x+e)*cos(f*x+e)^2+(308*A-436*B)*sin(f*x+e)+5*B*cos(f*x+e)^4+(49*A-103*B)*cos(f*x+e)^2+588*A-716*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
109,1,95,145,1.100000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x)","-\frac{2 c^{3} \left(\sin \left(f x +e \right)-1\right) \left(-3 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-50 A +82 B \right) \sin \left(f x +e \right)+\left(-5 A +16 B \right) \left(\cos^{2}\left(f x +e \right)\right)-110 A +142 B \right)}{15 a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*c^3/a*(sin(f*x+e)-1)*(-3*B*cos(f*x+e)^2*sin(f*x+e)+(-50*A+82*B)*sin(f*x+e)+(-5*A+16*B)*cos(f*x+e)^2-110*A+142*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
110,1,73,108,1.120000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x)","\frac{2 c^{2} \left(\sin \left(f x +e \right)-1\right) \left(\sin \left(f x +e \right) \left(3 A -7 B \right)-B \left(\cos^{2}\left(f x +e \right)\right)+9 A -13 B \right)}{3 a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/3*c^2/a*(sin(f*x+e)-1)*(sin(f*x+e)*(3*A-7*B)-B*cos(f*x+e)^2+9*A-13*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
111,1,53,69,1.019000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x)","\frac{2 c \left(\sin \left(f x +e \right)-1\right) \left(-B \sin \left(f x +e \right)+A -2 B \right)}{a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2*c/a*(sin(f*x+e)-1)*(-B*sin(f*x+e)+A-2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
112,1,130,81,1.294000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(\sin \left(f x +e \right)-1\right) \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, A +\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, B -2 \sqrt{c}\, A +2 \sqrt{c}\, B \right)}{2 a \sqrt{c}\, \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/2/a*(sin(f*x+e)-1)*(2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(1/2)*A+2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(1/2)*B-2*c^(1/2)*A+2*c^(1/2)*B)/c^(1/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
113,1,225,119,1.280000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\sin \left(f x +e \right) \left(3 A \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -B \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -6 A \,c^{\frac{3}{2}}+2 B \,c^{\frac{3}{2}}\right)-3 A \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +B \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +2 A \,c^{\frac{3}{2}}-6 B \,c^{\frac{3}{2}}}{8 c^{\frac{5}{2}} a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/8/c^(5/2)/a*(sin(f*x+e)*(3*A*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c-B*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c-6*A*c^(3/2)+2*B*c^(3/2))-3*A*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c+B*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c+2*A*c^(3/2)-6*B*c^(3/2))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
114,1,350,157,1.783000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\sin \left(f x +e \right) \left(-30 A \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+40 A \,c^{\frac{5}{2}}+18 B \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-24 B \,c^{\frac{5}{2}}\right)+\left(-15 A \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+30 A \,c^{\frac{5}{2}}+9 B \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-18 B \,c^{\frac{5}{2}}\right) \left(\cos^{2}\left(f x +e \right)\right)+30 A \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-24 A \,c^{\frac{5}{2}}-18 B \sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+40 B \,c^{\frac{5}{2}}}{64 c^{\frac{9}{2}} a \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/64/c^(9/2)/a*(sin(f*x+e)*(-30*A*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+40*A*c^(5/2)+18*B*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-24*B*c^(5/2))+(-15*A*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+30*A*c^(5/2)+9*B*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-18*B*c^(5/2))*cos(f*x+e)^2+30*A*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2-24*A*c^(5/2)-18*B*(c+c*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*c^2+40*B*c^(5/2))/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
115,1,143,218,1.360000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^2,x)","-\frac{2 c^{5} \left(\sin \left(f x +e \right)-1\right) \left(15 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(196 A -544 B \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(7448 A -13592 B \right) \sin \left(f x +e \right)+\left(21 A -114 B \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-1848 A +3732 B \right) \left(\cos^{2}\left(f x +e \right)\right)+6888 A -13032 B \right)}{105 a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/105*c^5/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(15*B*sin(f*x+e)*cos(f*x+e)^4+(196*A-544*B)*cos(f*x+e)^2*sin(f*x+e)+(7448*A-13592*B)*sin(f*x+e)+(21*A-114*B)*cos(f*x+e)^4+(-1848*A+3732*B)*cos(f*x+e)^2+6888*A-13032*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
116,1,121,181,1.507000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^2,x)","\frac{2 c^{4} \left(\sin \left(f x +e \right)-1\right) \left(\left(-5 A +23 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(-340 A +724 B \right) \sin \left(f x +e \right)+3 B \left(\cos^{4}\left(f x +e \right)\right)+\left(75 A -189 B \right) \left(\cos^{2}\left(f x +e \right)\right)-300 A +684 B \right)}{15 a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*c^4/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*((-5*A+23*B)*sin(f*x+e)*cos(f*x+e)^2+(-340*A+724*B)*sin(f*x+e)+3*B*cos(f*x+e)^4+(75*A-189*B)*cos(f*x+e)^2-300*A+684*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
117,1,105,138,1.267000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x)","-\frac{2 c^{3} \left(\sin \left(f x +e \right)-1\right) \left(-B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(18 A -50 B \right) \sin \left(f x +e \right)+\left(-3 A +12 B \right) \left(\cos^{2}\left(f x +e \right)\right)+14 A -46 B \right)}{3 a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*c^3/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(-B*cos(f*x+e)^2*sin(f*x+e)+(18*A-50*B)*sin(f*x+e)+(-3*A+12*B)*cos(f*x+e)^2+14*A-46*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
118,1,81,103,1.416000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x)","-\frac{2 c^{2} \left(\sin \left(f x +e \right)-1\right) \left(\sin \left(f x +e \right) \left(3 A -15 B \right)+3 B \left(\cos^{2}\left(f x +e \right)\right)+A -13 B \right)}{3 a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*c^2/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(sin(f*x+e)*(3*A-15*B)+3*B*cos(f*x+e)^2+A-13*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
119,1,63,70,1.308000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x)","\frac{2 c \left(\sin \left(f x +e \right)-1\right) \left(3 B \sin \left(f x +e \right)+A +2 B \right)}{3 a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/3*c/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(3*B*sin(f*x+e)+A+2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
120,1,168,116,1.780000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(\sin \left(f x +e \right)-1\right) \left(-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c A -3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c B +10 A \,c^{\frac{5}{2}}+6 A \,c^{\frac{5}{2}} \sin \left(f x +e \right)+2 B \,c^{\frac{5}{2}}+6 B \,c^{\frac{5}{2}} \sin \left(f x +e \right)\right)}{12 a^{2} c^{\frac{5}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/12/a^2*(sin(f*x+e)-1)/c^(5/2)/(1+sin(f*x+e))*(-3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(3/2)*c*A-3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(3/2)*c*B+10*A*c^(5/2)+6*A*c^(5/2)*sin(f*x+e)+2*B*c^(5/2)+6*B*c^(5/2)*sin(f*x+e))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
121,1,258,152,1.555000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\sin \left(f x +e \right) \left(15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c A +3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c B -20 A \,c^{\frac{5}{2}}-4 B \,c^{\frac{5}{2}}\right)+\left(30 A \,c^{\frac{5}{2}}+6 B \,c^{\frac{5}{2}}\right) \left(\cos^{2}\left(f x +e \right)\right)-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c A -3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{3}{2}} c B -4 A \,c^{\frac{5}{2}}-20 B \,c^{\frac{5}{2}}}{48 c^{\frac{7}{2}} a^{2} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/48/c^(7/2)/a^2*(sin(f*x+e)*(15*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(3/2)*c*A+3*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(3/2)*c*B-20*A*c^(5/2)-4*B*c^(5/2))+(30*A*c^(5/2)+6*B*c^(5/2))*cos(f*x+e)^2-15*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(3/2)*c*A-3*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(3/2)*c*B-4*A*c^(5/2)-20*B*c^(5/2))/(1+sin(f*x+e))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
122,1,426,198,1.735000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x)","-\frac{-86 A \,c^{\frac{7}{2}}+122 B \,c^{\frac{7}{2}}+70 A \,c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)-10 B \,c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)+322 A \,c^{\frac{7}{2}} \sin \left(f x +e \right)-46 B \,c^{\frac{7}{2}} \sin \left(f x +e \right)-210 A \,c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)+30 B \,c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)+105 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{2}-15 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{2}\left(f x +e \right)\right) c^{2}-210 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{2}+30 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c^{2}+105 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-15 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}}{384 c^{\frac{11}{2}} a^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/384/c^(11/2)/a^2*(-86*A*c^(7/2)+122*B*c^(7/2)+70*A*c^(7/2)*sin(f*x+e)^2-10*B*c^(7/2)*sin(f*x+e)^2+322*A*c^(7/2)*sin(f*x+e)-46*B*c^(7/2)*sin(f*x+e)-210*A*c^(7/2)*sin(f*x+e)^3+30*B*c^(7/2)*sin(f*x+e)^3+105*A*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^2-15*B*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^2*c^2-210*A*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^2+30*B*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c^2+105*A*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2-15*B*(c*(1+sin(f*x+e)))^(3/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2)/(1+sin(f*x+e))/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","B"
123,1,143,218,1.471000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^3,x)","-\frac{2 c^{5} \left(\sin \left(f x +e \right)-1\right) \left(3 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(100 A -336 B \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-1000 A +3048 B \right) \sin \left(f x +e \right)+\left(5 A -30 B \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(680 A -1980 B \right) \left(\cos^{2}\left(f x +e \right)\right)-1048 A +3096 B \right)}{15 a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*c^5/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*(3*B*sin(f*x+e)*cos(f*x+e)^4+(100*A-336*B)*cos(f*x+e)^2*sin(f*x+e)+(-1000*A+3048*B)*sin(f*x+e)+(5*A-30*B)*cos(f*x+e)^4+(680*A-1980*B)*cos(f*x+e)^2-1048*A+3096*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
124,1,121,189,1.600000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^3,x)","\frac{2 c^{4} \left(\sin \left(f x +e \right)-1\right) \left(\left(-15 A +85 B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(180 A -820 B \right) \sin \left(f x +e \right)+5 B \left(\cos^{4}\left(f x +e \right)\right)+\left(-135 A +545 B \right) \left(\cos^{2}\left(f x +e \right)\right)+204 A -844 B \right)}{15 a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*c^4/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*((-15*A+85*B)*sin(f*x+e)*cos(f*x+e)^2+(180*A-820*B)*sin(f*x+e)+5*B*cos(f*x+e)^4+(-135*A+545*B)*cos(f*x+e)^2+204*A-844*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
125,1,105,144,1.602000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x)","\frac{2 c^{3} \left(\sin \left(f x +e \right)-1\right) \left(15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(10 A -170 B \right) \sin \left(f x +e \right)+\left(-15 A +120 B \right) \left(\cos^{2}\left(f x +e \right)\right)+22 A -182 B \right)}{15 a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*c^3/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*(15*B*cos(f*x+e)^2*sin(f*x+e)+(10*A-170*B)*sin(f*x+e)+(-15*A+120*B)*cos(f*x+e)^2+22*A-182*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
126,1,83,109,1.464000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x)","-\frac{2 c^{2} \left(\sin \left(f x +e \right)-1\right) \left(\sin \left(f x +e \right) \left(5 A +15 B \right)-15 B \left(\cos^{2}\left(f x +e \right)\right)-A +21 B \right)}{15 a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*c^2/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*(sin(f*x+e)*(5*A+15*B)-15*B*cos(f*x+e)^2-A+21*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
127,1,65,77,1.407000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x)","\frac{2 c \left(\sin \left(f x +e \right)-1\right) \left(5 B \sin \left(f x +e \right)+3 A +2 B \right)}{15 a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/15*c/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*(5*B*sin(f*x+e)+3*A+2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
128,1,200,151,1.941000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(\sin \left(f x +e \right)-1\right) \left(74 c^{\frac{9}{2}} A +80 A \,c^{\frac{9}{2}} \sin \left(f x +e \right)+30 A \,c^{\frac{9}{2}} \left(\sin^{2}\left(f x +e \right)\right)-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{2} A +26 c^{\frac{9}{2}} B +80 B \,c^{\frac{9}{2}} \sin \left(f x +e \right)+30 B \,c^{\frac{9}{2}} \left(\sin^{2}\left(f x +e \right)\right)-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{2} B \right)}{120 a^{3} c^{\frac{9}{2}} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"1/120/a^3*(sin(f*x+e)-1)/c^(9/2)/(1+sin(f*x+e))^2*(74*c^(9/2)*A+80*A*c^(9/2)*sin(f*x+e)+30*A*c^(9/2)*sin(f*x+e)^2-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(5/2)*c^2*A+26*c^(9/2)*B+80*B*c^(9/2)*sin(f*x+e)+30*B*c^(9/2)*sin(f*x+e)^2-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*(c*(1+sin(f*x+e)))^(5/2)*c^2*B)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
129,1,308,197,1.689000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x)","-\frac{278 A \,c^{\frac{7}{2}}-18 B \,c^{\frac{7}{2}}-350 A \,c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)-150 B \,c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)+42 A \,c^{\frac{7}{2}} \sin \left(f x +e \right)+18 B \,c^{\frac{7}{2}} \sin \left(f x +e \right)-210 A \,c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)-90 B \,c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)+45 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c -105 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -45 B \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +105 A \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sin \left(f x +e \right) c}{480 c^{\frac{9}{2}} a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/480/c^(9/2)/a^3*(278*A*c^(7/2)-18*B*c^(7/2)-350*A*c^(7/2)*sin(f*x+e)^2-150*B*c^(7/2)*sin(f*x+e)^2+42*A*c^(7/2)*sin(f*x+e)+18*B*c^(7/2)*sin(f*x+e)-210*A*c^(7/2)*sin(f*x+e)^3-90*B*c^(7/2)*sin(f*x+e)^3+45*B*(c*(1+sin(f*x+e)))^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c-105*A*(c*(1+sin(f*x+e)))^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c-45*B*(c*(1+sin(f*x+e)))^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c+105*A*(c*(1+sin(f*x+e)))^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)*c)/(1+sin(f*x+e))^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
130,1,410,227,2.058000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(1260 c^{\frac{9}{2}} A +140 c^{\frac{9}{2}} B \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(-1890 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} A +864 c^{\frac{9}{2}} A -210 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} B +96 c^{\frac{9}{2}} B \right) \sin \left(f x +e \right)+\left(-1890 c^{\frac{9}{2}} A -210 c^{\frac{9}{2}} B \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-945 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} A +252 c^{\frac{9}{2}} A -105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} B +28 c^{\frac{9}{2}} B \right) \left(\cos^{2}\left(f x +e \right)\right)+1890 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} A +96 c^{\frac{9}{2}} A +210 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c +c \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(c +c \sin \left(f x +e \right)\right)^{\frac{5}{2}} c^{2} B +864 c^{\frac{9}{2}} B}{3840 c^{\frac{13}{2}} a^{3} \left(1+\sin \left(f x +e \right)\right)^{2} \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-1/3840/c^(13/2)/a^3*((1260*c^(9/2)*A+140*c^(9/2)*B)*sin(f*x+e)*cos(f*x+e)^2+(-1890*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*A+864*c^(9/2)*A-210*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*B+96*c^(9/2)*B)*sin(f*x+e)+(-1890*c^(9/2)*A-210*c^(9/2)*B)*cos(f*x+e)^4+(-945*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*A+252*c^(9/2)*A-105*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*B+28*c^(9/2)*B)*cos(f*x+e)^2+1890*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*A+96*c^(9/2)*A+210*2^(1/2)*arctanh(1/2*(c+c*sin(f*x+e))^(1/2)*2^(1/2)/c^(1/2))*(c+c*sin(f*x+e))^(5/2)*c^2*B+864*c^(9/2)*B)/(1+sin(f*x+e))^2/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
131,1,174,82,0.873000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-4 B \left(\cos^{4}\left(f x +e \right)\right)+5 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-20 A \left(\cos^{2}\left(f x +e \right)\right)+28 B \left(\cos^{2}\left(f x +e \right)\right)-35 A \sin \left(f x +e \right)+25 B \sin \left(f x +e \right)+40 A -24 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{20 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+4\right) \cos \left(f x +e \right)}"," ",0,"1/20/f*(-4*B*cos(f*x+e)^4+5*A*cos(f*x+e)^2*sin(f*x+e)-15*B*cos(f*x+e)^2*sin(f*x+e)-20*A*cos(f*x+e)^2+28*B*cos(f*x+e)^2-35*A*sin(f*x+e)+25*B*sin(f*x+e)+40*A-24*B)*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/(cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)+4)/cos(f*x+e)","B"
132,1,129,82,0.853000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(3 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A \left(\cos^{2}\left(f x +e \right)\right)-8 B \left(\cos^{2}\left(f x +e \right)\right)+12 A \sin \left(f x +e \right)-9 B \sin \left(f x +e \right)-16 A +8 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{12 f \left(2 \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2\right) \cos \left(f x +e \right)}"," ",0,"1/12/f*(3*B*cos(f*x+e)^2*sin(f*x+e)+4*A*cos(f*x+e)^2-8*B*cos(f*x+e)^2+12*A*sin(f*x+e)-9*B*sin(f*x+e)-16*A+8*B)*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/(2*sin(f*x+e)+cos(f*x+e)^2-2)/cos(f*x+e)","A"
133,1,91,82,0.825000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-2 B \left(\cos^{2}\left(f x +e \right)\right)+3 A \sin \left(f x +e \right)-3 B \sin \left(f x +e \right)-6 A +2 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{6 f \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right)}"," ",0,"1/6/f*(-2*B*cos(f*x+e)^2+3*A*sin(f*x+e)-3*B*sin(f*x+e)-6*A+2*B)*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/cos(f*x+e)","A"
134,1,57,82,0.803000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(B \sin \left(f x +e \right)+2 A \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{2 f \cos \left(f x +e \right)}"," ",0,"1/2/f*(B*sin(f*x+e)+2*A)*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)","A"
135,1,395,92,0.728000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(2 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+B \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \left(\cos^{2}\left(f x +e \right)\right)+2 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \sin \left(f x +e \right)-2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+B \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{f \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/f*(2*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+B*sin(f*x+e)*cos(f*x+e)+2*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-B*cos(f*x+e)^2+2*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*ln(2/(cos(f*x+e)+1))-B*sin(f*x+e)-2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*ln(2/(cos(f*x+e)+1))+B)*(a*(1+sin(f*x+e)))^(1/2)/(1-cos(f*x+e)+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(1/2)","B"
136,1,403,91,0.689000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+A \left(\cos^{2}\left(f x +e \right)\right)-A \sin \left(f x +e \right) \cos \left(f x +e \right)+B \left(\cos^{2}\left(f x +e \right)\right)-B \sin \left(f x +e \right) \cos \left(f x +e \right)+B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \sin \left(f x +e \right)+B \sin \left(f x +e \right)-2 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A -B \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{f \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/f*(B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+A*cos(f*x+e)^2-A*sin(f*x+e)*cos(f*x+e)+B*cos(f*x+e)^2-B*sin(f*x+e)*cos(f*x+e)+B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-4*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*sin(f*x+e)+B*sin(f*x+e)-2*B*ln(2/(cos(f*x+e)+1))+4*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A-B)*(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e)-sin(f*x+e))/(-c*(sin(f*x+e)-1))^(3/2)","B"
137,1,137,82,0.710000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(A \left(\cos^{2}\left(f x +e \right)\right)-A \sin \left(f x +e \right) \cos \left(f x +e \right)-B \left(\cos^{2}\left(f x +e \right)\right)+B \sin \left(f x +e \right) \cos \left(f x +e \right)+2 A \cos \left(f x +e \right)+3 A \sin \left(f x +e \right)-B \sin \left(f x +e \right)-3 A +B \right) \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{2 f \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/2/f*(A*cos(f*x+e)^2-A*sin(f*x+e)*cos(f*x+e)-B*cos(f*x+e)^2+B*sin(f*x+e)*cos(f*x+e)+2*A*cos(f*x+e)+3*A*sin(f*x+e)-B*sin(f*x+e)-3*A+B)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e)-sin(f*x+e))/(-c*(sin(f*x+e)-1))^(5/2)","A"
138,1,205,82,0.723000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 A \left(\cos^{3}\left(f x +e \right)\right)-B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \left(\cos^{3}\left(f x +e \right)\right)+6 A \sin \left(f x +e \right) \cos \left(f x +e \right)-8 A \left(\cos^{2}\left(f x +e \right)\right)-3 B \sin \left(f x +e \right) \cos \left(f x +e \right)+4 B \left(\cos^{2}\left(f x +e \right)\right)-14 A \sin \left(f x +e \right)-8 A \cos \left(f x +e \right)+4 B \sin \left(f x +e \right)+B \cos \left(f x +e \right)+14 A -4 B \right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/6/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(2*A*cos(f*x+e)^2*sin(f*x+e)+2*A*cos(f*x+e)^3-B*cos(f*x+e)^2*sin(f*x+e)-B*cos(f*x+e)^3+6*A*sin(f*x+e)*cos(f*x+e)-8*A*cos(f*x+e)^2-3*B*sin(f*x+e)*cos(f*x+e)+4*B*cos(f*x+e)^2-14*A*sin(f*x+e)-8*A*cos(f*x+e)+4*B*sin(f*x+e)+B*cos(f*x+e)+14*A-4*B)/(-c*(sin(f*x+e)-1))^(7/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
139,1,185,128,0.842000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(5 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 A \left(\cos^{4}\left(f x +e \right)\right)-12 B \left(\cos^{4}\left(f x +e \right)\right)+15 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-10 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 A \left(\cos^{2}\left(f x +e \right)\right)+4 B \left(\cos^{2}\left(f x +e \right)\right)+15 A \sin \left(f x +e \right)-10 B \sin \left(f x +e \right)-24 A +8 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{30 f \left(2 \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2\right) \cos \left(f x +e \right)^{3}}"," ",0,"1/30/f*(5*B*sin(f*x+e)*cos(f*x+e)^4+6*A*cos(f*x+e)^4-12*B*cos(f*x+e)^4+15*A*cos(f*x+e)^2*sin(f*x+e)-10*B*cos(f*x+e)^2*sin(f*x+e)-12*A*cos(f*x+e)^2+4*B*cos(f*x+e)^2+15*A*sin(f*x+e)-10*B*sin(f*x+e)-24*A+8*B)*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/(2*sin(f*x+e)+cos(f*x+e)^2-2)/cos(f*x+e)^3","A"
140,1,147,128,0.790000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(-12 B \left(\cos^{4}\left(f x +e \right)\right)+15 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-20 A \left(\cos^{2}\left(f x +e \right)\right)+4 B \left(\cos^{2}\left(f x +e \right)\right)+15 A \sin \left(f x +e \right)-15 B \sin \left(f x +e \right)-40 A +8 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{60 f \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right)^{3}}"," ",0,"1/60/f*(-12*B*cos(f*x+e)^4+15*A*cos(f*x+e)^2*sin(f*x+e)-15*B*cos(f*x+e)^2*sin(f*x+e)-20*A*cos(f*x+e)^2+4*B*cos(f*x+e)^2+15*A*sin(f*x+e)-15*B*sin(f*x+e)-40*A+8*B)*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/(sin(f*x+e)-1)/cos(f*x+e)^3","A"
141,1,86,116,0.748000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(3 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A \left(\cos^{2}\left(f x +e \right)\right)+3 B \sin \left(f x +e \right)+8 A \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{12 f \cos \left(f x +e \right)^{3}}"," ",0,"1/12/f*(3*B*cos(f*x+e)^2*sin(f*x+e)+4*A*cos(f*x+e)^2+3*B*sin(f*x+e)+8*A)*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/cos(f*x+e)^3","A"
142,1,91,84,0.798000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(-2 B \left(\cos^{2}\left(f x +e \right)\right)+3 A \sin \left(f x +e \right)+3 B \sin \left(f x +e \right)+6 A +2 B \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{6 f \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right)}"," ",0,"1/6/f*(-2*B*cos(f*x+e)^2+3*A*sin(f*x+e)+3*B*sin(f*x+e)+6*A+2*B)*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/(1+sin(f*x+e))/cos(f*x+e)","A"
143,1,494,131,0.699000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(B \left(\cos^{3}\left(f x +e \right)\right)+B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 A \left(\cos^{2}\left(f x +e \right)\right)-2 A \sin \left(f x +e \right) \cos \left(f x +e \right)-8 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+3 B \left(\cos^{2}\left(f x +e \right)\right)-4 B \sin \left(f x +e \right) \cos \left(f x +e \right)-8 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \sin \left(f x +e \right)+8 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \cos \left(f x +e \right)+3 B \sin \left(f x +e \right)+8 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A -3 B \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{2 f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/2/f*(B*cos(f*x+e)^3+B*cos(f*x+e)^2*sin(f*x+e)+2*A*cos(f*x+e)^2-2*A*sin(f*x+e)*cos(f*x+e)-8*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-8*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+3*B*cos(f*x+e)^2-4*B*sin(f*x+e)*cos(f*x+e)-8*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-8*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*A*sin(f*x+e)+8*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*A*ln(2/(cos(f*x+e)+1))-B*cos(f*x+e)+3*B*sin(f*x+e)+8*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*B*ln(2/(cos(f*x+e)+1))-2*A-3*B)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
144,1,748,142,0.672000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(2 A \sin \left(f x +e \right)-2 A \sin \left(f x +e \right) \cos \left(f x +e \right)-B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A -4 B +2 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \sin \left(f x +e \right) \cos \left(f x +e \right)-12 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 B \left(\cos^{2}\left(f x +e \right)\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+6 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-6 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 B \sin \left(f x +e \right)+B \cos \left(f x +e \right)-B \left(\cos^{3}\left(f x +e \right)\right)+4 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+12 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/f*(-6*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*sin(f*x+e)-2*A*sin(f*x+e)*cos(f*x+e)-4*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-B*cos(f*x+e)^2*sin(f*x+e)-2*A-4*B+A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-3*B*sin(f*x+e)*cos(f*x+e)-12*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+6*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-6*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+6*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+4*B*cos(f*x+e)^2-B*cos(f*x+e)^3+4*B*sin(f*x+e)+B*cos(f*x+e)+2*A*cos(f*x+e)^2+4*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*ln(2/(cos(f*x+e)+1))+12*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
145,1,594,135,0.662000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(A \sin \left(f x +e \right)-A \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-A +3 B +B \sin \left(f x +e \right) \cos \left(f x +e \right)+8 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \left(\cos^{2}\left(f x +e \right)\right)-2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-4 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)+6 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \sin \left(f x +e \right)-2 B \cos \left(f x +e \right)+2 B \left(\cos^{3}\left(f x +e \right)\right)-8 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(6*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*sin(f*x+e)-A*sin(f*x+e)*cos(f*x+e)-3*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+2*B*cos(f*x+e)^2*sin(f*x+e)-A+3*B-2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3+B*sin(f*x+e)*cos(f*x+e)+8*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+4*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+2*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-4*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-3*B*cos(f*x+e)^2+2*B*cos(f*x+e)^3-3*B*sin(f*x+e)-2*B*cos(f*x+e)+A*cos(f*x+e)^2-8*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(5/2)","B"
146,1,223,84,0.659000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(A \left(\cos^{3}\left(f x +e \right)\right)+A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+B \left(\cos^{3}\left(f x +e \right)\right)+B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 A \left(\cos^{2}\left(f x +e \right)\right)+3 A \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \left(\cos^{2}\left(f x +e \right)\right)-3 B \sin \left(f x +e \right) \cos \left(f x +e \right)-7 A \cos \left(f x +e \right)-10 A \sin \left(f x +e \right)-B \cos \left(f x +e \right)+2 B \sin \left(f x +e \right)+10 A -2 B \right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}"," ",0,"1/6/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(A*cos(f*x+e)^3+A*cos(f*x+e)^2*sin(f*x+e)+B*cos(f*x+e)^3+B*cos(f*x+e)^2*sin(f*x+e)-4*A*cos(f*x+e)^2+3*A*sin(f*x+e)*cos(f*x+e)+2*B*cos(f*x+e)^2-3*B*sin(f*x+e)*cos(f*x+e)-7*A*cos(f*x+e)-10*A*sin(f*x+e)-B*cos(f*x+e)+2*B*sin(f*x+e)+10*A-2*B)/(-c*(sin(f*x+e)-1))^(7/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)","B"
147,1,217,128,0.678000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(A \left(\cos^{4}\left(f x +e \right)\right)-A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A \left(\cos^{3}\left(f x +e \right)\right)+5 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 A \left(\cos^{2}\left(f x +e \right)\right)+7 A \sin \left(f x +e \right) \cos \left(f x +e \right)+3 B \left(\cos^{2}\left(f x +e \right)\right)-3 B \sin \left(f x +e \right) \cos \left(f x +e \right)-10 A \cos \left(f x +e \right)-17 A \sin \left(f x +e \right)+3 B \sin \left(f x +e \right)+17 A -3 B \right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}"," ",0,"1/6/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(A*cos(f*x+e)^4-A*cos(f*x+e)^3*sin(f*x+e)+4*A*cos(f*x+e)^3+5*A*cos(f*x+e)^2*sin(f*x+e)-12*A*cos(f*x+e)^2+7*A*sin(f*x+e)*cos(f*x+e)+3*B*cos(f*x+e)^2-3*B*sin(f*x+e)*cos(f*x+e)-10*A*cos(f*x+e)-17*A*sin(f*x+e)+3*B*sin(f*x+e)+17*A-3*B)/(-c*(sin(f*x+e)-1))^(9/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)","A"
148,1,339,136,0.689000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x)","-\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(9 A \left(\cos^{5}\left(f x +e \right)\right)+9 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \left(\cos^{5}\left(f x +e \right)\right)-B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-54 A \left(\cos^{4}\left(f x +e \right)\right)+45 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 B \left(\cos^{4}\left(f x +e \right)\right)-5 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-108 A \left(\cos^{3}\left(f x +e \right)\right)-153 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 B \left(\cos^{3}\left(f x +e \right)\right)+17 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+288 A \left(\cos^{2}\left(f x +e \right)\right)-135 A \sin \left(f x +e \right) \cos \left(f x +e \right)-52 B \left(\cos^{2}\left(f x +e \right)\right)+35 B \sin \left(f x +e \right) \cos \left(f x +e \right)+159 A \cos \left(f x +e \right)+294 A \sin \left(f x +e \right)-11 B \cos \left(f x +e \right)-46 B \sin \left(f x +e \right)-294 A +46 B \right)}{60 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}"," ",0,"-1/60/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(9*A*cos(f*x+e)^5+9*A*cos(f*x+e)^4*sin(f*x+e)-B*cos(f*x+e)^5-B*sin(f*x+e)*cos(f*x+e)^4-54*A*cos(f*x+e)^4+45*A*cos(f*x+e)^3*sin(f*x+e)+6*B*cos(f*x+e)^4-5*B*cos(f*x+e)^3*sin(f*x+e)-108*A*cos(f*x+e)^3-153*A*cos(f*x+e)^2*sin(f*x+e)+12*B*cos(f*x+e)^3+17*B*cos(f*x+e)^2*sin(f*x+e)+288*A*cos(f*x+e)^2-135*A*sin(f*x+e)*cos(f*x+e)-52*B*cos(f*x+e)^2+35*B*sin(f*x+e)*cos(f*x+e)+159*A*cos(f*x+e)+294*A*sin(f*x+e)-11*B*cos(f*x+e)-46*B*sin(f*x+e)-294*A+46*B)/(-c*(sin(f*x+e)-1))^(11/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)","B"
149,1,203,174,0.901000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-30 B \left(\cos^{6}\left(f x +e \right)\right)+35 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-35 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-42 A \left(\cos^{4}\left(f x +e \right)\right)+6 B \left(\cos^{4}\left(f x +e \right)\right)+35 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-35 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-56 A \left(\cos^{2}\left(f x +e \right)\right)+8 B \left(\cos^{2}\left(f x +e \right)\right)+35 A \sin \left(f x +e \right)-35 B \sin \left(f x +e \right)-112 A +16 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{210 f \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right)^{5}}"," ",0,"1/210/f*(-30*B*cos(f*x+e)^6+35*A*cos(f*x+e)^4*sin(f*x+e)-35*B*sin(f*x+e)*cos(f*x+e)^4-42*A*cos(f*x+e)^4+6*B*cos(f*x+e)^4+35*A*cos(f*x+e)^2*sin(f*x+e)-35*B*cos(f*x+e)^2*sin(f*x+e)-56*A*cos(f*x+e)^2+8*B*cos(f*x+e)^2+35*A*sin(f*x+e)-35*B*sin(f*x+e)-112*A+16*B)*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/(sin(f*x+e)-1)/cos(f*x+e)^5","A"
150,1,114,156,0.769000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(5 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 A \left(\cos^{4}\left(f x +e \right)\right)+5 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 A \left(\cos^{2}\left(f x +e \right)\right)+5 B \sin \left(f x +e \right)+16 A \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{30 f \cos \left(f x +e \right)^{5}}"," ",0,"1/30/f*(5*B*sin(f*x+e)*cos(f*x+e)^4+6*A*cos(f*x+e)^4+5*B*cos(f*x+e)^2*sin(f*x+e)+8*A*cos(f*x+e)^2+5*B*sin(f*x+e)+16*A)*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/cos(f*x+e)^5","A"
151,1,147,124,0.794000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(-12 B \left(\cos^{4}\left(f x +e \right)\right)+15 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+20 A \left(\cos^{2}\left(f x +e \right)\right)+4 B \left(\cos^{2}\left(f x +e \right)\right)+15 A \sin \left(f x +e \right)+15 B \sin \left(f x +e \right)+40 A +8 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{60 f \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right)^{3}}"," ",0,"1/60/f*(-12*B*cos(f*x+e)^4+15*A*cos(f*x+e)^2*sin(f*x+e)+15*B*cos(f*x+e)^2*sin(f*x+e)+20*A*cos(f*x+e)^2+4*B*cos(f*x+e)^2+15*A*sin(f*x+e)+15*B*sin(f*x+e)+40*A+8*B)*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/(1+sin(f*x+e))/cos(f*x+e)^3","A"
152,1,129,84,0.804000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(3 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A \left(\cos^{2}\left(f x +e \right)\right)+8 B \left(\cos^{2}\left(f x +e \right)\right)-12 A \sin \left(f x +e \right)-9 B \sin \left(f x +e \right)-16 A -8 B \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{12 f \left(\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \cos \left(f x +e \right)}"," ",0,"1/12/f*(3*B*cos(f*x+e)^2*sin(f*x+e)+4*A*cos(f*x+e)^2+8*B*cos(f*x+e)^2-12*A*sin(f*x+e)-9*B*sin(f*x+e)-16*A-8*B)*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^2-2*sin(f*x+e)-2)/cos(f*x+e)","A"
153,1,590,173,0.724000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(15 A \sin \left(f x +e \right)-18 A \sin \left(f x +e \right) \cos \left(f x +e \right)+7 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-15 A -17 B +24 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-26 B \sin \left(f x +e \right) \cos \left(f x +e \right)-48 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+19 B \left(\cos^{2}\left(f x +e \right)\right)+2 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+17 B \sin \left(f x +e \right)+3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 A \cos \left(f x +e \right)-2 B \left(\cos^{4}\left(f x +e \right)\right)-9 B \cos \left(f x +e \right)+3 A \left(\cos^{3}\left(f x +e \right)\right)+9 B \left(\cos^{3}\left(f x +e \right)\right)+48 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+15 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{6 f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/6/f*(2*B*cos(f*x+e)^3*sin(f*x+e)+15*A*sin(f*x+e)-18*A*sin(f*x+e)*cos(f*x+e)-48*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*A*cos(f*x+e)^2*sin(f*x+e)+7*B*cos(f*x+e)^2*sin(f*x+e)-2*B*cos(f*x+e)^4-15*A-17*B+3*A*cos(f*x+e)^3+24*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-26*B*sin(f*x+e)*cos(f*x+e)-48*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+19*B*cos(f*x+e)^2+9*B*cos(f*x+e)^3+17*B*sin(f*x+e)-3*A*cos(f*x+e)-9*B*cos(f*x+e)+15*A*cos(f*x+e)^2+48*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*A*ln(2/(cos(f*x+e)+1))+48*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(1/2)","B"
154,1,846,190,0.638000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(-12 A \sin \left(f x +e \right)+10 A \sin \left(f x +e \right) \cos \left(f x +e \right)+6 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+32 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 A +22 B -16 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+15 B \sin \left(f x +e \right) \cos \left(f x +e \right)+64 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+32 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-21 B \left(\cos^{2}\left(f x +e \right)\right)+16 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-16 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+16 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-32 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+32 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-22 B \sin \left(f x +e \right)+2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 A \cos \left(f x +e \right)-B \left(\cos^{4}\left(f x +e \right)\right)-7 B \cos \left(f x +e \right)+2 A \left(\cos^{3}\left(f x +e \right)\right)+7 B \left(\cos^{3}\left(f x +e \right)\right)-32 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+16 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-64 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+32 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-12 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{2 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+2 \cos \left(f x +e \right)-4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(32*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)^3*sin(f*x+e)-12*A*sin(f*x+e)+10*A*sin(f*x+e)*cos(f*x+e)+32*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-16*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)^2*sin(f*x+e)+6*B*cos(f*x+e)^2*sin(f*x+e)-B*cos(f*x+e)^4+12*A+22*B+2*A*cos(f*x+e)^3-8*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+16*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-16*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+16*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+15*B*sin(f*x+e)*cos(f*x+e)+64*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-32*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+32*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-16*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+8*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-16*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+16*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-32*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-21*B*cos(f*x+e)^2+7*B*cos(f*x+e)^3-22*B*sin(f*x+e)-2*A*cos(f*x+e)-7*B*cos(f*x+e)-12*A*cos(f*x+e)^2-32*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+16*A*ln(2/(cos(f*x+e)+1))-64*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+32*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(3/2)","B"
155,1,1092,190,0.648000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(-2 A \sin \left(f x +e \right)+9 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A +14 B +A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 B \sin \left(f x +e \right) \cos \left(f x +e \right)+40 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-20 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+20 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-10 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-15 B \left(\cos^{2}\left(f x +e \right)\right)-10 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+10 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-20 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+5 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-10 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)+30 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-15 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-14 B \sin \left(f x +e \right)+2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 A \cos \left(f x +e \right)+B \left(\cos^{4}\left(f x +e \right)\right)-8 B \cos \left(f x +e \right)+2 A \left(\cos^{3}\left(f x +e \right)\right)+8 B \left(\cos^{3}\left(f x +e \right)\right)-8 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-40 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+20 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/f*(30*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^3*sin(f*x+e)-2*A*sin(f*x+e)+8*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-15*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)^2*sin(f*x+e)+9*B*cos(f*x+e)^2*sin(f*x+e)+B*cos(f*x+e)^4+2*A+14*B+2*A*cos(f*x+e)^3-10*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+5*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3-3*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+6*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+4*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+6*B*sin(f*x+e)*cos(f*x+e)+40*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-20*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+20*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-10*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-4*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-10*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+5*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+10*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-20*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-15*B*cos(f*x+e)^2-2*A*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*B*cos(f*x+e)^3-14*B*sin(f*x+e)-2*A*cos(f*x+e)-8*B*cos(f*x+e)-2*A*cos(f*x+e)^2-8*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*A*ln(2/(cos(f*x+e)+1))-40*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+20*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(5/2)","B"
156,1,832,176,0.688000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-4 A \sin \left(f x +e \right)+4 A \sin \left(f x +e \right) \cos \left(f x +e \right)+13 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A +16 B +10 B \sin \left(f x +e \right) \cos \left(f x +e \right)+48 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-23 B \left(\cos^{2}\left(f x +e \right)\right)-24 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-6 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-7 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-24 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+9 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-18 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+48 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-16 B \sin \left(f x +e \right)+6 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+7 B \left(\cos^{4}\left(f x +e \right)\right)-6 B \cos \left(f x +e \right)+A \left(\cos^{4}\left(f x +e \right)\right)+6 B \left(\cos^{3}\left(f x +e \right)\right)-48 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-5 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{3 f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}"," ",0,"1/3/f*(48*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-7*B*cos(f*x+e)^3*sin(f*x+e)-4*A*sin(f*x+e)+4*A*sin(f*x+e)*cos(f*x+e)-A*cos(f*x+e)^3*sin(f*x+e)-24*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+A*cos(f*x+e)^2*sin(f*x+e)+13*B*cos(f*x+e)^2*sin(f*x+e)+7*B*cos(f*x+e)^4+4*A+16*B-18*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+9*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3+10*B*sin(f*x+e)*cos(f*x+e)+48*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-24*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+12*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+12*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-24*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+3*B*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))-6*B*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-23*B*cos(f*x+e)^2+A*cos(f*x+e)^4+6*B*cos(f*x+e)^3-16*B*sin(f*x+e)+6*B*cos(f*x+e)^3*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*B*cos(f*x+e)^3*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-6*B*cos(f*x+e)-5*A*cos(f*x+e)^2-48*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(7/2)","B"
157,1,309,84,0.678000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(A \left(\cos^{4}\left(f x +e \right)\right)-A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \left(\cos^{4}\left(f x +e \right)\right)+B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 A \left(\cos^{3}\left(f x +e \right)\right)+5 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 B \left(\cos^{3}\left(f x +e \right)\right)+B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-9 A \left(\cos^{2}\left(f x +e \right)\right)+4 A \sin \left(f x +e \right) \cos \left(f x +e \right)+3 B \left(\cos^{2}\left(f x +e \right)\right)-4 B \sin \left(f x +e \right) \cos \left(f x +e \right)-10 A \cos \left(f x +e \right)-14 A \sin \left(f x +e \right)-2 B \cos \left(f x +e \right)+2 B \sin \left(f x +e \right)+14 A -2 B \right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right)}"," ",0,"-1/6/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(A*cos(f*x+e)^4-A*cos(f*x+e)^3*sin(f*x+e)-B*cos(f*x+e)^4+B*cos(f*x+e)^3*sin(f*x+e)+4*A*cos(f*x+e)^3+5*A*cos(f*x+e)^2*sin(f*x+e)+2*B*cos(f*x+e)^3+B*cos(f*x+e)^2*sin(f*x+e)-9*A*cos(f*x+e)^2+4*A*sin(f*x+e)*cos(f*x+e)+3*B*cos(f*x+e)^2-4*B*sin(f*x+e)*cos(f*x+e)-10*A*cos(f*x+e)-14*A*sin(f*x+e)-2*B*cos(f*x+e)+2*B*sin(f*x+e)+14*A-2*B)/(-c*(sin(f*x+e)-1))^(9/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)","B"
158,1,368,128,0.697000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(4 A \left(\cos^{5}\left(f x +e \right)\right)+4 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \left(\cos^{5}\left(f x +e \right)\right)-B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-24 A \left(\cos^{4}\left(f x +e \right)\right)+20 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 B \left(\cos^{4}\left(f x +e \right)\right)-5 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 A \left(\cos^{3}\left(f x +e \right)\right)-68 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 B \left(\cos^{3}\left(f x +e \right)\right)+2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+118 A \left(\cos^{2}\left(f x +e \right)\right)-50 A \sin \left(f x +e \right) \cos \left(f x +e \right)-22 B \left(\cos^{2}\left(f x +e \right)\right)+20 B \sin \left(f x +e \right) \cos \left(f x +e \right)+74 A \cos \left(f x +e \right)+124 A \sin \left(f x +e \right)+4 B \cos \left(f x +e \right)-16 B \sin \left(f x +e \right)-124 A +16 B \right)}{30 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right)}"," ",0,"1/30/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(4*A*cos(f*x+e)^5+4*A*cos(f*x+e)^4*sin(f*x+e)-B*cos(f*x+e)^5-B*sin(f*x+e)*cos(f*x+e)^4-24*A*cos(f*x+e)^4+20*A*cos(f*x+e)^3*sin(f*x+e)+6*B*cos(f*x+e)^4-5*B*cos(f*x+e)^3*sin(f*x+e)-48*A*cos(f*x+e)^3-68*A*cos(f*x+e)^2*sin(f*x+e)-3*B*cos(f*x+e)^3+2*B*cos(f*x+e)^2*sin(f*x+e)+118*A*cos(f*x+e)^2-50*A*sin(f*x+e)*cos(f*x+e)-22*B*cos(f*x+e)^2+20*B*sin(f*x+e)*cos(f*x+e)+74*A*cos(f*x+e)+124*A*sin(f*x+e)+4*B*cos(f*x+e)-16*B*sin(f*x+e)-124*A+16*B)/(-c*(sin(f*x+e)-1))^(11/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)","B"
159,1,423,172,0.718000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(13/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(444 A \sin \left(f x +e \right)-202 A \sin \left(f x +e \right) \cos \left(f x +e \right)+29 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-444 A +52 B -B \left(\cos^{6}\left(f x +e \right)\right)+46 B \sin \left(f x +e \right) \cos \left(f x +e \right)+49 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-7 A \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)+B \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-75 B \left(\cos^{2}\left(f x +e \right)\right)-17 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-7 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+119 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-52 B \sin \left(f x +e \right)-343 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+242 A \cos \left(f x +e \right)+24 B \left(\cos^{4}\left(f x +e \right)\right)-6 B \cos \left(f x +e \right)-168 A \left(\cos^{4}\left(f x +e \right)\right)+42 A \left(\cos^{5}\left(f x +e \right)\right)-6 B \left(\cos^{5}\left(f x +e \right)\right)-224 A \left(\cos^{3}\left(f x +e \right)\right)+12 B \left(\cos^{3}\left(f x +e \right)\right)+545 A \left(\cos^{2}\left(f x +e \right)\right)+7 A \left(\cos^{6}\left(f x +e \right)\right)\right)}{60 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}} \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right)}"," ",0,"1/60/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(-17*B*cos(f*x+e)^3*sin(f*x+e)+444*A*sin(f*x+e)-202*A*sin(f*x+e)*cos(f*x+e)+119*A*cos(f*x+e)^3*sin(f*x+e)+49*A*cos(f*x+e)^4*sin(f*x+e)-7*B*sin(f*x+e)*cos(f*x+e)^4-343*A*cos(f*x+e)^2*sin(f*x+e)+29*B*cos(f*x+e)^2*sin(f*x+e)+24*B*cos(f*x+e)^4-444*A+52*B-224*A*cos(f*x+e)^3+46*B*sin(f*x+e)*cos(f*x+e)+42*A*cos(f*x+e)^5-6*B*cos(f*x+e)^5-B*cos(f*x+e)^6+B*cos(f*x+e)^5*sin(f*x+e)-7*A*cos(f*x+e)^5*sin(f*x+e)-75*B*cos(f*x+e)^2-168*A*cos(f*x+e)^4+12*B*cos(f*x+e)^3-52*B*sin(f*x+e)+242*A*cos(f*x+e)-6*B*cos(f*x+e)+7*A*cos(f*x+e)^6+545*A*cos(f*x+e)^2)/(-c*(sin(f*x+e)-1))^(13/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)","B"
160,1,259,220,0.826000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2),x)","\frac{\left(-280 B \left(\cos^{8}\left(f x +e \right)\right)+315 A \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-315 B \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-360 A \left(\cos^{6}\left(f x +e \right)\right)+40 B \left(\cos^{6}\left(f x +e \right)\right)+315 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-315 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-432 A \left(\cos^{4}\left(f x +e \right)\right)+48 B \left(\cos^{4}\left(f x +e \right)\right)+315 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-315 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-576 A \left(\cos^{2}\left(f x +e \right)\right)+64 B \left(\cos^{2}\left(f x +e \right)\right)+315 A \sin \left(f x +e \right)-315 B \sin \left(f x +e \right)-1152 A +128 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{2520 f \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right)^{7}}"," ",0,"1/2520/f*(-280*B*cos(f*x+e)^8+315*A*cos(f*x+e)^6*sin(f*x+e)-315*B*cos(f*x+e)^6*sin(f*x+e)-360*A*cos(f*x+e)^6+40*B*cos(f*x+e)^6+315*A*cos(f*x+e)^4*sin(f*x+e)-315*B*sin(f*x+e)*cos(f*x+e)^4-432*A*cos(f*x+e)^4+48*B*cos(f*x+e)^4+315*A*cos(f*x+e)^2*sin(f*x+e)-315*B*cos(f*x+e)^2*sin(f*x+e)-576*A*cos(f*x+e)^2+64*B*cos(f*x+e)^2+315*A*sin(f*x+e)-315*B*sin(f*x+e)-1152*A+128*B)*(-c*(sin(f*x+e)-1))^(9/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)-1)/cos(f*x+e)^7","A"
161,1,142,196,0.839000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(35 B \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+40 A \left(\cos^{6}\left(f x +e \right)\right)+35 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+48 A \left(\cos^{4}\left(f x +e \right)\right)+35 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+64 A \left(\cos^{2}\left(f x +e \right)\right)+35 B \sin \left(f x +e \right)+128 A \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{280 f \cos \left(f x +e \right)^{7}}"," ",0,"1/280/f*(35*B*cos(f*x+e)^6*sin(f*x+e)+40*A*cos(f*x+e)^6+35*B*sin(f*x+e)*cos(f*x+e)^4+48*A*cos(f*x+e)^4+35*B*cos(f*x+e)^2*sin(f*x+e)+64*A*cos(f*x+e)^2+35*B*sin(f*x+e)+128*A)*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/cos(f*x+e)^7","A"
162,1,203,168,0.850000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(-30 B \left(\cos^{6}\left(f x +e \right)\right)+35 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+35 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+42 A \left(\cos^{4}\left(f x +e \right)\right)+6 B \left(\cos^{4}\left(f x +e \right)\right)+35 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+35 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+56 A \left(\cos^{2}\left(f x +e \right)\right)+8 B \left(\cos^{2}\left(f x +e \right)\right)+35 A \sin \left(f x +e \right)+35 B \sin \left(f x +e \right)+112 A +16 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{210 f \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right)^{5}}"," ",0,"1/210/f*(-30*B*cos(f*x+e)^6+35*A*cos(f*x+e)^4*sin(f*x+e)+35*B*sin(f*x+e)*cos(f*x+e)^4+42*A*cos(f*x+e)^4+6*B*cos(f*x+e)^4+35*A*cos(f*x+e)^2*sin(f*x+e)+35*B*cos(f*x+e)^2*sin(f*x+e)+56*A*cos(f*x+e)^2+8*B*cos(f*x+e)^2+35*A*sin(f*x+e)+35*B*sin(f*x+e)+112*A+16*B)*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/(1+sin(f*x+e))/cos(f*x+e)^5","A"
163,1,185,124,0.803000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(5 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 A \left(\cos^{4}\left(f x +e \right)\right)+12 B \left(\cos^{4}\left(f x +e \right)\right)-15 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-10 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 A \left(\cos^{2}\left(f x +e \right)\right)-4 B \left(\cos^{2}\left(f x +e \right)\right)-15 A \sin \left(f x +e \right)-10 B \sin \left(f x +e \right)-24 A -8 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{30 f \left(\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \cos \left(f x +e \right)^{3}}"," ",0,"1/30/f*(5*B*sin(f*x+e)*cos(f*x+e)^4+6*A*cos(f*x+e)^4+12*B*cos(f*x+e)^4-15*A*cos(f*x+e)^2*sin(f*x+e)-10*B*cos(f*x+e)^2*sin(f*x+e)-12*A*cos(f*x+e)^2-4*B*cos(f*x+e)^2-15*A*sin(f*x+e)-10*B*sin(f*x+e)-24*A-8*B)*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^2-2*sin(f*x+e)-2)/cos(f*x+e)^3","A"
164,1,174,84,0.824000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(-4 B \left(\cos^{4}\left(f x +e \right)\right)+5 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+20 A \left(\cos^{2}\left(f x +e \right)\right)+28 B \left(\cos^{2}\left(f x +e \right)\right)-35 A \sin \left(f x +e \right)-25 B \sin \left(f x +e \right)-40 A -24 B \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{20 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-4\right) \cos \left(f x +e \right)}"," ",0,"1/20/f*(-4*B*cos(f*x+e)^4+5*A*cos(f*x+e)^2*sin(f*x+e)+15*B*cos(f*x+e)^2*sin(f*x+e)+20*A*cos(f*x+e)^2+28*B*cos(f*x+e)^2-35*A*sin(f*x+e)-25*B*sin(f*x+e)-40*A-24*B)*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/cos(f*x+e)","B"
165,1,671,215,0.688000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(-64 A \sin \left(f x +e \right)+88 A \sin \left(f x +e \right) \cos \left(f x +e \right)-32 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+192 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+64 A +67 B -96 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+192 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+112 B \sin \left(f x +e \right) \cos \left(f x +e \right)+192 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+192 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-80 B \left(\cos^{2}\left(f x +e \right)\right)-16 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-4 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-67 B \sin \left(f x +e \right)-20 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 A \cos \left(f x +e \right)+13 B \left(\cos^{4}\left(f x +e \right)\right)+45 B \cos \left(f x +e \right)+4 A \left(\cos^{4}\left(f x +e \right)\right)+3 B \left(\cos^{5}\left(f x +e \right)\right)-24 A \left(\cos^{3}\left(f x +e \right)\right)-48 B \left(\cos^{3}\left(f x +e \right)\right)-192 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-192 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-68 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{12 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/12/f*(-16*B*cos(f*x+e)^3*sin(f*x+e)-64*A*sin(f*x+e)+88*A*sin(f*x+e)*cos(f*x+e)-4*A*cos(f*x+e)^3*sin(f*x+e)+3*B*sin(f*x+e)*cos(f*x+e)^4+192*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-20*A*cos(f*x+e)^2*sin(f*x+e)-32*B*cos(f*x+e)^2*sin(f*x+e)+13*B*cos(f*x+e)^4+64*A+67*B-24*A*cos(f*x+e)^3-96*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+192*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+112*B*sin(f*x+e)*cos(f*x+e)+192*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+192*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+3*B*cos(f*x+e)^5-80*B*cos(f*x+e)^2+4*A*cos(f*x+e)^4-48*B*cos(f*x+e)^3-67*B*sin(f*x+e)+24*A*cos(f*x+e)+45*B*cos(f*x+e)-68*A*cos(f*x+e)^2-192*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+96*A*ln(2/(cos(f*x+e)+1))-192*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+96*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(1/2)","B"
166,1,927,245,0.646000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(-102 A \sin \left(f x +e \right)+75 A \sin \left(f x +e \right) \cos \left(f x +e \right)+48 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+288 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+102 A +166 B -144 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+144 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-72 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+107 B \sin \left(f x +e \right) \cos \left(f x +e \right)+480 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-240 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+240 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-120 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-155 B \left(\cos^{2}\left(f x +e \right)\right)+144 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-72 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+72 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-144 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+13 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+120 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-240 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-2 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+3 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+240 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-120 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-166 B \sin \left(f x +e \right)+24 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-27 A \cos \left(f x +e \right)-11 B \left(\cos^{4}\left(f x +e \right)\right)-59 B \cos \left(f x +e \right)-3 A \left(\cos^{4}\left(f x +e \right)\right)-2 B \left(\cos^{5}\left(f x +e \right)\right)+27 A \left(\cos^{3}\left(f x +e \right)\right)+61 B \left(\cos^{3}\left(f x +e \right)\right)-288 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+144 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-480 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+240 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-99 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{6 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/6/f*(240*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+13*B*cos(f*x+e)^3*sin(f*x+e)-102*A*sin(f*x+e)+75*A*sin(f*x+e)*cos(f*x+e)+3*A*cos(f*x+e)^3*sin(f*x+e)-2*B*sin(f*x+e)*cos(f*x+e)^4+288*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-120*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+24*A*cos(f*x+e)^2*sin(f*x+e)+48*B*cos(f*x+e)^2*sin(f*x+e)-11*B*cos(f*x+e)^4+102*A+166*B+27*A*cos(f*x+e)^3-72*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+144*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-144*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+144*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-72*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+107*B*sin(f*x+e)*cos(f*x+e)+480*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-240*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+240*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-120*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+72*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-144*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*cos(f*x+e)^5+120*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-240*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-155*B*cos(f*x+e)^2-3*A*cos(f*x+e)^4+61*B*cos(f*x+e)^3-166*B*sin(f*x+e)-27*A*cos(f*x+e)-59*B*cos(f*x+e)-99*A*cos(f*x+e)^2-288*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+144*A*ln(2/(cos(f*x+e)+1))-480*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+240*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(3/2)","B"
167,1,1191,237,0.646000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(32 A \sin \left(f x +e \right)-12 A \sin \left(f x +e \right) \cos \left(f x +e \right)-63 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-96 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 A -100 B +24 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-46 B \sin \left(f x +e \right) \cos \left(f x +e \right)-288 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+144 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-144 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+72 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+109 B \left(\cos^{2}\left(f x +e \right)\right)+72 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-36 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-72 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+36 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-12 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+10 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-72 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+144 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-36 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)+72 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+2 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-216 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+108 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+100 B \sin \left(f x +e \right)-12 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-22 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+20 A \cos \left(f x +e \right)-9 B \left(\cos^{4}\left(f x +e \right)\right)+54 B \cos \left(f x +e \right)-2 A \left(\cos^{4}\left(f x +e \right)\right)-B \left(\cos^{5}\left(f x +e \right)\right)-20 A \left(\cos^{3}\left(f x +e \right)\right)-53 B \left(\cos^{3}\left(f x +e \right)\right)+96 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+288 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-144 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+34 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{2 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/2/f*(-216*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+10*B*cos(f*x+e)^3*sin(f*x+e)+32*A*sin(f*x+e)-12*A*sin(f*x+e)*cos(f*x+e)+2*A*cos(f*x+e)^3*sin(f*x+e)-B*sin(f*x+e)*cos(f*x+e)^4-96*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+108*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-22*A*cos(f*x+e)^2*sin(f*x+e)-63*B*cos(f*x+e)^2*sin(f*x+e)-9*B*cos(f*x+e)^4-32*A-100*B-20*A*cos(f*x+e)^3+72*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3-36*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3+36*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-72*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+48*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-46*B*sin(f*x+e)*cos(f*x+e)-288*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+144*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-144*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+72*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+48*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^5+72*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-36*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)-72*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+144*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+109*B*cos(f*x+e)^2+24*A*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^4-12*A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*A*cos(f*x+e)^2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-53*B*cos(f*x+e)^3+100*B*sin(f*x+e)+20*A*cos(f*x+e)+54*B*cos(f*x+e)+34*A*cos(f*x+e)^2+96*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*A*ln(2/(cos(f*x+e)+1))+288*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-144*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(5/2)","B"
168,1,1455,236,0.661000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-20 A \sin \left(f x +e \right)+14 A \sin \left(f x +e \right) \cos \left(f x +e \right)+98 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+48 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+20 A +116 B -24 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 A \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+62 B \sin \left(f x +e \right) \cos \left(f x +e \right)+336 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-168 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+168 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-84 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-18 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-160 B \left(\cos^{2}\left(f x +e \right)\right)-168 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+84 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-42 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+21 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+9 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+3 A \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 A \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-41 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+84 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-168 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+63 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-126 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-3 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-8 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+336 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-168 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-116 B \sin \left(f x +e \right)-3 A \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 A \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+42 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-21 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+14 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-6 A \cos \left(f x +e \right)+44 B \left(\cos^{4}\left(f x +e \right)\right)-54 B \cos \left(f x +e \right)+8 A \left(\cos^{4}\left(f x +e \right)\right)-3 B \left(\cos^{5}\left(f x +e \right)\right)+6 A \left(\cos^{3}\left(f x +e \right)\right)+57 B \left(\cos^{3}\left(f x +e \right)\right)-48 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-336 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+168 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-28 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{3 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}"," ",0,"1/3/f*(336*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-41*B*cos(f*x+e)^3*sin(f*x+e)-20*A*sin(f*x+e)+14*A*sin(f*x+e)*cos(f*x+e)-8*A*cos(f*x+e)^3*sin(f*x+e)-3*B*sin(f*x+e)*cos(f*x+e)^4+48*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-168*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+14*A*cos(f*x+e)^2*sin(f*x+e)+98*B*cos(f*x+e)^2*sin(f*x+e)+44*B*cos(f*x+e)^4+20*A+116*B+6*A*cos(f*x+e)^3-126*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+63*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3-24*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+48*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*A*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+62*B*sin(f*x+e)*cos(f*x+e)+336*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-168*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+168*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-84*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+12*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*B*cos(f*x+e)^5-168*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+84*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+84*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-168*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-6*A*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*A*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))+21*B*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))-42*B*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-160*B*cos(f*x+e)^2-18*A*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+9*A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+8*A*cos(f*x+e)^4+12*A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)^2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+57*B*cos(f*x+e)^3-116*B*sin(f*x+e)-3*A*sin(f*x+e)*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+6*A*sin(f*x+e)*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+42*B*cos(f*x+e)^3*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-21*B*cos(f*x+e)^3*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-6*A*cos(f*x+e)-54*B*cos(f*x+e)-28*A*cos(f*x+e)^2-48*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*A*ln(2/(cos(f*x+e)+1))-336*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+168*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(7/2)","B"
169,1,1019,221,0.717000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(6 A \sin \left(f x +e \right)-6 A \sin \left(f x +e \right) \cos \left(f x +e \right)+39 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-6 A +34 B +6 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \left(\cos^{5}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+14 B \sin \left(f x +e \right) \cos \left(f x +e \right)+96 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 B \cos \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-53 B \left(\cos^{2}\left(f x +e \right)\right)-72 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+36 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-30 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+15 B \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-11 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-48 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+24 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-48 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{3}\left(f x +e \right)\right)-8 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+3 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+120 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-60 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-34 B \sin \left(f x +e \right)+24 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 B \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+19 B \left(\cos^{4}\left(f x +e \right)\right)-20 B \cos \left(f x +e \right)-3 A \left(\cos^{4}\left(f x +e \right)\right)-8 B \left(\cos^{5}\left(f x +e \right)\right)+28 B \left(\cos^{3}\left(f x +e \right)\right)-96 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+9 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{3 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}"," ",0,"-1/3/f*(120*B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-11*B*cos(f*x+e)^3*sin(f*x+e)-3*B*cos(f*x+e)^5*ln(2/(cos(f*x+e)+1))+6*A*sin(f*x+e)-6*A*sin(f*x+e)*cos(f*x+e)+3*A*cos(f*x+e)^3*sin(f*x+e)-8*B*sin(f*x+e)*cos(f*x+e)^4-60*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-3*A*cos(f*x+e)^2*sin(f*x+e)+39*B*cos(f*x+e)^2*sin(f*x+e)+19*B*cos(f*x+e)^4-6*A+34*B-48*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^3+24*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3+14*B*sin(f*x+e)*cos(f*x+e)+96*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+48*B*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+6*B*cos(f*x+e)^5*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*B*cos(f*x+e)^5-72*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)+36*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+24*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-48*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+15*B*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))-30*B*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-53*B*cos(f*x+e)^2-3*A*cos(f*x+e)^4+6*B*sin(f*x+e)*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*B*sin(f*x+e)*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))+28*B*cos(f*x+e)^3-34*B*sin(f*x+e)+24*B*cos(f*x+e)^3*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*B*cos(f*x+e)^3*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-20*B*cos(f*x+e)+9*A*cos(f*x+e)^2-96*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+48*B*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(9/2)","B"
170,1,389,84,0.701000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(A \left(\cos^{5}\left(f x +e \right)\right)+A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+B \left(\cos^{5}\left(f x +e \right)\right)+B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-6 A \left(\cos^{4}\left(f x +e \right)\right)+5 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 B \left(\cos^{4}\left(f x +e \right)\right)-5 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-17 A \left(\cos^{3}\left(f x +e \right)\right)-22 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-7 B \left(\cos^{3}\left(f x +e \right)\right)-2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+32 A \left(\cos^{2}\left(f x +e \right)\right)-10 A \sin \left(f x +e \right) \cos \left(f x +e \right)-8 B \left(\cos^{2}\left(f x +e \right)\right)+10 B \sin \left(f x +e \right) \cos \left(f x +e \right)+26 A \cos \left(f x +e \right)+36 A \sin \left(f x +e \right)+6 B \cos \left(f x +e \right)-4 B \sin \left(f x +e \right)-36 A +4 B \right)}{10 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right)}"," ",0,"1/10/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(A*cos(f*x+e)^5+A*cos(f*x+e)^4*sin(f*x+e)+B*cos(f*x+e)^5+B*sin(f*x+e)*cos(f*x+e)^4-6*A*cos(f*x+e)^4+5*A*cos(f*x+e)^3*sin(f*x+e)+4*B*cos(f*x+e)^4-5*B*cos(f*x+e)^3*sin(f*x+e)-17*A*cos(f*x+e)^3-22*A*cos(f*x+e)^2*sin(f*x+e)-7*B*cos(f*x+e)^3-2*B*cos(f*x+e)^2*sin(f*x+e)+32*A*cos(f*x+e)^2-10*A*sin(f*x+e)*cos(f*x+e)-8*B*cos(f*x+e)^2+10*B*sin(f*x+e)*cos(f*x+e)+26*A*cos(f*x+e)+36*A*sin(f*x+e)+6*B*cos(f*x+e)-4*B*sin(f*x+e)-36*A+4*B)/(-c*(sin(f*x+e)-1))^(11/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)","B"
171,1,393,128,0.730000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(13/2),x)","-\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(3 A \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 A \left(\cos^{6}\left(f x +e \right)\right)-21 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-18 A \left(\cos^{5}\left(f x +e \right)\right)-51 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+72 A \left(\cos^{4}\left(f x +e \right)\right)+15 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-15 B \left(\cos^{4}\left(f x +e \right)\right)+157 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+106 A \left(\cos^{3}\left(f x +e \right)\right)-5 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+10 B \left(\cos^{3}\left(f x +e \right)\right)+78 A \sin \left(f x +e \right) \cos \left(f x +e \right)-235 A \left(\cos^{2}\left(f x +e \right)\right)-30 B \sin \left(f x +e \right) \cos \left(f x +e \right)+35 B \left(\cos^{2}\left(f x +e \right)\right)-196 A \sin \left(f x +e \right)-118 A \cos \left(f x +e \right)+20 B \sin \left(f x +e \right)-10 B \cos \left(f x +e \right)+196 A -20 B \right)}{30 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right)}"," ",0,"-1/30/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(3*A*cos(f*x+e)^5*sin(f*x+e)-3*A*cos(f*x+e)^6-21*A*cos(f*x+e)^4*sin(f*x+e)-18*A*cos(f*x+e)^5-51*A*cos(f*x+e)^3*sin(f*x+e)+72*A*cos(f*x+e)^4+15*B*cos(f*x+e)^3*sin(f*x+e)-15*B*cos(f*x+e)^4+157*A*cos(f*x+e)^2*sin(f*x+e)+106*A*cos(f*x+e)^3-5*B*cos(f*x+e)^2*sin(f*x+e)+10*B*cos(f*x+e)^3+78*A*sin(f*x+e)*cos(f*x+e)-235*A*cos(f*x+e)^2-30*B*sin(f*x+e)*cos(f*x+e)+35*B*cos(f*x+e)^2-196*A*sin(f*x+e)-118*A*cos(f*x+e)+20*B*sin(f*x+e)-10*B*cos(f*x+e)+196*A-20*B)/(-c*(sin(f*x+e)-1))^(13/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)","B"
172,1,505,178,0.765000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(15/2),x)","-\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(-5016 A \sin \left(f x +e \right)+2268 A \sin \left(f x +e \right) \cos \left(f x +e \right)-352 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5016 A -472 B +24 B \left(\cos^{6}\left(f x +e \right)\right)-476 B \sin \left(f x +e \right) \cos \left(f x +e \right)-1209 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+273 A \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 B \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+828 B \left(\cos^{2}\left(f x +e \right)\right)+287 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+39 A \left(\cos^{7}\left(f x +e \right)\right)+93 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-1911 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+472 B \sin \left(f x +e \right)-3 B \left(\cos^{7}\left(f x +e \right)\right)+5136 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-21 B \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-2748 A \cos \left(f x +e \right)-380 B \left(\cos^{4}\left(f x +e \right)\right)-4 B \cos \left(f x +e \right)+39 A \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+3120 A \left(\cos^{4}\left(f x +e \right)\right)-936 A \left(\cos^{5}\left(f x +e \right)\right)+72 B \left(\cos^{5}\left(f x +e \right)\right)+3225 A \left(\cos^{3}\left(f x +e \right)\right)-65 B \left(\cos^{3}\left(f x +e \right)\right)-7404 A \left(\cos^{2}\left(f x +e \right)\right)-312 A \left(\cos^{6}\left(f x +e \right)\right)\right)}{420 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{15}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right)}"," ",0,"-1/420/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(287*B*cos(f*x+e)^3*sin(f*x+e)-5016*A*sin(f*x+e)+2268*A*sin(f*x+e)*cos(f*x+e)+39*A*cos(f*x+e)^6*sin(f*x+e)-1911*A*cos(f*x+e)^3*sin(f*x+e)-1209*A*cos(f*x+e)^4*sin(f*x+e)+93*B*sin(f*x+e)*cos(f*x+e)^4+5136*A*cos(f*x+e)^2*sin(f*x+e)-352*B*cos(f*x+e)^2*sin(f*x+e)-380*B*cos(f*x+e)^4+5016*A-472*B+3225*A*cos(f*x+e)^3-476*B*sin(f*x+e)*cos(f*x+e)-3*B*cos(f*x+e)^6*sin(f*x+e)-936*A*cos(f*x+e)^5+72*B*cos(f*x+e)^5+24*B*cos(f*x+e)^6-21*B*cos(f*x+e)^5*sin(f*x+e)+273*A*cos(f*x+e)^5*sin(f*x+e)+828*B*cos(f*x+e)^2+3120*A*cos(f*x+e)^4-65*B*cos(f*x+e)^3+472*B*sin(f*x+e)-2748*A*cos(f*x+e)-4*B*cos(f*x+e)-312*A*cos(f*x+e)^6-7404*A*cos(f*x+e)^2+39*A*cos(f*x+e)^7-3*B*cos(f*x+e)^7)/(-c*(sin(f*x+e)-1))^(15/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)","B"
173,1,560,216,0.810000," ","int((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(17/2),x)","-\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(-3076 A \sin \left(f x +e \right)+1468 A \sin \left(f x +e \right) \cos \left(f x +e \right)-300 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3076 A -268 B +40 B \left(\cos^{6}\left(f x +e \right)\right)-204 B \sin \left(f x +e \right) \cos \left(f x +e \right)-1332 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+372 A \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-9 B \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+504 B \left(\cos^{2}\left(f x +e \right)\right)-B \left(\cos^{8}\left(f x +e \right)\right)+164 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+96 A \left(\cos^{7}\left(f x +e \right)\right)+111 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+B \left(\cos^{7}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 A \left(\cos^{7}\left(f x +e \right)\right) \sin \left(f x +e \right)-1548 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+268 B \sin \left(f x +e \right)-8 B \left(\cos^{7}\left(f x +e \right)\right)+3880 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-31 B \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-1608 A \cos \left(f x +e \right)-275 B \left(\cos^{4}\left(f x +e \right)\right)+64 B \cos \left(f x +e \right)+108 A \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 A \left(\cos^{8}\left(f x +e \right)\right)+2880 A \left(\cos^{4}\left(f x +e \right)\right)-960 A \left(\cos^{5}\left(f x +e \right)\right)+80 B \left(\cos^{5}\left(f x +e \right)\right)+2332 A \left(\cos^{3}\left(f x +e \right)\right)-136 B \left(\cos^{3}\left(f x +e \right)\right)-5348 A \left(\cos^{2}\left(f x +e \right)\right)-480 A \left(\cos^{6}\left(f x +e \right)\right)\right)}{140 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{17}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right)}"," ",0,"-1/140/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(164*B*cos(f*x+e)^3*sin(f*x+e)-3076*A*sin(f*x+e)+1468*A*sin(f*x+e)*cos(f*x+e)+108*A*cos(f*x+e)^6*sin(f*x+e)-1548*A*cos(f*x+e)^3*sin(f*x+e)-1332*A*cos(f*x+e)^4*sin(f*x+e)+111*B*sin(f*x+e)*cos(f*x+e)^4+3880*A*cos(f*x+e)^2*sin(f*x+e)-300*B*cos(f*x+e)^2*sin(f*x+e)-275*B*cos(f*x+e)^4+3076*A-268*B+2332*A*cos(f*x+e)^3-204*B*sin(f*x+e)*cos(f*x+e)-9*B*cos(f*x+e)^6*sin(f*x+e)-960*A*cos(f*x+e)^5+80*B*cos(f*x+e)^5+40*B*cos(f*x+e)^6-31*B*cos(f*x+e)^5*sin(f*x+e)+372*A*cos(f*x+e)^5*sin(f*x+e)-B*cos(f*x+e)^8+504*B*cos(f*x+e)^2+2880*A*cos(f*x+e)^4-136*B*cos(f*x+e)^3+268*B*sin(f*x+e)-1608*A*cos(f*x+e)-12*A*cos(f*x+e)^7*sin(f*x+e)+B*cos(f*x+e)^7*sin(f*x+e)+64*B*cos(f*x+e)-480*A*cos(f*x+e)^6-5348*A*cos(f*x+e)^2+96*A*cos(f*x+e)^7-8*B*cos(f*x+e)^7+12*A*cos(f*x+e)^8)/(-c*(sin(f*x+e)-1))^(17/2)/(cos(f*x+e)^4+sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3-4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2-4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)+8*sin(f*x+e)+8)","B"
174,1,595,177,0.717000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(48 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-15 A \sin \left(f x +e \right)+18 A \sin \left(f x +e \right) \cos \left(f x +e \right)+7 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-15 A +17 B -24 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-26 B \sin \left(f x +e \right) \cos \left(f x +e \right)+24 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-19 B \left(\cos^{2}\left(f x +e \right)\right)+2 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+17 B \sin \left(f x +e \right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 A \cos \left(f x +e \right)+2 B \left(\cos^{4}\left(f x +e \right)\right)+9 B \cos \left(f x +e \right)+3 A \left(\cos^{3}\left(f x +e \right)\right)-9 B \left(\cos^{3}\left(f x +e \right)\right)-24 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+15 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}{6 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"-1/6/f*(2*B*cos(f*x+e)^3*sin(f*x+e)+48*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-15*A*sin(f*x+e)+18*A*sin(f*x+e)*cos(f*x+e)-3*A*cos(f*x+e)^2*sin(f*x+e)+7*B*cos(f*x+e)^2*sin(f*x+e)+2*B*cos(f*x+e)^4-15*A+17*B+3*A*cos(f*x+e)^3-24*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-26*B*sin(f*x+e)*cos(f*x+e)+24*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-24*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-48*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+48*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+48*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-19*B*cos(f*x+e)^2-9*B*cos(f*x+e)^3+17*B*sin(f*x+e)-3*A*cos(f*x+e)+9*B*cos(f*x+e)+15*A*cos(f*x+e)^2-24*A*ln(2/(cos(f*x+e)+1))+24*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/(a*(1+sin(f*x+e)))^(1/2)","B"
175,1,501,132,0.676000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-B \left(\cos^{3}\left(f x +e \right)\right)+B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 A \left(\cos^{2}\left(f x +e \right)\right)+2 A \sin \left(f x +e \right) \cos \left(f x +e \right)+4 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \left(\cos^{2}\left(f x +e \right)\right)-4 B \sin \left(f x +e \right) \cos \left(f x +e \right)-4 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \sin \left(f x +e \right)-4 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \cos \left(f x +e \right)+3 B \sin \left(f x +e \right)+4 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A +3 B \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}{2 f \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"1/2/f*(-B*cos(f*x+e)^3+B*cos(f*x+e)^2*sin(f*x+e)+2*A*cos(f*x+e)^2+2*A*sin(f*x+e)*cos(f*x+e)+4*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-8*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+8*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*B*cos(f*x+e)^2-4*B*sin(f*x+e)*cos(f*x+e)-4*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+8*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-8*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*sin(f*x+e)-4*A*ln(2/(cos(f*x+e)+1))+8*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)+3*B*sin(f*x+e)+4*B*ln(2/(cos(f*x+e)+1))-8*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A+3*B)*(-c*(sin(f*x+e)-1))^(3/2)/(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(a*(1+sin(f*x+e)))^(1/2)","B"
176,1,399,88,0.680000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(2 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+B \left(\cos^{2}\left(f x +e \right)\right)+B \sin \left(f x +e \right) \cos \left(f x +e \right)-2 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \sin \left(f x +e \right)+2 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}{f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"-1/f*(2*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+B*cos(f*x+e)^2+B*sin(f*x+e)*cos(f*x+e)-2*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+2*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*ln(2/(cos(f*x+e)+1))-B*sin(f*x+e)+2*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln(2/(cos(f*x+e)+1))-B)*(-c*(sin(f*x+e)-1))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))/(a*(1+sin(f*x+e)))^(1/2)","B"
177,1,165,101,0.592000," ","int((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \cos \left(f x +e \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/f*(A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln(2/(cos(f*x+e)+1))+B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e)))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(1/2)","A"
178,1,302,91,0.595000," ","int((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \sin \left(f x +e \right)+B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \sin \left(f x +e \right)\right) \cos \left(f x +e \right)}{2 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*sin(f*x+e)+B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*sin(f*x+e))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
179,1,465,135,0.618000," ","int((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \left(\cos^{2}\left(f x +e \right)\right)+2 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 A \sin \left(f x +e \right)-2 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \sin \left(f x +e \right)+2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \right) \cos \left(f x +e \right)}{4 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/4/f*(A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*cos(f*x+e)^2+2*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*A*sin(f*x+e)-2*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*sin(f*x+e)+2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(5/2)","B"
180,1,939,245,0.657000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(-288 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+480 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+102 A \sin \left(f x +e \right)-75 A \sin \left(f x +e \right) \cos \left(f x +e \right)+48 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+102 A -166 B +144 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-72 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+107 B \sin \left(f x +e \right) \cos \left(f x +e \right)-240 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+120 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+155 B \left(\cos^{2}\left(f x +e \right)\right)-72 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-72 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+13 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+120 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-2 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+144 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-240 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-288 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+480 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+120 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-166 B \sin \left(f x +e \right)+144 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-240 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+144 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-240 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-27 A \cos \left(f x +e \right)+11 B \left(\cos^{4}\left(f x +e \right)\right)+59 B \cos \left(f x +e \right)-3 A \left(\cos^{4}\left(f x +e \right)\right)+2 B \left(\cos^{5}\left(f x +e \right)\right)+27 A \left(\cos^{3}\left(f x +e \right)\right)-61 B \left(\cos^{3}\left(f x +e \right)\right)+144 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-240 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-99 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}{6 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-\left(\cos^{4}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)+4 \cos \left(f x +e \right)-8\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/6/f*(13*B*cos(f*x+e)^3*sin(f*x+e)-288*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+480*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+102*A*sin(f*x+e)-75*A*sin(f*x+e)*cos(f*x+e)-3*A*cos(f*x+e)^3*sin(f*x+e)-2*B*sin(f*x+e)*cos(f*x+e)^4+120*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)^2*sin(f*x+e)+48*B*cos(f*x+e)^2*sin(f*x+e)+11*B*cos(f*x+e)^4+102*A-166*B+27*A*cos(f*x+e)^3-72*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+144*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-72*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+107*B*sin(f*x+e)*cos(f*x+e)-240*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+120*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+144*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-240*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-72*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*B*cos(f*x+e)^5+120*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+144*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-240*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-288*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+480*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+155*B*cos(f*x+e)^2-3*A*cos(f*x+e)^4-61*B*cos(f*x+e)^3-166*B*sin(f*x+e)+144*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-240*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-27*A*cos(f*x+e)+59*B*cos(f*x+e)-99*A*cos(f*x+e)^2+144*A*ln(2/(cos(f*x+e)+1))-240*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)+8*cos(f*x+e)^2+8*sin(f*x+e)+4*cos(f*x+e)-8)/(a*(1+sin(f*x+e)))^(3/2)","B"
181,1,853,190,0.627000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(-32 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+64 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 A \sin \left(f x +e \right)-10 A \sin \left(f x +e \right) \cos \left(f x +e \right)+6 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 A -22 B +16 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+15 B \sin \left(f x +e \right) \cos \left(f x +e \right)-32 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+21 B \left(\cos^{2}\left(f x +e \right)\right)-8 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+16 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+16 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+64 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+16 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-22 B \sin \left(f x +e \right)+16 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+16 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-32 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 A \cos \left(f x +e \right)+B \left(\cos^{4}\left(f x +e \right)\right)+7 B \cos \left(f x +e \right)+2 A \left(\cos^{3}\left(f x +e \right)\right)-7 B \left(\cos^{3}\left(f x +e \right)\right)+16 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-32 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-12 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}{2 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(B*cos(f*x+e)^3*sin(f*x+e)-32*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+64*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+12*A*sin(f*x+e)-10*A*sin(f*x+e)*cos(f*x+e)+16*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^2*sin(f*x+e)+6*B*cos(f*x+e)^2*sin(f*x+e)+B*cos(f*x+e)^4+12*A-22*B+2*A*cos(f*x+e)^3-8*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+16*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-8*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+15*B*sin(f*x+e)*cos(f*x+e)-32*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+16*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+16*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-32*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+16*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+16*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-32*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-32*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+64*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+21*B*cos(f*x+e)^2-7*B*cos(f*x+e)^3-22*B*sin(f*x+e)+16*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-32*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*cos(f*x+e)+7*B*cos(f*x+e)-12*A*cos(f*x+e)^2+16*A*ln(2/(cos(f*x+e)+1))-32*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/(a*(1+sin(f*x+e)))^(3/2)","B"
182,1,759,143,0.642000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(4 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \sin \left(f x +e \right)+2 A \sin \left(f x +e \right) \cos \left(f x +e \right)-B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 A +4 B -2 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \sin \left(f x +e \right) \cos \left(f x +e \right)+6 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 B \left(\cos^{2}\left(f x +e \right)\right)+A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-2 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 B \sin \left(f x +e \right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \cos \left(f x +e \right)+B \left(\cos^{3}\left(f x +e \right)\right)-2 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}{f \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/f*(4*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*sin(f*x+e)+2*A*sin(f*x+e)*cos(f*x+e)-3*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-B*cos(f*x+e)^2*sin(f*x+e)-2*A+4*B+A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-3*B*sin(f*x+e)*cos(f*x+e)+6*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-3*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+6*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-3*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-2*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+6*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+4*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*B*cos(f*x+e)^2+B*cos(f*x+e)^3+4*B*sin(f*x+e)-2*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+6*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)+2*A*cos(f*x+e)^2-2*A*ln(2/(cos(f*x+e)+1))+6*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(3/2)/(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(a*(1+sin(f*x+e)))^(3/2)","B"
183,1,408,92,0.651000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(2 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+A \left(\cos^{2}\left(f x +e \right)\right)+A \sin \left(f x +e \right) \cos \left(f x +e \right)-B \left(\cos^{2}\left(f x +e \right)\right)-B \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-A \sin \left(f x +e \right)+B \sin \left(f x +e \right)-4 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-A +B \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}{f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/f*(2*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+2*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+A*cos(f*x+e)^2+A*sin(f*x+e)*cos(f*x+e)-B*cos(f*x+e)^2-B*sin(f*x+e)*cos(f*x+e)+2*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-4*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-A*sin(f*x+e)+B*sin(f*x+e)-4*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*ln(2/(cos(f*x+e)+1))-A+B)*(-c*(sin(f*x+e)-1))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)","B"
184,1,303,91,0.604000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \sin \left(f x +e \right)+B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right)\right) \cos \left(f x +e \right)}{2 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/2/f*(A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*sin(f*x+e)+B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
185,1,130,132,0.563000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{2}\left(f x +e \right)\right)+A \sin \left(f x +e \right)+B \right) \cos \left(f x +e \right)}{2 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^2+A*sin(f*x+e)+B)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(3/2)","A"
186,1,429,193,0.553000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(3 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \left(\cos^{2}\left(f x +e \right)\right)+3 B \left(\cos^{2}\left(f x +e \right)\right)-3 A \sin \left(f x +e \right)+B \sin \left(f x +e \right)+A -3 B \right) \cos \left(f x +e \right)}{8 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/8/f*(3*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-3*A*cos(f*x+e)^2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2+B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-3*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*cos(f*x+e)^2*sin(f*x+e)+3*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*cos(f*x+e)^2*sin(f*x+e)-B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*cos(f*x+e)^2+3*B*cos(f*x+e)^2-3*A*sin(f*x+e)+B*sin(f*x+e)+A-3*B)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)","B"
187,1,1287,293,0.675000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(-1152 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2688 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+396 A \sin \left(f x +e \right)-174 A \sin \left(f x +e \right) \cos \left(f x +e \right)+581 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+396 A -932 B +576 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-288 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+442 B \sin \left(f x +e \right) \cos \left(f x +e \right)-1344 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+672 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 A \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+288 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-672 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+1023 B \left(\cos^{2}\left(f x +e \right)\right)+336 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-432 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+144 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-288 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-108 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+672 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-336 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)+15 B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-144 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 B \left(\cos^{6}\left(f x +e \right)\right)+576 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-1344 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-1152 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2688 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+36 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+1008 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-932 B \sin \left(f x +e \right)+672 B \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-288 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+864 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2016 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+576 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-1344 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-255 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 B \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right)-222 A \cos \left(f x +e \right)-93 B \left(\cos^{4}\left(f x +e \right)\right)+490 B \cos \left(f x +e \right)+33 A \left(\cos^{4}\left(f x +e \right)\right)+3 A \left(\cos^{5}\left(f x +e \right)\right)-17 B \left(\cos^{5}\left(f x +e \right)\right)+219 A \left(\cos^{3}\left(f x +e \right)\right)-473 B \left(\cos^{3}\left(f x +e \right)\right)+576 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-1344 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-429 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}{6 f \left(\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\cos^{5}\left(f x +e \right)+4 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-5 \left(\cos^{4}\left(f x +e \right)\right)-12 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{3}\left(f x +e \right)\right)-8 \sin \left(f x +e \right) \cos \left(f x +e \right)+20 \left(\cos^{2}\left(f x +e \right)\right)+16 \sin \left(f x +e \right)+8 \cos \left(f x +e \right)-16\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/6/f*(-108*B*cos(f*x+e)^3*sin(f*x+e)-1152*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2688*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+396*A*sin(f*x+e)-174*A*sin(f*x+e)*cos(f*x+e)+36*A*cos(f*x+e)^3*sin(f*x+e)-3*A*cos(f*x+e)^4*sin(f*x+e)+15*B*sin(f*x+e)*cos(f*x+e)^4+1008*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-255*A*cos(f*x+e)^2*sin(f*x+e)+581*B*cos(f*x+e)^2*sin(f*x+e)-93*B*cos(f*x+e)^4+396*A-932*B+219*A*cos(f*x+e)^3-336*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3-432*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+576*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-288*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+442*B*sin(f*x+e)*cos(f*x+e)-1344*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+672*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+864*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2016*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-288*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+3*A*cos(f*x+e)^5-17*B*cos(f*x+e)^5+2*B*cos(f*x+e)^6+336*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+672*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+2*B*cos(f*x+e)^5*sin(f*x+e)+576*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-1344*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-1152*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2688*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+1023*B*cos(f*x+e)^2+144*A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+33*A*cos(f*x+e)^4-144*A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-288*A*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+672*B*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-473*B*cos(f*x+e)^3-932*B*sin(f*x+e)+576*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-1344*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+288*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-672*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-222*A*cos(f*x+e)+490*B*cos(f*x+e)-429*A*cos(f*x+e)^2+576*A*ln(2/(cos(f*x+e)+1))-1344*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(9/2)/(sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3-5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)+20*cos(f*x+e)^2+16*sin(f*x+e)+8*cos(f*x+e)-16)/(a*(1+sin(f*x+e)))^(5/2)","B"
188,1,1206,237,0.640000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(-96 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+288 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+32 A \sin \left(f x +e \right)-12 A \sin \left(f x +e \right) \cos \left(f x +e \right)+63 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+32 A -100 B +48 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+46 B \sin \left(f x +e \right) \cos \left(f x +e \right)-144 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+72 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-72 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+109 B \left(\cos^{2}\left(f x +e \right)\right)+36 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-36 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+12 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-10 B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+72 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-36 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)+B \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-12 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-144 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+288 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+108 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-100 B \sin \left(f x +e \right)+72 B \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+72 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-216 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-144 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-22 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-20 A \cos \left(f x +e \right)-9 B \left(\cos^{4}\left(f x +e \right)\right)+54 B \cos \left(f x +e \right)+2 A \left(\cos^{4}\left(f x +e \right)\right)-B \left(\cos^{5}\left(f x +e \right)\right)+20 A \left(\cos^{3}\left(f x +e \right)\right)-53 B \left(\cos^{3}\left(f x +e \right)\right)+48 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-144 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-34 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}{2 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-\left(\cos^{4}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)+4 \cos \left(f x +e \right)-8\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/2/f*(-10*B*cos(f*x+e)^3*sin(f*x+e)-96*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+288*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+32*A*sin(f*x+e)-12*A*sin(f*x+e)*cos(f*x+e)+2*A*cos(f*x+e)^3*sin(f*x+e)+B*sin(f*x+e)*cos(f*x+e)^4+108*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-22*A*cos(f*x+e)^2*sin(f*x+e)+63*B*cos(f*x+e)^2*sin(f*x+e)-9*B*cos(f*x+e)^4+32*A-100*B+20*A*cos(f*x+e)^3-36*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3-36*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+48*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+46*B*sin(f*x+e)*cos(f*x+e)-144*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+72*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+72*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-216*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-B*cos(f*x+e)^5+36*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+72*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+48*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-144*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+288*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+109*B*cos(f*x+e)^2+12*A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+2*A*cos(f*x+e)^4-12*A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-24*A*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+72*B*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-53*B*cos(f*x+e)^3-100*B*sin(f*x+e)+48*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-144*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-72*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-20*A*cos(f*x+e)+54*B*cos(f*x+e)-34*A*cos(f*x+e)^2+48*A*ln(2/(cos(f*x+e)+1))-144*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)+8*cos(f*x+e)^2+8*sin(f*x+e)+4*cos(f*x+e)-8)/(a*(1+sin(f*x+e)))^(5/2)","B"
189,1,1106,189,0.631000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(-8 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+40 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \sin \left(f x +e \right)+9 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 A -14 B +4 A \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 B \sin \left(f x +e \right) \cos \left(f x +e \right)-20 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+10 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-10 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+15 B \left(\cos^{2}\left(f x +e \right)\right)+5 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \cos \left(f x +e \right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-B \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right)+10 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-5 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 A \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-20 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+40 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+15 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-14 B \sin \left(f x +e \right)+10 B \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-30 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+4 A \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-20 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 A \cos \left(f x +e \right)-B \left(\cos^{4}\left(f x +e \right)\right)+8 B \cos \left(f x +e \right)+2 A \left(\cos^{3}\left(f x +e \right)\right)-8 B \left(\cos^{3}\left(f x +e \right)\right)+4 A \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-20 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}{f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(-B*cos(f*x+e)^3*sin(f*x+e)-8*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+40*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*sin(f*x+e)+15*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^2*sin(f*x+e)+9*B*cos(f*x+e)^2*sin(f*x+e)-B*cos(f*x+e)^4+2*A-14*B+2*A*cos(f*x+e)^3-5*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3-3*A*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+4*A*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+6*B*sin(f*x+e)*cos(f*x+e)-20*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+10*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+6*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-30*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*cos(f*x+e)*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+5*B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+10*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+4*A*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-20*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+40*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+15*B*cos(f*x+e)^2+A*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))-A*cos(f*x+e)^2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*A*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+10*B*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*B*cos(f*x+e)^3-14*B*sin(f*x+e)+4*A*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-20*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-10*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-2*A*cos(f*x+e)+8*B*cos(f*x+e)-2*A*cos(f*x+e)^2+4*A*ln(2/(cos(f*x+e)+1))-20*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/(a*(1+sin(f*x+e)))^(5/2)","B"
190,1,606,135,0.644000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(8 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-A \sin \left(f x +e \right)+A \sin \left(f x +e \right) \cos \left(f x +e \right)+2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-A -3 B +B \sin \left(f x +e \right) \cos \left(f x +e \right)-4 B \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 B \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+3 B \left(\cos^{2}\left(f x +e \right)\right)+B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \left(\cos^{3}\left(f x +e \right)\right)-4 B \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+8 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 B \sin \left(f x +e \right)+2 B \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 B \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \cos \left(f x +e \right)-2 B \left(\cos^{3}\left(f x +e \right)\right)-4 B \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+A \left(\cos^{2}\left(f x +e \right)\right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}{f \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(8*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-A*sin(f*x+e)+A*sin(f*x+e)*cos(f*x+e)+3*B*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+2*B*cos(f*x+e)^2*sin(f*x+e)-A-3*B-B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^3+B*sin(f*x+e)*cos(f*x+e)-4*B*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*B*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-6*B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*ln(2/(cos(f*x+e)+1))*cos(f*x+e)^2*sin(f*x+e)+2*B*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-4*B*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*B*cos(f*x+e)^2+2*B*cos(f*x+e)^3*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*cos(f*x+e)^3-3*B*sin(f*x+e)-4*B*sin(f*x+e)*cos(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2+2*B*cos(f*x+e)+A*cos(f*x+e)^2-4*B*ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(3/2)/(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(a*(1+sin(f*x+e)))^(5/2)","B"
191,1,135,84,0.661000," ","int((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\sin \left(f x +e \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(A \left(\cos^{2}\left(f x +e \right)\right)+A \sin \left(f x +e \right) \cos \left(f x +e \right)+B \left(\cos^{2}\left(f x +e \right)\right)+B \sin \left(f x +e \right) \cos \left(f x +e \right)+2 A \cos \left(f x +e \right)-3 A \sin \left(f x +e \right)-B \sin \left(f x +e \right)-3 A -B \right)}{2 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/2/f*sin(f*x+e)*(-c*(sin(f*x+e)-1))^(1/2)*(A*cos(f*x+e)^2+A*sin(f*x+e)*cos(f*x+e)+B*cos(f*x+e)^2+B*sin(f*x+e)*cos(f*x+e)+2*A*cos(f*x+e)-3*A*sin(f*x+e)-B*sin(f*x+e)-3*A-B)/(a*(1+sin(f*x+e)))^(5/2)/(-1+cos(f*x+e)+sin(f*x+e))","A"
192,1,466,133,0.626000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(-A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 A \left(\cos^{2}\left(f x +e \right)\right)+2 B \sin \left(f x +e \right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 A \sin \left(f x +e \right)-2 A \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \sin \left(f x +e \right)-2 B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 A \right) \cos \left(f x +e \right)}{4 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/4/f*(-A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*A*cos(f*x+e)^2+2*B*sin(f*x+e)*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*A*sin(f*x+e)-2*A*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*sin(f*x+e)-2*B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*A)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
193,1,431,184,0.569000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 A \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+B \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-B \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-2 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 A \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-B \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+A \left(\cos^{2}\left(f x +e \right)\right)+3 B \left(\cos^{2}\left(f x +e \right)\right)-3 A \sin \left(f x +e \right)-B \sin \left(f x +e \right)-A -3 B \right) \cos \left(f x +e \right)}{8 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/8/f*(3*A*cos(f*x+e)^2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*A*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2+B*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^2*sin(f*x+e)-B*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)^2-2*A*cos(f*x+e)^2*sin(f*x+e)+3*A*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*A*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*B*cos(f*x+e)^2*sin(f*x+e)+B*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-B*cos(f*x+e)^2*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+A*cos(f*x+e)^2+3*B*cos(f*x+e)^2-3*A*sin(f*x+e)-B*sin(f*x+e)-A-3*B)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
194,1,151,215,0.602000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(3 A \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 A \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 B \left(\cos^{4}\left(f x +e \right)\right)+3 A \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 A \sin \left(f x +e \right)+2 B \right) \cos \left(f x +e \right)}{8 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/8/f*(3*A*cos(f*x+e)^4*ln((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*A*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*B*cos(f*x+e)^4+3*A*cos(f*x+e)^2*sin(f*x+e)+2*A*sin(f*x+e)+2*B)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
195,0,0,154,5.774000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^n,x)","F"
196,0,0,131,8.099000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","F"
197,0,0,131,8.309000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","F"
198,0,0,125,4.976000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x)","F"
199,0,0,105,2.533000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
200,0,0,111,1.087000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x)","F"
201,0,0,134,8.469000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c -c \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","F"
202,0,0,134,9.297000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c -c \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","F"
203,0,0,110,0.983000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","F"
204,0,0,110,1.115000," ","int((A+B*sin(f*x+e))*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","\int \frac{\left(A +B \sin \left(f x +e \right)\right) \left(c +c \sin \left(f x +e \right)\right)^{m}}{\sqrt{a -a \sin \left(f x +e \right)}}\, dx"," ",0,"int((A+B*sin(f*x+e))*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","F"
205,0,0,265,1.342000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x)","F"
206,0,0,160,1.282000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x)","F"
207,0,0,100,1.280000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \sqrt{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x)","F"
208,0,0,110,0.016000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x)","F"
209,0,0,122,1.006000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","F"
210,0,0,122,1.038000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","F"
211,0,0,259,5.935000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-4-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-m),x)","F"
212,0,0,187,6.181000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-3-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-m),x)","F"
213,0,0,112,5.410000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-2-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-m),x)","F"
214,0,0,141,2.870000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-m),x)","F"
215,0,0,136,4.367000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^m),x)","F"
216,0,0,146,3.809000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-m),x)","F"
217,0,0,147,6.070000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{2-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-m),x)","F"
218,0,0,34,8.038000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^n*(B*(3-n)-B*(4+n)*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{3} \left(c -c \sin \left(f x +e \right)\right)^{n} \left(B \left(3-n \right)-B \left(4+n \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^n*(B*(3-n)-B*(4+n)*sin(f*x+e)),x)","F"
219,0,0,34,8.063000," ","int((a-a*sin(f*x+e))^3*(c+c*sin(f*x+e))^n*(B*(3-n)+B*(4+n)*sin(f*x+e)),x)","\int \left(a -a \sin \left(f x +e \right)\right)^{3} \left(c +c \sin \left(f x +e \right)\right)^{n} \left(B \left(3-n \right)+B \left(4+n \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a-a*sin(f*x+e))^3*(c+c*sin(f*x+e))^n*(B*(3-n)+B*(4+n)*sin(f*x+e)),x)","F"
220,0,0,33,7.862000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3*(B*(m-3)-B*(4+m)*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{3} \left(B \left(m -3\right)-B \left(4+m \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3*(B*(m-3)-B*(4+m)*sin(f*x+e)),x)","F"
221,0,0,35,8.121000," ","int((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^3*(B*(m-3)+B*(4+m)*sin(f*x+e)),x)","\int \left(a -a \sin \left(f x +e \right)\right)^{m} \left(c +c \sin \left(f x +e \right)\right)^{3} \left(B \left(m -3\right)+B \left(4+m \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^3*(B*(m-3)+B*(4+m)*sin(f*x+e)),x)","F"
222,0,0,36,7.658000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(B*(m-n)-B*(n+m+1)*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n} \left(B \left(m -n \right)-B \left(n +m +1\right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(B*(m-n)-B*(n+m+1)*sin(f*x+e)),x)","F"
223,0,0,37,8.398000," ","int((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^n*(B*(m-n)+B*(n+m+1)*sin(f*x+e)),x)","\int \left(a -a \sin \left(f x +e \right)\right)^{m} \left(c +c \sin \left(f x +e \right)\right)^{n} \left(B \left(m -n \right)+B \left(n +m +1\right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^n*(B*(m-n)+B*(n+m+1)*sin(f*x+e)),x)","F"
224,1,158,126,0.597000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{\frac{a^{3} A \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{7}-2 a^{3} A \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+2 a^{3} A \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{a^{3} A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/7*a^3*A*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c)-2*a^3*A*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)+2*a^3*A*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-1/3*a^3*A*(2+sin(d*x+c)^2)*cos(d*x+c))","A"
225,1,136,109,0.497000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{-a^{3} A \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+\frac{2 a^{3} A \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}-\frac{2 a^{3} A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+a^{3} A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-a^3*A*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)+2/5*a^3*A*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)-2/3*a^3*A*(2+sin(d*x+c)^2)*cos(d*x+c)+a^3*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
226,1,117,86,0.401000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{\frac{a^{3} A \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}-2 a^{3} A \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+2 a^{3} A \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-a^{3} A \cos \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*a^3*A*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)-2*a^3*A*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+2*a^3*A*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-a^3*A*cos(d*x+c))","A"
227,1,89,74,0.406000," ","int((a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{-a^{3} A \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+\frac{2 a^{3} A \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}-2 a^{3} A \cos \left(d x +c \right)+a^{3} A \left(d x +c \right)}{d}"," ",0,"1/d*(-a^3*A*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+2/3*a^3*A*(2+sin(d*x+c)^2)*cos(d*x+c)-2*a^3*A*cos(d*x+c)+a^3*A*(d*x+c))","A"
228,1,99,74,0.433000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{A \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{3 d}+\frac{2 a^{3} A \cos \left(d x +c \right)}{3 d}+\frac{a^{3} A \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+a^{3} A x +\frac{a^{3} A c}{d}+\frac{a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*A*cos(d*x+c)*sin(d*x+c)^2*a^3+2/3*a^3*A*cos(d*x+c)/d+a^3*A*cos(d*x+c)*sin(d*x+c)/d+a^3*A*x+1/d*a^3*A*c+1/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))","A"
229,1,95,75,0.361000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{a^{3} A \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{3} A x}{2}-\frac{a^{3} A c}{2 d}+\frac{2 a^{3} A \cos \left(d x +c \right)}{d}+\frac{2 a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} A \cot \left(d x +c \right)}{d}"," ",0,"1/2*a^3*A*cos(d*x+c)*sin(d*x+c)/d-1/2*a^3*A*x-1/2/d*a^3*A*c+2*a^3*A*cos(d*x+c)/d+2/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))-a^3*A*cot(d*x+c)/d","A"
230,1,94,74,0.555000," ","int(csc(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{a^{3} A \cos \left(d x +c \right)}{d}-2 a^{3} A x -\frac{2 a^{3} A c}{d}-\frac{2 a^{3} A \cot \left(d x +c \right)}{d}-\frac{a^{3} A \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"a^3*A*cos(d*x+c)/d-2*a^3*A*x-2/d*a^3*A*c-2*a^3*A*cot(d*x+c)/d-1/2*a^3*A*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))","A"
231,1,103,76,0.526000," ","int(csc(d*x+c)^4*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","-a^{3} A x -\frac{a^{3} A c}{d}-\frac{a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} A \cot \left(d x +c \right) \csc \left(d x +c \right)}{d}-\frac{2 a^{3} A \cot \left(d x +c \right)}{3 d}-\frac{a^{3} A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-a^3*A*x-1/d*a^3*A*c-1/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))-a^3*A*cot(d*x+c)*csc(d*x+c)/d-2/3*a^3*A*cot(d*x+c)/d-1/3/d*a^3*A*cot(d*x+c)*csc(d*x+c)^2","A"
232,1,109,78,0.621000," ","int(csc(d*x+c)^5*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","-\frac{5 a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}+\frac{2 a^{3} A \cot \left(d x +c \right)}{3 d}-\frac{2 a^{3} A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} A \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}"," ",0,"-5/8/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))+2/3*a^3*A*cot(d*x+c)/d-2/3/d*a^3*A*cot(d*x+c)*csc(d*x+c)^2-1/4*a^3*A*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a^3*A*cot(d*x+c)*csc(d*x+c)/d","A"
233,1,132,95,0.715000," ","int(csc(d*x+c)^6*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{7 a^{3} A \cot \left(d x +c \right)}{15 d}+\frac{a^{3} A \cot \left(d x +c \right) \csc \left(d x +c \right)}{4 d}-\frac{a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{a^{3} A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} A \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{3} A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"7/15*a^3*A*cot(d*x+c)/d+1/4*a^3*A*cot(d*x+c)*csc(d*x+c)/d-1/4/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))-1/2*a^3*A*cot(d*x+c)*csc(d*x+c)^3/d-1/5/d*a^3*A*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^3*A*cot(d*x+c)*csc(d*x+c)^2","A"
234,1,155,118,0.732000," ","int(csc(d*x+c)^7*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x)","\frac{3 a^{3} A \cot \left(d x +c \right) \csc \left(d x +c \right)}{16 d}-\frac{3 a^{3} A \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}+\frac{4 a^{3} A \cot \left(d x +c \right)}{15 d}+\frac{2 a^{3} A \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 a^{3} A \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{a^{3} A \cot \left(d x +c \right) \left(\csc^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a^{3} A \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{24 d}"," ",0,"3/16*a^3*A*cot(d*x+c)*csc(d*x+c)/d-3/16/d*a^3*A*ln(csc(d*x+c)-cot(d*x+c))+4/15*a^3*A*cot(d*x+c)/d+2/15/d*a^3*A*cot(d*x+c)*csc(d*x+c)^2-2/5/d*a^3*A*cot(d*x+c)*csc(d*x+c)^4-1/6*a^3*A*cot(d*x+c)*csc(d*x+c)^5/d-5/24*a^3*A*cot(d*x+c)*csc(d*x+c)^3/d","A"
235,1,257,119,0.446000," ","int(sin(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","-\frac{A \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 A \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{19 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{4 A}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{10 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{18 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d*A/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-8/d*A/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/d*A/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-8/d*A/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2-19/d*A/a^3*arctan(tan(1/2*d*x+1/2*c))-16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4+4/3/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3-10/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2-18/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","B"
236,1,155,97,0.433000," ","int(sin(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{2 A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{8 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{4 A}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{6 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/d*A/a^3/(1+tan(1/2*d*x+1/2*c)^2)+8/d*A/a^3*arctan(tan(1/2*d*x+1/2*c))+16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5-8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4+4/3/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3+6/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
237,1,131,83,0.428000," ","int(sin(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","-\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{4 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{2 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/d*A/a^3*arctan(tan(1/2*d*x+1/2*c))-16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4-4/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3-2/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2-2/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
238,1,71,76,0.415000," ","int(sin(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{4 A \left(-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}\right)}{d \,a^{3}}"," ",0,"4/d*A/a^3*(-1/2/(tan(1/2*d*x+1/2*c)+1)^2-2/(tan(1/2*d*x+1/2*c)+1)^4+5/3/(tan(1/2*d*x+1/2*c)+1)^3+4/5/(tan(1/2*d*x+1/2*c)+1)^5)","A"
239,1,86,54,0.414000," ","int((A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{2 A \left(-\frac{8}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{14}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}\right)}{d \,a^{3}}"," ",0,"2/d*A/a^3*(-8/5/(tan(1/2*d*x+1/2*c)+1)^5+3/(tan(1/2*d*x+1/2*c)+1)^2-1/(tan(1/2*d*x+1/2*c)+1)+4/(tan(1/2*d*x+1/2*c)+1)^4-14/3/(tan(1/2*d*x+1/2*c)+1)^3)","A"
240,1,130,92,0.729000," ","int(csc(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{12 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{10 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/d*A/a^3*ln(tan(1/2*d*x+1/2*c))+16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5-8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4+12/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3-10/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
241,1,169,107,0.732000," ","int(csc(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{3} d}-\frac{A}{2 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{4 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{44 A}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{14 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{18 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2*A/a^3/d*tan(1/2*d*x+1/2*c)-1/2*A/a^3/d/tan(1/2*d*x+1/2*c)-4/d*A/a^3*ln(tan(1/2*d*x+1/2*c))-16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4-44/3/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3+14/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2-18/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
242,1,209,128,0.870000," ","int(csc(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{A \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}-\frac{2 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{3} d}-\frac{A}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 A}{a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{19 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{52 A}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{18 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{32 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/8/d*A/a^3*tan(1/2*d*x+1/2*c)^2-2*A/a^3/d*tan(1/2*d*x+1/2*c)-1/8/d*A/a^3/tan(1/2*d*x+1/2*c)^2+2*A/a^3/d/tan(1/2*d*x+1/2*c)+19/2/d*A/a^3*ln(tan(1/2*d*x+1/2*c))+16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5-8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4+52/3/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3-18/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2+32/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
243,1,249,145,0.826000," ","int(csc(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x)","\frac{A \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{3}}-\frac{A \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{39 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d}-\frac{A}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{A}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{39 A}{8 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{18 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{16 A}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{8 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{20 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{22 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{50 A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/24/d*A/a^3*tan(1/2*d*x+1/2*c)^3-1/2/d*A/a^3*tan(1/2*d*x+1/2*c)^2+39/8*A/a^3/d*tan(1/2*d*x+1/2*c)-1/24/d*A/a^3/tan(1/2*d*x+1/2*c)^3+1/2/d*A/a^3/tan(1/2*d*x+1/2*c)^2-39/8*A/a^3/d/tan(1/2*d*x+1/2*c)-18/d*A/a^3*ln(tan(1/2*d*x+1/2*c))-16/5/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^5+8/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^4-20/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^3+22/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)^2-50/d*A/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
244,1,422,315,0.525000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{-A \,c^{3} a \cos \left(f x +e \right)+3 A \,c^{2} d a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-A c \,d^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+A \,d^{3} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+B \,c^{3} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,c^{2} d a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B c \,d^{2} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{B \,d^{3} a \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+A \,c^{3} a \left(f x +e \right)-3 A \,c^{2} d a \cos \left(f x +e \right)+3 A c \,d^{2} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{A \,d^{3} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-B \,c^{3} a \cos \left(f x +e \right)+3 B \,c^{2} d a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B c \,d^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+B \,d^{3} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(-A*c^3*a*cos(f*x+e)+3*A*c^2*d*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-A*c*d^2*a*(2+sin(f*x+e)^2)*cos(f*x+e)+A*d^3*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+B*c^3*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*c^2*d*a*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*c*d^2*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/5*B*d^3*a*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+A*c^3*a*(f*x+e)-3*A*c^2*d*a*cos(f*x+e)+3*A*c*d^2*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*A*d^3*a*(2+sin(f*x+e)^2)*cos(f*x+e)-B*c^3*a*cos(f*x+e)+3*B*c^2*d*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*c*d^2*a*(2+sin(f*x+e)^2)*cos(f*x+e)+B*d^3*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e))","A"
245,1,274,203,0.408000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{-A \,c^{2} a \cos \left(f x +e \right)+2 A c d a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{A \,d^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+B \,c^{2} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 B c d a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+B \,d^{2} a \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+A \,c^{2} a \left(f x +e \right)-2 A c d a \cos \left(f x +e \right)+A \,d^{2} a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,c^{2} a \cos \left(f x +e \right)+2 B c d a \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{B \,d^{2} a \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-A*c^2*a*cos(f*x+e)+2*A*c*d*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*A*d^2*a*(2+sin(f*x+e)^2)*cos(f*x+e)+B*c^2*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*B*c*d*a*(2+sin(f*x+e)^2)*cos(f*x+e)+B*d^2*a*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+A*c^2*a*(f*x+e)-2*A*c*d*a*cos(f*x+e)+A*d^2*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*c^2*a*cos(f*x+e)+2*B*c*d*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*B*d^2*a*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
246,1,147,103,0.304000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{-\frac{B a d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+A a d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+B a c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+B a d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-A a c \cos \left(f x +e \right)-A a d \cos \left(f x +e \right)-B a c \cos \left(f x +e \right)+A a c \left(f x +e \right)}{f}"," ",0,"1/f*(-1/3*B*a*d*(2+sin(f*x+e)^2)*cos(f*x+e)+A*a*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+B*a*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+B*a*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-A*a*c*cos(f*x+e)-A*a*d*cos(f*x+e)-B*a*c*cos(f*x+e)+A*a*c*(f*x+e))","A"
247,1,59,44,0.157000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x)","\frac{a B \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a A \cos \left(f x +e \right)-a B \cos \left(f x +e \right)+a A \left(f x +e \right)}{f}"," ",0,"1/f*(a*B*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a*A*cos(f*x+e)-a*B*cos(f*x+e)+a*A*(f*x+e))","A"
248,1,294,93,0.404000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","-\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f d \sqrt{c^{2}-d^{2}}}+\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \sqrt{c^{2}-d^{2}}}+\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \sqrt{c^{2}-d^{2}}}-\frac{2 a B}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 a A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d}-\frac{2 a B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2}}+\frac{2 a B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d}"," ",0,"-2/f*a/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+2/f*a/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+2/f*a/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-2/f*a/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2/f*a/d*B/(1+tan(1/2*f*x+1/2*e)^2)+2/f*a/d*A*arctan(tan(1/2*f*x+1/2*e))-2/f*a/d^2*B*arctan(tan(1/2*f*x+1/2*e))*c+2/f*a/d*B*arctan(tan(1/2*f*x+1/2*e))","B"
249,1,434,119,0.493000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","-\frac{2 a d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}+\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a B c}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 a B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}"," ",0,"-2*a/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)/c*tan(1/2*f*x+1/2*e)*A+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*B-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A+2*a/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c+2*a/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-2*a/f/d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-2*a/f/d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+2*a/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+2*a/f*B/d^2*arctan(tan(1/2*f*x+1/2*e))","B"
250,1,2021,167,0.515000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{c^{2}-d^{2}}}-\frac{a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A d}{f \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{c^{2}-d^{2}}}-\frac{6 a c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A \,d^{3}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} c \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{3 a c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{3}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} c \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{5 a c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{2 a c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{3}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) c}+\frac{4 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{3}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) c}+\frac{2 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{4}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) c^{2}}+\frac{a c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{3 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{2 a A \,c^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{a A \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{2 a B \,c^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{2 a \,c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{2 a \,c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}-\frac{a \,c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{2 a A c d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{a B c d}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{a \,c^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{c^{2}-d^{2}}}-\frac{2 a \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B d}{f \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{c^{2}-d^{2}}}-\frac{4 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{6 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}+\frac{4 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B \,d^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right)}"," ",0,"-4*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^2*B*d^2+6*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*A*d^2+4*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*B*d^2-a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*B+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*A*c*d+a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*B*c*d+a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3*B+2*a/f/(c^3+c^2*d-c*d^2-d^3)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c-a/f/(c^3+c^2*d-c*d^2-d^3)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*d-6*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*B*d+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*A*d^3-3*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3*A*d+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3*A*d^3-5*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)*A*d-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3*B*d+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*c*tan(1/2*f*x+1/2*e)^2*A*d+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)/c*tan(1/2*f*x+1/2*e)^2*B*d^3+4*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)/c*tan(1/2*f*x+1/2*e)^2*A*d^3+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)/c^2*tan(1/2*f*x+1/2*e)^2*A*d^4+a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*c*tan(1/2*f*x+1/2*e)^2*B*d-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*A*c^2+a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*A*d^2-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*B*c^2+a/f/(c^3+c^2*d-c*d^2-d^3)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2*a/f/(c^3+c^2*d-c*d^2-d^3)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*d-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*c^2*tan(1/2*f*x+1/2*e)^2*A-2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*c^2*tan(1/2*f*x+1/2*e)^2*B+2*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3*A*d^2-3*a/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^2*A*d^2","B"
251,1,745,450,0.639000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{a^{2} A \,c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{2} A \,c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a^{2} A c \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{a^{2} A \,d^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-\frac{B \,a^{2} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 B \,a^{2} c^{2} d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 B \,a^{2} c \,d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+B \,a^{2} d^{3} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)-2 a^{2} A \,c^{3} \cos \left(f x +e \right)+6 a^{2} A \,c^{2} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-2 a^{2} A c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+2 a^{2} A \,d^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+2 B \,a^{2} c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-2 B \,a^{2} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+6 B \,a^{2} c \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 B \,a^{2} d^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+a^{2} A \,c^{3} \left(f x +e \right)-3 a^{2} A \,c^{2} d \cos \left(f x +e \right)+3 a^{2} A c \,d^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{a^{2} A \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-B \,a^{2} c^{3} \cos \left(f x +e \right)+3 B \,a^{2} c^{2} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+B \,a^{2} d^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(a^2*A*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*A*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^2*A*c*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/5*a^2*A*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-1/3*B*a^2*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^2*c^2*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/5*B*a^2*c*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+B*a^2*d^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-2*a^2*A*c^3*cos(f*x+e)+6*a^2*A*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a^2*A*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a^2*A*d^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+2*B*a^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*B*a^2*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+6*B*a^2*c*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/5*B*a^2*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*A*c^3*(f*x+e)-3*a^2*A*c^2*d*cos(f*x+e)+3*a^2*A*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^2*A*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)-B*a^2*c^3*cos(f*x+e)+3*B*a^2*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+B*a^2*d^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e))","A"
252,1,496,324,0.515000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{a^{2} A \,c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 a^{2} A c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} A \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{B \,a^{2} c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 B \,a^{2} c d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{B \,a^{2} d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-2 a^{2} A \,c^{2} \cos \left(f x +e \right)+4 a^{2} A c d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 a^{2} A \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 B \,a^{2} c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{4 B \,a^{2} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 B \,a^{2} d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+a^{2} A \,c^{2} \left(f x +e \right)-2 a^{2} A c d \cos \left(f x +e \right)+a^{2} A \,d^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{2} c^{2} \cos \left(f x +e \right)+2 B \,a^{2} c d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{B \,a^{2} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(a^2*A*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*a^2*A*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*A*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/3*B*a^2*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*B*a^2*c*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/5*B*a^2*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-2*a^2*A*c^2*cos(f*x+e)+4*a^2*A*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*a^2*A*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*B*a^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4/3*B*a^2*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+2*B*a^2*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+a^2*A*c^2*(f*x+e)-2*a^2*A*c*d*cos(f*x+e)+a^2*A*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^2*c^2*cos(f*x+e)+2*B*a^2*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*B*a^2*d^2*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
253,1,278,156,0.409000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{a^{2} A c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{a^{2} A d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-\frac{B \,a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+B \,a^{2} d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-2 a^{2} A c \cos \left(f x +e \right)+2 a^{2} A d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+2 B \,a^{2} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{2 B \,a^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} A c \left(f x +e \right)-a^{2} A d \cos \left(f x +e \right)-B \,a^{2} c \cos \left(f x +e \right)+B \,a^{2} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(a^2*A*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^2*A*d*(2+sin(f*x+e)^2)*cos(f*x+e)-1/3*B*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)+B*a^2*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2*a^2*A*c*cos(f*x+e)+2*a^2*A*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*B*a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*B*a^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*A*c*(f*x+e)-a^2*A*d*cos(f*x+e)-B*a^2*c*cos(f*x+e)+B*a^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
254,1,117,86,0.297000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x)","\frac{a^{2} A \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{B \,a^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a^{2} A \cos \left(f x +e \right)+2 B \,a^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{2} A \left(f x +e \right)-B \,a^{2} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*A*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*B*a^2*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a^2*A*cos(f*x+e)+2*B*a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*A*(f*x+e)-B*a^2*cos(f*x+e))","A"
255,1,713,160,0.430000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f d \sqrt{c^{2}-d^{2}}}+\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{3}}{f \,d^{3} \sqrt{c^{2}-d^{2}}}+\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \sqrt{c^{2}-d^{2}}}+\frac{a^{2} B \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{2} A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 a^{2} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{4 a^{2} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{a^{2} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{2} A}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 a^{2} B c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{4 a^{2} B}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c}{f \,d^{2}}+\frac{4 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f d}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2}}{f \,d^{3}}-\frac{4 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c}{f \,d^{2}}+\frac{3 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f d}"," ",0,"2/f*a^2/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-4/f*a^2/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+2/f*a^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-2/f*a^2/d^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3+4/f*a^2/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-2/f*a^2/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+1/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^3-2/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*A*tan(1/2*f*x+1/2*e)^2+2/f*a^2/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*c-4/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2-1/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)-2/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*A+2/f*a^2/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B*c-4/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)^2*B-2/f*a^2/d^2*arctan(tan(1/2*f*x+1/2*e))*A*c+4/f*a^2/d*arctan(tan(1/2*f*x+1/2*e))*A+2/f*a^2/d^3*arctan(tan(1/2*f*x+1/2*e))*B*c^2-4/f*a^2/d^2*arctan(tan(1/2*f*x+1/2*e))*B*c+3/f*a^2/d*arctan(tan(1/2*f*x+1/2*e))*B","B"
256,1,848,193,0.512000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{2} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}-\frac{2 a^{2} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{2} A c}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{2} A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{2} B \,c^{2}}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{2} B c}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f d \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{3}}{f \,d^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{6 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} B}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 a^{2} A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}-\frac{4 a^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{3}}+\frac{4 a^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}"," ",0,"2*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*A-2*a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)/c*tan(1/2*f*x+1/2*e)*A-2*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*c*tan(1/2*f*x+1/2*e)*B+2*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*B+2*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A*c-2*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A-2*a^2/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c^2+2*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c-2*a^2/f/d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-2*a^2/f/d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+4*a^2/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+4*a^2/f/d^3/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3-6*a^2/f/d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+2*a^2/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B-2*a^2/f/d^2*B/(1+tan(1/2*f*x+1/2*e)^2)+2*a^2/f/d^2*A*arctan(tan(1/2*f*x+1/2*e))-4*a^2/f/d^3*B*arctan(tan(1/2*f*x+1/2*e))*c+4*a^2/f/d^2*B*arctan(tan(1/2*f*x+1/2*e))","B"
257,1,1916,206,0.544000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","-\frac{a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{3}}{f \,d^{3} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{4 a^{2} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 a^{2} d^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right) c}-\frac{2 a^{2} d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} c \left(c^{2}+2 c d +d^{2}\right)}+\frac{7 a^{2} c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 a^{2} d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right) c^{2}}+\frac{2 a^{2} c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{8 a^{2} d^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right) c}+\frac{a^{2} c^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 a^{2} d^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right) c}+\frac{a^{2} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 a^{2} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 a^{2} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{3 a^{2} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{3 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{a^{2} B c}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 a^{2} A c}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{a^{2} d A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{a^{2} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{12 a^{2} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{12 a^{2} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 a^{2} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 a^{2} B \,c^{2}}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 a^{2} B \,c^{3}}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 a^{2} d \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{a^{2} d \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{8 a^{2} d \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 a^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{2 a^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{3}}"," ",0,"-a^2/f/d/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2*a^2/f/d^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3-2*a^2/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^3*A-4*a^2/f/d^2/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2+a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^3*B-8*a^2/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*A-2*a^2/f*d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*A+2*a^2/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*B+4*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*B-2*a^2/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*B-2*a^2/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+7*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c-4*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c+3*a^2/f/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A+a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^3*A+4*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^3*B-4*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*A+3*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*B-a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+12*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-12*a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-4*a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+4*a^2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^2+2*a^2/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^3-4*a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A-a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*A+8*a^2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*B+4*a^2/f/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+2*a^2/f*B/d^3*arctan(tan(1/2*f*x+1/2*e))","B"
258,1,1077,588,0.653000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{-\frac{a^{3} A \,c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-\frac{a^{3} A \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 B \,a^{3} c \,d^{2} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+3 a^{3} A \,c^{2} d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+9 B \,a^{3} c^{2} d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{B \,a^{3} d^{3} \left(\frac{16}{5}+\sin^{6}\left(f x +e \right)+\frac{6 \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(f x +e \right)\right)}{5}\right) \cos \left(f x +e \right)}{7}+9 B \,a^{3} c \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 B \,a^{3} d^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+9 a^{3} A c \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 a^{3} A \,d^{3} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-B \,a^{3} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B \,a^{3} d^{3} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+3 a^{3} A \,d^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+B \,a^{3} c^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+a^{3} A \,d^{3} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+B \,a^{3} d^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+3 B \,a^{3} c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{3} A \,c^{3} \left(f x +e \right)-3 a^{3} A \,c^{3} \cos \left(f x +e \right)+3 a^{3} A \,c^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{3} c^{3} \cos \left(f x +e \right)+9 a^{3} A \,c^{2} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+3 B \,a^{3} c^{2} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+3 a^{3} A c \,d^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-3 a^{3} A \,c^{2} d \cos \left(f x +e \right)-B \,a^{3} c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 a^{3} A \,c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-\frac{9 B \,a^{3} c \,d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-3 a^{3} A c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 B \,a^{3} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-\frac{3 a^{3} A c \,d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-\frac{3 B \,a^{3} c^{2} d \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}}{f}"," ",0,"1/f*(-B*a^3*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^3*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*A*c^3*(f*x+e)+3*B*a^3*d^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)-3*a^3*A*c^3*cos(f*x+e)+3*a^3*A*d^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+B*a^3*c^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3*a^3*A*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*A*d^3*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+B*a^3*d^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-B*a^3*c^3*cos(f*x+e)-3/5*a^3*A*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-B*a^3*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)-1/3*a^3*A*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)-1/3*a^3*A*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)-1/7*B*a^3*d^3*(16/5+sin(f*x+e)^6+6/5*sin(f*x+e)^4+8/5*sin(f*x+e)^2)*cos(f*x+e)+9*B*a^3*c*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/5*B*a^3*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+9*a^3*A*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*B*a^3*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+9*a^3*A*c*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3*a^3*A*c^2*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+9*B*a^3*c^2*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3*B*a^3*c*d^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+3*a^3*A*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^3*A*c^2*d*cos(f*x+e)-3*a^3*A*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)-9/5*B*a^3*c*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-3*a^3*A*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)-3*B*a^3*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)-3/5*a^3*A*c*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-3/5*B*a^3*c^2*d*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e))","A"
259,1,725,449,0.625000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{-\frac{a^{3} A \,c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 a^{3} A c d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{a^{3} A \,d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+B \,a^{3} c^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{2 B \,a^{3} c d \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+B \,a^{3} d^{2} \left(-\frac{\left(\sin^{5}\left(f x +e \right)+\frac{5 \left(\sin^{3}\left(f x +e \right)\right)}{4}+\frac{15 \sin \left(f x +e \right)}{8}\right) \cos \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)+3 a^{3} A \,c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-2 a^{3} A c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a^{3} A \,d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-B \,a^{3} c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+6 B \,a^{3} c d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{3 B \,a^{3} d^{2} \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}-3 a^{3} A \,c^{2} \cos \left(f x +e \right)+6 a^{3} A c d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{3} A \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B \,a^{3} c^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-2 B \,a^{3} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B \,a^{3} d^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+a^{3} A \,c^{2} \left(f x +e \right)-2 a^{3} A c d \cos \left(f x +e \right)+a^{3} A \,d^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{3} c^{2} \cos \left(f x +e \right)+2 B \,a^{3} c d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\frac{B \,a^{3} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-1/3*a^3*A*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a^3*A*c*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/5*a^3*A*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+B*a^3*c^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-2/5*B*a^3*c*d*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+B*a^3*d^2*(-1/6*(sin(f*x+e)^5+5/4*sin(f*x+e)^3+15/8*sin(f*x+e))*cos(f*x+e)+5/16*f*x+5/16*e)+3*a^3*A*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a^3*A*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^3*A*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-B*a^3*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)+6*B*a^3*c*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3/5*B*a^3*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-3*a^3*A*c^2*cos(f*x+e)+6*a^3*A*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*A*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^3*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*B*a^3*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^3*d^2*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+a^3*A*c^2*(f*x+e)-2*a^3*A*c*d*cos(f*x+e)+a^3*A*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^3*c^2*cos(f*x+e)+2*B*a^3*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*B*a^3*d^2*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
260,1,414,189,0.512000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{-\frac{a^{3} A c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{3} A d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+B \,a^{3} c \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-\frac{B \,a^{3} d \left(\frac{8}{3}+\sin^{4}\left(f x +e \right)+\frac{4 \left(\sin^{2}\left(f x +e \right)\right)}{3}\right) \cos \left(f x +e \right)}{5}+3 a^{3} A c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-a^{3} A d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-B \,a^{3} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 B \,a^{3} d \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)-3 a^{3} A c \cos \left(f x +e \right)+3 a^{3} A d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+3 B \,a^{3} c \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{3} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+a^{3} A c \left(f x +e \right)-a^{3} A d \cos \left(f x +e \right)-B \,a^{3} c \cos \left(f x +e \right)+B \,a^{3} d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(-1/3*a^3*A*c*(2+sin(f*x+e)^2)*cos(f*x+e)+a^3*A*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+B*a^3*c*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-1/5*B*a^3*d*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*a^3*A*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*A*d*(2+sin(f*x+e)^2)*cos(f*x+e)-B*a^3*c*(2+sin(f*x+e)^2)*cos(f*x+e)+3*B*a^3*d*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)-3*a^3*A*c*cos(f*x+e)+3*a^3*A*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*B*a^3*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^3*d*(2+sin(f*x+e)^2)*cos(f*x+e)+a^3*A*c*(f*x+e)-a^3*A*d*cos(f*x+e)-B*a^3*c*cos(f*x+e)+B*a^3*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
261,1,178,117,0.410000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x)","\frac{-\frac{a^{3} A \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)+3 a^{3} A \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-B \,a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 a^{3} A \cos \left(f x +e \right)+3 B \,a^{3} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)+a^{3} A \left(f x +e \right)-B \,a^{3} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-1/3*a^3*A*(2+sin(f*x+e)^2)*cos(f*x+e)+B*a^3*(-1/4*(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)+3/8*f*x+3/8*e)+3*a^3*A*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-B*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)-3*a^3*A*cos(f*x+e)+3*B*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*A*(f*x+e)-B*a^3*cos(f*x+e))","A"
262,1,1357,233,0.479000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","-\frac{6 a^{3} A}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{22 a^{3} B}{3 f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{3 a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 a^{3} A \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 a^{3} B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 a^{3} A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{16 a^{3} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{3 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{2 a^{3} A c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 a^{3} B \,c^{2}}{f \,d^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 a^{3} B c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2}}{f \,d^{3}}-\frac{7 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c}{f \,d^{2}}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,c^{2}}{f \,d^{3}}-\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c}{f \,d^{2}}-\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{3}}{f \,d^{4}}-\frac{2 a^{3} B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f \,d^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 a^{3} B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{4 a^{3} A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 a^{3} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f \,d^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{12 a^{3} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{3}}{f \,d^{3} \sqrt{c^{2}-d^{2}}}+\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f d \sqrt{c^{2}-d^{2}}}+\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{4}}{f \,d^{4} \sqrt{c^{2}-d^{2}}}-\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{3}}{f \,d^{3} \sqrt{c^{2}-d^{2}}}+\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \sqrt{c^{2}-d^{2}}}+\frac{2 a^{3} A \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{7 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f d}+\frac{5 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f d}+\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \sqrt{c^{2}-d^{2}}}"," ",0,"2/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^4*c-2/f*a^3/d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4*c^2+6/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4*c+4/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^2*c-4/f*a^3/d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2*c^2+12/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2*c+1/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B*c-16/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2-1/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A+6/f*a^3/d^3*arctan(tan(1/2*f*x+1/2*e))*B*c^2-7/f*a^3/d^2*arctan(tan(1/2*f*x+1/2*e))*B*c-3/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B+2/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*A*c-2/f*a^3/d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*B*c^2+2/f*a^3/d^3*arctan(tan(1/2*f*x+1/2*e))*A*c^2-6/f*a^3/d^2*arctan(tan(1/2*f*x+1/2*e))*A*c+6/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*B*c-2/f*a^3/d^4*arctan(tan(1/2*f*x+1/2*e))*B*c^3+1/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A+3/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B-6/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^4-6/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4-12/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^2-2/f*a^3/d^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^3+6/f*a^3/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-6/f*a^3/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+2/f*a^3/d^4/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^4-6/f*a^3/d^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3+6/f*a^3/d^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-2/f*a^3/d/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-1/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B*c+7/f*a^3/d*arctan(tan(1/2*f*x+1/2*e))*A+5/f*a^3/d*arctan(tan(1/2*f*x+1/2*e))*B-6/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*A-22/3/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^3*B+2/f*a^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A","B"
263,1,1534,272,0.555000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{2 a^{3} c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{4 a^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{3} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}+\frac{4 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{3}}{f \,d^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{8 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f d \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) c^{4} B}{f \,d^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{3}}{f \,d^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{8 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,d^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{10 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f d \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{4 a^{3} A c}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{3} B \,c^{3}}{f \,d^{3} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{4 a^{3} B \,c^{2}}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{3} B c}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{4 a^{3} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{3} A \,c^{2}}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 a^{3} A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 a^{3} B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{4 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c}{f \,d^{3}}+\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2}}{f \,d^{4}}-\frac{12 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c}{f \,d^{3}}+\frac{6 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 a^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{a^{3} B \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 a^{3} B c}{f \,d^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{a^{3} B \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A}{f \,d^{2}}+\frac{7 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B}{f \,d^{2}}-\frac{2 a^{3} A}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 a^{3} B}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 a^{3} A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}"," ",0,"-2*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)/c*tan(1/2*f*x+1/2*e)*A+2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*c^2*tan(1/2*f*x+1/2*e)*B-4*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*c*tan(1/2*f*x+1/2*e)*B+4*a^3/f/d^3/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^3-2*a^3/f/d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-8*a^3/f/d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c-6*a^3/f/d^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*c^4*B+6*a^3/f/d^3/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3+8*a^3/f/d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-10*a^3/f/d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*c*tan(1/2*f*x+1/2*e)*A+4*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A*c+2*a^3/f/d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c^3-4*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c^2+2*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c+4*a^3/f/d^3/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*c-2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A*c^2-a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)+4*a^3/f/d^3/(1+tan(1/2*f*x+1/2*e)^2)^2*B*c-4*a^3/f/d^3*arctan(tan(1/2*f*x+1/2*e))*A*c+6*a^3/f/d^4*arctan(tan(1/2*f*x+1/2*e))*B*c^2-12*a^3/f/d^3*arctan(tan(1/2*f*x+1/2*e))*B*c+6*a^3/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+2*a^3/f/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+4*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*A+2*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*B+a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^3-2*a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*A*tan(1/2*f*x+1/2*e)^2-6*a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2-2*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A-2*a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*A-6*a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*B+6*a^3/f/d^2*arctan(tan(1/2*f*x+1/2*e))*A+7*a^3/f/d^2*arctan(tan(1/2*f*x+1/2*e))*B","B"
264,1,2906,294,0.564000," ","int((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-3*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^3*B+2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*A+4*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*A-10*a^3/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*A-9*a^3/f/d/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-4*a^3/f/d^2/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-2*a^3/f*d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*A-4*a^3/f/d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^4*tan(1/2*f*x+1/2*e)^2*B-13*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^3/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+6*a^3/f/d^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3+a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^3*A-2*a^3/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^3*A-9*a^3/f/d^2/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*B-3*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^3*B-2*a^3/f/d^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^3-5*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-a^3/f/d/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+6*a^3/f/d^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*c^4*B-a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*B-2*a^3/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*B+7*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-2*a^3/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A-6*a^3/f/d^4*B*arctan(tan(1/2*f*x+1/2*e))*c-a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*A+22*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-5*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*B+11*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+5*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^3*A+6*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^3*B-2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^3+7*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^2+2*a^3/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c^3-4*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+7*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*A+14*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*B-16*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-4*a^3/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+4*a^3/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c^2-4*a^3/f/d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^4*B-a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c-5*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c+7*a^3/f/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+6*a^3/f/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B-2*a^3/f/d^3*B/(1+tan(1/2*f*x+1/2*e)^2)+2*a^3/f/d^3*A*arctan(tan(1/2*f*x+1/2*e))+6*a^3/f/d^3*B*arctan(tan(1/2*f*x+1/2*e))","B"
265,1,1110,212,0.437000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x)","-\frac{12 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2} d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{12 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{3 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{3 \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{\tan \left(\frac{f x}{2}+\frac{e}{2}\right) B \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 A c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 B \,c^{2} d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 B c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{\left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{\left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{2 A \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{4 A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{\tan \left(\frac{f x}{2}+\frac{e}{2}\right) A \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 A \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{2 A \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2} d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 B \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,c^{2} d}{a f}-\frac{6 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c \,d^{2}}{a f}-\frac{6 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2} d}{a f}+\frac{9 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c \,d^{2}}{a f}+\frac{6 A \,c^{2} d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 A c \,d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 B \,c^{2} d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 B c \,d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{10 B \,d^{3}}{3 a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{3 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{3}}{a f}+\frac{2 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{3}}{a f}-\frac{3 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{3}}{a f}-\frac{2 A \,c^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A \,d^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B \,c^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 B \,d^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-12/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2*c^2*d+12/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2*c*d^2-3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B*c*d^2+3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B*c*d^2-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^4*c*d^2-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4*c^2*d+6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4*c*d^2-12/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^2*c*d^2+1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*B*d^3-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*c*d^2-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*c^2*d+6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*c*d^2+6/a/f*arctan(tan(1/2*f*x+1/2*e))*A*c^2*d-6/a/f*arctan(tan(1/2*f*x+1/2*e))*A*c*d^2-6/a/f*arctan(tan(1/2*f*x+1/2*e))*B*c^2*d+9/a/f*arctan(tan(1/2*f*x+1/2*e))*B*c*d^2+6/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c^2*d-6/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c*d^2-6/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c^2*d+6/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c*d^2+1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*A*d^3-1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*B*d^3+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^4*d^3-2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^4*d^3+4/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*tan(1/2*f*x+1/2*e)^2*d^3-8/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*tan(1/2*f*x+1/2*e)^2*d^3-1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*A*d^3-10/3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*B*d^3+3/a/f*arctan(tan(1/2*f*x+1/2*e))*A*d^3+2/a/f*arctan(tan(1/2*f*x+1/2*e))*B*c^3-3/a/f*arctan(tan(1/2*f*x+1/2*e))*B*d^3-2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c^3+2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*d^3+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*A*d^3+2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c^3-2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*d^3","B"
266,1,524,139,0.416000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x)","\frac{B \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{4 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{B \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 A \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{4 B c d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 B \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c d}{a f}-\frac{2 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{2}}{a f}+\frac{2 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2}}{a f}-\frac{4 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c d}{a f}+\frac{3 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{2}}{a f}-\frac{2 A \,c^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A c d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 A \,d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B \,c^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4 B c d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B \,d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^3*d^2-2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A*tan(1/2*f*x+1/2*e)^2*d^2-4/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*c*d+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*d^2-1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)*d^2-2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A*d^2-4/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*c*d+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*d^2+4/a/f*arctan(tan(1/2*f*x+1/2*e))*A*c*d-2/a/f*arctan(tan(1/2*f*x+1/2*e))*A*d^2+2/a/f*arctan(tan(1/2*f*x+1/2*e))*B*c^2-4/a/f*arctan(tan(1/2*f*x+1/2*e))*B*c*d+3/a/f*arctan(tan(1/2*f*x+1/2*e))*B*d^2-2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c^2+4/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c*d-2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*d^2+2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c^2-4/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c*d+2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*d^2","B"
267,1,179,67,0.360000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x)","-\frac{2 B d}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d}{a f}+\frac{2 B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a f}-\frac{2 B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d}{a f}-\frac{2 A c}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B c}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 B d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/a/f*B*d/(1+tan(1/2*f*x+1/2*e)^2)+2/a/f*A*arctan(tan(1/2*f*x+1/2*e))*d+2/a/f*B*arctan(tan(1/2*f*x+1/2*e))*c-2/a/f*B*arctan(tan(1/2*f*x+1/2*e))*d-2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*c+2/a/f/(tan(1/2*f*x+1/2*e)+1)*A*d+2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*c-2/a/f/(tan(1/2*f*x+1/2*e)+1)*B*d","B"
268,1,65,35,0.227000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\frac{2 B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f}-\frac{2 A}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2/a/f*B*arctan(tan(1/2*f*x+1/2*e))-2/a/f/(tan(1/2*f*x+1/2*e)+1)*A+2/a/f/(tan(1/2*f*x+1/2*e)+1)*B","A"
269,1,176,96,0.545000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x)","-\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A d}{a f \left(c -d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{a f \left(c -d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 A}{a f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B}{a f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/a/f/(c-d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*d+2/a/f/(c-d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2/a/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)*A+2/a/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)*B","A"
270,1,615,176,0.576000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","-\frac{2 d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{a f \left(c -d \right)^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}+\frac{2 d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{a f \left(c -d \right)^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 d^{2} A}{a f \left(c -d \right)^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 d B c}{a f \left(c -d \right)^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{4 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c d}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,d^{2}}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c d}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,d^{2}}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 A}{a f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B}{a f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d^3/(c+d)/c*tan(1/2*f*x+1/2*e)*A+2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d^2/(c+d)*tan(1/2*f*x+1/2*e)*B-2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d^2/(c+d)*A+2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d/(c+d)*B*c-4/a/f/(c-d)^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c*d-2/a/f/(c-d)^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*d^2+2/a/f/(c-d)^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2+2/a/f/(c-d)^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c*d+2/a/f/(c-d)^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*d^2-2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*A+2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*B","B"
271,1,2482,274,0.559000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-4/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^5/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*A+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^6/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*A+4/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*B+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*B+9/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*B+6/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+11/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-7/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^5/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+4/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*B-6/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-11/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*A-6/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2/(c^2+2*c*d+d^2)*A*c^2-2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3/(c^2+2*c*d+d^2)*A*c+4/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d/(c^2+2*c*d+d^2)*B*c^3+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2/(c^2+2*c*d+d^2)*B*c^2+1/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3/(c^2+2*c*d+d^2)*B*c+4/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A-3/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*d^3+2/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3+2/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*d^3+1/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^4/(c^2+2*c*d+d^2)*A+5/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B+4/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2*d+7/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c*d^2-6/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c*d^2+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^5/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*B-17/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^5/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-6/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*A-6/a/f/(c-d)^3/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2*d-2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d^3/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*A+2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*B-2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A","B"
272,1,946,218,0.427000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x)","\frac{6 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A c \,d^{2}}{a^{2} f}+\frac{6 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,c^{2}}{a^{2} f}-\frac{12 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B c \,d^{2}}{a^{2} f}-\frac{6 B c \,d^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{B \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 A \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 B \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{B \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 B \,d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{2 A \,d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 A \,c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{6 A c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{6 B \,c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 B c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 A \,c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 A c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 B \,c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{6 A c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 B \,c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{12 B c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 A \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B \,c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 B \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A \,c^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) A \,d^{3}}{a^{2} f}+\frac{7 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) B \,d^{3}}{a^{2} f}-\frac{2 A \,c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4 A \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 B \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A \,c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 A \,d^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,c^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 B \,d^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-6/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*c*d^2+6/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A*c*d^2+6/a^2/f*d*arctan(tan(1/2*f*x+1/2*e))*B*c^2-12/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B*c*d^2+1/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^3*d^3-2/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A*tan(1/2*f*x+1/2*e)^2*d^3-6/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*c*d^2+4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*d^3-2/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*A*d^3-6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^2*d+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c*d^2+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c^2*d-6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c*d^2+4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^2*d-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c*d^2-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^2*d+4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c*d^2+4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)^2*d^3-1/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*B*tan(1/2*f*x+1/2*e)*d^3+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*c*d^2+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*c^2*d-12/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*c*d^2-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*d^3-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c^3+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*d^3-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^3-4/a^2/f*arctan(tan(1/2*f*x+1/2*e))*A*d^3+7/a^2/f*arctan(tan(1/2*f*x+1/2*e))*B*d^3-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*c^3-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*d^3+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*d^3+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^3+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*d^3+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^3-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*d^3","B"
273,1,489,126,0.414000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x)","-\frac{2 B \,d^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a^{2} f}+\frac{4 d B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f}-\frac{4 B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a^{2} f}-\frac{2 A \,c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 B c d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4 B \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A \,c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A c d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 A \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B \,c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 B c d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A \,c^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 A c d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 A \,d^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,c^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 B c d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,d^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-2/a^2/f*B*d^2/(1+tan(1/2*f*x+1/2*e)^2)+2/a^2/f*A*arctan(tan(1/2*f*x+1/2*e))*d^2+4/a^2/f*d*B*arctan(tan(1/2*f*x+1/2*e))*c-4/a^2/f*B*arctan(tan(1/2*f*x+1/2*e))*d^2-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*c^2+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*d^2+4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*c*d-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*d^2+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^2-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c*d+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*d^2-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c^2+4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c*d-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*d^2-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^2+8/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c*d-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*d^2+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^2-8/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c*d+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*d^2","B"
274,1,252,81,0.431000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","\frac{2 B d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{2 A c}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 A c}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 A d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B c}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 B d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A c}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 A d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B c}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 B d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"2/a^2/f*B*d*arctan(tan(1/2*f*x+1/2*e))-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*A*c+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*B*d+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*A*d-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*B*d-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*A*d+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*B*d","B"
275,1,70,61,0.330000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","\frac{-\frac{2 \left(2 A -2 B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{-2 A +2 B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}}{f \,a^{2}}"," ",0,"2/f/a^2*(-1/3*(2*A-2*B)/(tan(1/2*f*x+1/2*e)+1)^3-A/(tan(1/2*f*x+1/2*e)+1)-1/2*(-2*A+2*B)/(tan(1/2*f*x+1/2*e)+1)^2)","A"
276,1,327,143,0.561000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x)","\frac{2 d^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \,a^{2} \left(c -d \right)^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 d \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f \,a^{2} \left(c -d \right)^{2} \sqrt{c^{2}-d^{2}}}+\frac{2 A}{f \,a^{2} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B}{f \,a^{2} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A}{3 f \,a^{2} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B}{3 f \,a^{2} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 A c}{f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A d}{f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 B d}{f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2/f/a^2*d^2/(c-d)^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-2/f/a^2*d/(c-d)^2/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+2/f/a^2/(c-d)/(tan(1/2*f*x+1/2*e)+1)^2*A-2/f/a^2/(c-d)/(tan(1/2*f*x+1/2*e)+1)^2*B-4/3/f/a^2/(c-d)/(tan(1/2*f*x+1/2*e)+1)^3*A+4/3/f/a^2/(c-d)/(tan(1/2*f*x+1/2*e)+1)^3*B-2/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*A*c+4/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*A*d-2/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*B*d","B"
277,1,770,264,0.554000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x)","\frac{2 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \,a^{2} \left(c -d \right)^{3} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}-\frac{2 d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \,a^{2} \left(c -d \right)^{3} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 d^{3} A}{f \,a^{2} \left(c -d \right)^{3} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 d^{2} B c}{f \,a^{2} \left(c -d \right)^{3} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{6 d^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f \,a^{2} \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{4 d^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \,a^{2} \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{4 d \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,a^{2} \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{4 d^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f \,a^{2} \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 d^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \,a^{2} \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 A}{f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B}{f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 A}{3 f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B}{3 f \,a^{2} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 A c}{f \,a^{2} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 A d}{f \,a^{2} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4 B d}{f \,a^{2} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2/f/a^2/(c-d)^3*d^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)/c*tan(1/2*f*x+1/2*e)*A-2/f/a^2/(c-d)^3*d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*B+2/f/a^2/(c-d)^3*d^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A-2/f/a^2/(c-d)^3*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c+6/f/a^2/(c-d)^3*d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+4/f/a^2/(c-d)^3*d^3/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-4/f/a^2/(c-d)^3*d/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2-4/f/a^2/(c-d)^3*d^2/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-2/f/a^2/(c-d)^3*d^3/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+2/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*A-2/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*B-4/3/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*A+4/3/f/a^2/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*B-2/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A*c+6/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A*d-4/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*B*d","B"
278,1,2641,373,0.586000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-4/f/a^2*d^4/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B-1/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c+4/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+15/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*A-8/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*B+12/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-4/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+8/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c^2+4/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c-6/f/a^2*d^2/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^3+7/f/a^2*d^4/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A-4/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^2-2/f/a^2/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*A*c+8/f/a^2/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*A*d-6/f/a^2/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*B*d+2/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*A-2/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*B-4/3/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*A-4/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*B-13/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*B-2/f/a^2*d^6/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*B+23/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-13/f/a^2*d^3/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+9/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A-2/f/a^2*d^6/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A-7/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B-4/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B+8/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*A-2/f/a^2*d^6/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A-1/f/a^2*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A-17/f/a^2*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+16/f/a^2*d^3/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+4/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*A+8/f/a^2*d^6/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*A-2/f/a^2*d^7/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*A-6/f/a^2*d^2/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*B-12/f/a^2*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-6/f/a^2*d/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3-12/f/a^2*d^2/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2+12/f/a^2*d^2/(c-d)^4/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2+4/3/f/a^2/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*B","B"
279,1,936,217,0.434000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x)","\frac{6 d^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f}+\frac{6 B c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{24 B \,c^{2} d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{24 B c \,d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{6 A \,c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 B \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 A \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 B \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 A \,c^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 A \,d^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 B \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{4 B \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 A \,c^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 A \,d^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 B \,c^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{8 B \,d^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{2 d^{3} A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}+\frac{6 B c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{12 A \,c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 A c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 B \,c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{12 A \,c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{2 A \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{12 A c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{12 B \,c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{12 B c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{24 A \,c^{2} d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{24 A c \,d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 d^{3} B}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{6 d^{3} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 A \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A \,c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{4 A \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}"," ",0,"6/a^3/f*d^2*B*arctan(tan(1/2*f*x+1/2*e))*c+6/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B*c*d^2-24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*c^2*d+24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*c*d^2-6/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^2*d-6/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B*d^3+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^3+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A*d^3-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c^3-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B*d^3-16/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^3+4/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*d^3+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^3-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*c^3+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*d^3-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*c^3+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*d^3+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*c^3-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*d^3-2/a^3/f*d^3*B/(1+tan(1/2*f*x+1/2*e)^2)+2/a^3/f*d^3*A*arctan(tan(1/2*f*x+1/2*e))+6/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c*d^2+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^2*d-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c*d^2-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^2*d+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c*d^2-12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*c^2*d+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A*d^3+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*c*d^2+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*c^2*d-12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*c*d^2+24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*c^2*d-24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*c*d^2-6/a^3/f*d^3*B*arctan(tan(1/2*f*x+1/2*e))-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A*c^3+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*c^3-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*d^3","B"
280,1,617,158,0.418000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x)","-\frac{2 B \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 B \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 B \,d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 A \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 B \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 A \,c^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{8 A \,d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 B \,c^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 B \,d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16 A \,c^{2}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 A \,d^{2}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B \,d^{2}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 A \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{4 A \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{16 B c d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{4 B \,c^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{8 A c d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{16 B c d}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 A c d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 A c d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{8 B c d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{16 A c d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}"," ",0,"-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B*c^2+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*B*d^2+2/a^3/f*B*d^2*arctan(tan(1/2*f*x+1/2*e))-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*A*c^2+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*B*d^2+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c^2-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*d^2-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*c^2-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*d^2+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*c^2+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*d^2-16/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c^2-8/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*d^2+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c^2+4/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*d^2+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*c^2+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*d^2-16/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*B*c*d-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*c^2+8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*A*c*d-16/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*B*c*d-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*A*c*d-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*A*c*d+8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*B*c*d+16/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*A*c*d","B"
281,1,151,121,0.439000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\frac{-\frac{2 \left(8 A c -6 A d -6 B c +4 B d \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{-8 A c +8 A d +8 B c -8 B d}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{-4 A c +2 A d +2 B c}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(4 A c -4 A d -4 B c +4 B d \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 A c}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3}}"," ",0,"2/f/a^3*(-1/3*(8*A*c-6*A*d-6*B*c+4*B*d)/(tan(1/2*f*x+1/2*e)+1)^3-1/4*(-8*A*c+8*A*d+8*B*c-8*B*d)/(tan(1/2*f*x+1/2*e)+1)^4-1/2*(-4*A*c+2*A*d+2*B*c)/(tan(1/2*f*x+1/2*e)+1)^2-1/5*(4*A*c-4*A*d-4*B*c+4*B*d)/(tan(1/2*f*x+1/2*e)+1)^5-A*c/(tan(1/2*f*x+1/2*e)+1))","A"
282,1,114,96,0.324000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\frac{-\frac{2 \left(8 A -6 B \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 \left(4 A -4 B \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 A}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{-4 A +2 B}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{-8 A +8 B}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}}{f \,a^{3}}"," ",0,"2/f/a^3*(-1/3*(8*A-6*B)/(tan(1/2*f*x+1/2*e)+1)^3-1/5*(4*A-4*B)/(tan(1/2*f*x+1/2*e)+1)^5-A/(tan(1/2*f*x+1/2*e)+1)-1/2*(-4*A+2*B)/(tan(1/2*f*x+1/2*e)+1)^2-1/4*(-8*A+8*B)/(tan(1/2*f*x+1/2*e)+1)^4)","A"
283,1,606,218,0.540000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x)","-\frac{2 d^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \,a^{3} \left(c -d \right)^{3} \sqrt{c^{2}-d^{2}}}+\frac{2 d^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f \,a^{3} \left(c -d \right)^{3} \sqrt{c^{2}-d^{2}}}+\frac{4 A}{f \,a^{3} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{4 B}{f \,a^{3} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 A}{5 f \,a^{3} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 B}{5 f \,a^{3} \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{4 A c}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 A d}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B c}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 B d}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 A c}{3 f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{20 A d}{3 f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B c}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{16 B d}{3 f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 A \,c^{2}}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 A c d}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 A \,d^{2}}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 B \,d^{2}}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/f/a^3*d^3/(c-d)^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+2/f/a^3*d^2/(c-d)^3/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+4/f/a^3/(c-d)/(tan(1/2*f*x+1/2*e)+1)^4*A-4/f/a^3/(c-d)/(tan(1/2*f*x+1/2*e)+1)^4*B-8/5/f/a^3/(c-d)/(tan(1/2*f*x+1/2*e)+1)^5*A+8/5/f/a^3/(c-d)/(tan(1/2*f*x+1/2*e)+1)^5*B+4/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*A*c-6/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*A*d-2/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*B*c+4/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*B*d-16/3/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*A*c+20/3/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*A*d+4/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*B*c-16/3/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*B*d-2/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A*c^2+6/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A*c*d-6/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*A*d^2+2/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*B*d^2","B"
284,1,1049,368,0.570000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x)","-\frac{6 d^{4} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A}{f \,a^{3} \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 d^{4} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B}{f \,a^{3} \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B}{f \,a^{3} \left(c -d \right)^{4} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{2 d^{3} B c}{f \,a^{3} \left(c -d \right)^{4} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}-\frac{2 d^{4} A}{f \,a^{3} \left(c -d \right)^{4} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right)}+\frac{6 B \,d^{2}}{f \,a^{3} \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A c}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 A d}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 B c}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{6 B d}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8 A c d}{f \,a^{3} \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{16 A c}{3 f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 A d}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 B c}{f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{20 B d}{3 f \,a^{3} \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 A \,c^{2}}{f \,a^{3} \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{12 A \,d^{2}}{f \,a^{3} \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 A}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 d^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A c}{f \,a^{3} \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{6 d^{2} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,c^{2}}{f \,a^{3} \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{6 d^{3} \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B c}{f \,a^{3} \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A}{f \,a^{3} \left(c -d \right)^{4} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c +d \right) c}-\frac{8 A}{5 f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 B}{5 f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{4 B}{f \,a^{3} \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}"," ",0,"2/f/a^3*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*tan(1/2*f*x+1/2*e)*B-6/f/a^3*d^4/(c-d)^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+2/f/a^3*d^4/(c-d)^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+2/f/a^3*d^3/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*B*c+6/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*B*d^2+4/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*A*c-8/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*A*d-2/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*B*c+6/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*B*d-2/f/a^3*d^4/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)*A+8/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*A*c*d-16/3/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*A*c+8/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*A*d+4/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*B*c-20/3/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*B*d-2/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*A*c^2-12/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*A*d^2+4/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^4*A-2/f/a^3*d^5/(c-d)^4/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)/c*tan(1/2*f*x+1/2*e)*A-8/f/a^3*d^3/(c-d)^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+6/f/a^3*d^2/(c-d)^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2+6/f/a^3*d^3/(c-d)^4/(c+d)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c-8/5/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^5*A+8/5/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^5*B-4/f/a^3/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^4*B","B"
285,1,2918,493,0.650000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-10/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c^2-19/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*A-6/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A*c-6/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+8/f/a^3*d^3/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^3+6/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c^2-18/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+4/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B-13/f/a^3*d^5/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A+6/f/a^3*d^5/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B+12/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2*B+1/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*B*c-2/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*B*c+8/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*B*d-16/3/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*A*c+28/3/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*A*d+4/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*B*c-8/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*B*d-2/f/a^3/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*A*c^2-20/f/a^3/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*A*d^2+2/f/a^3*d^7/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+23/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+18/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*B+24/f/a^3*d^3/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^2+1/f/a^3*d^6/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*A+10/f/a^3/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*A*c*d+2/f/a^3*d^7/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*B-29/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*A+12/f/a^3*d^2/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c^3-20/f/a^3*d^3/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c^2-12/f/a^3*d^7/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^2*A-30/f/a^3*d^4/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*c+21/f/a^3*d^4/(c-d)^5/(c^2+2*c*d+d^2)/(c^2-d^2)^(1/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*c+2/f/a^3*d^8/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*A+8/f/a^3*d^3/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^3*tan(1/2*f*x+1/2*e)^2*B+6/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*B-11/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+2/f/a^3*d^7/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*A+9/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B+6/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3*B-10/f/a^3*d^4/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c^2*tan(1/2*f*x+1/2*e)^2*A-6/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*A+17/f/a^3*d^5/(c-d)^5/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)^2*B+12/f/a^3/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*B*d^2+4/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*A*c-10/f/a^3/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*A*d+4/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^4*A-4/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^4*B-8/5/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^5*A+8/5/f/a^3/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^5*B","B"
286,1,242,236,1.400000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3*(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a \left(\sin \left(f x +e \right)-1\right) \left(\left(-45 A \,d^{3}-135 B c \,d^{2}-40 B \,d^{3}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(315 A \,c^{2} d +252 A c \,d^{2}+117 A \,d^{3}+105 B \,c^{3}+252 B \,c^{2} d +351 B c \,d^{2}+104 B \,d^{3}\right) \sin \left(f x +e \right)+35 B \left(\cos^{4}\left(f x +e \right)\right) d^{3}+\left(-189 A c \,d^{2}-54 A \,d^{3}-189 B \,c^{2} d -162 B c \,d^{2}-118 B \,d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)+315 A \,c^{3}+630 A \,c^{2} d +693 A c \,d^{2}+198 A \,d^{3}+210 B \,c^{3}+693 B \,c^{2} d +594 B c \,d^{2}+211 B \,d^{3}\right)}{315 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/315*(1+sin(f*x+e))*a*(sin(f*x+e)-1)*((-45*A*d^3-135*B*c*d^2-40*B*d^3)*sin(f*x+e)*cos(f*x+e)^2+(315*A*c^2*d+252*A*c*d^2+117*A*d^3+105*B*c^3+252*B*c^2*d+351*B*c*d^2+104*B*d^3)*sin(f*x+e)+35*B*cos(f*x+e)^4*d^3+(-189*A*c*d^2-54*A*d^3-189*B*c^2*d-162*B*c*d^2-118*B*d^3)*cos(f*x+e)^2+315*A*c^3+630*A*c^2*d+693*A*c*d^2+198*A*d^3+210*B*c^3+693*B*c^2*d+594*B*c*d^2+211*B*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
287,1,161,176,1.437000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2*(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a \left(\sin \left(f x +e \right)-1\right) \left(-15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d^{2}+\left(70 A c d +28 A \,d^{2}+35 B \,c^{2}+56 B c d +39 B \,d^{2}\right) \sin \left(f x +e \right)+\left(-21 A \,d^{2}-42 B c d -18 B \,d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+105 A \,c^{2}+140 A c d +77 A \,d^{2}+70 B \,c^{2}+154 B c d +66 B \,d^{2}\right)}{105 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/105*(1+sin(f*x+e))*a*(sin(f*x+e)-1)*(-15*B*cos(f*x+e)^2*sin(f*x+e)*d^2+(70*A*c*d+28*A*d^2+35*B*c^2+56*B*c*d+39*B*d^2)*sin(f*x+e)+(-21*A*d^2-42*B*c*d-18*B*d^2)*cos(f*x+e)^2+105*A*c^2+140*A*c*d+77*A*d^2+70*B*c^2+154*B*c*d+66*B*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
288,1,102,106,1.362000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a \left(\sin \left(f x +e \right)-1\right) \left(3 B \left(\sin^{2}\left(f x +e \right)\right) d +5 A \sin \left(f x +e \right) d +5 B \sin \left(f x +e \right) c +4 B \sin \left(f x +e \right) d +15 A c +10 A d +10 B c +8 B d \right)}{15 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/15*(1+sin(f*x+e))*a*(sin(f*x+e)-1)*(3*B*sin(f*x+e)^2*d+5*A*sin(f*x+e)*d+5*B*sin(f*x+e)*c+4*B*sin(f*x+e)*d+15*A*c+10*A*d+10*B*c+8*B*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
289,1,58,54,1.019000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a \left(\sin \left(f x +e \right)-1\right) \left(B \sin \left(f x +e \right)+3 A +2 B \right)}{3 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/3*(1+sin(f*x+e))*a*(sin(f*x+e)-1)*(B*sin(f*x+e)+3*A+2*B)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
290,1,139,84,1.787000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x)","-\frac{2 \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a d -B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a c +B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\right)}{d \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a*d-B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a*c+B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2))/d/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
291,1,274,110,2.019000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a d \left(A d +B c +2 B d \right)+A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d +B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{2}+2 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d +A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, d -B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c \right)}{d \left(c +d \right) \left(c +d \sin \left(f x +e \right)\right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*d*(A*d+B*c+2*B*d)+A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d+B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2+2*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d+A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*d-B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c)/d/(c+d)/(c+d*sin(f*x+e))/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
292,1,628,168,2.426000," ","int((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x)","\frac{\left(-2 \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c d \left(3 A d +B c +4 B d \right)+\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{2} \left(3 A d +B c +4 B d \right) \left(\cos^{2}\left(f x +e \right)\right)+3 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{2}-3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d -3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{3}+B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c d +4 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{2}-a^{2} \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) B \,c^{3}-4 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d -B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{2}-4 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{3}-5 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c d -5 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{2}+B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2}-3 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c d -4 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{2}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(1+\sin \left(f x +e \right)\right)}{4 a \sqrt{a \left(c +d \right) d}\, \left(c +d \sin \left(f x +e \right)\right)^{2} \left(c +d \right)^{2} d \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/4/a*(-2*sin(f*x+e)*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d*(3*A*d+B*c+4*B*d)+arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^2*(3*A*d+B*c+4*B*d)*cos(f*x+e)^2+3*A*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^2-3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d-3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^3+B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d+4*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^2-a^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*B*c^3-4*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d-B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^2-4*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^3-5*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d-5*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^2+B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2-3*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d-4*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^2)*(-a*(sin(f*x+e)-1))^(1/2)*(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/d/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
293,1,312,350,1.369000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{2} \left(\sin \left(f x +e \right)-1\right) \left(315 B \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) d^{3}+\left(-1485 A c \,d^{2}-935 A \,d^{3}-1485 B \,c^{2} d -2805 B c \,d^{2}-1470 B \,d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(1155 A \,c^{3}+6237 A \,c^{2} d +6633 A c \,d^{2}+2431 A \,d^{3}+2079 B \,c^{3}+6633 B \,c^{2} d +7293 B c \,d^{2}+2499 B \,d^{3}\right) \sin \left(f x +e \right)+\left(385 A \,d^{3}+1155 B c \,d^{2}+735 B \,d^{3}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-2079 A \,c^{2} d -3861 A c \,d^{2}-1892 A \,d^{3}-693 B \,c^{3}-3861 B \,c^{2} d -5676 B c \,d^{2}-2478 B \,d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)+5775 A \,c^{3}+14553 A \,c^{2} d +14157 A c \,d^{2}+4499 A \,d^{3}+4851 B \,c^{3}+14157 B \,c^{2} d +13497 B c \,d^{2}+4431 B \,d^{3}\right)}{3465 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/3465*(1+sin(f*x+e))*a^2*(sin(f*x+e)-1)*(315*B*cos(f*x+e)^4*sin(f*x+e)*d^3+(-1485*A*c*d^2-935*A*d^3-1485*B*c^2*d-2805*B*c*d^2-1470*B*d^3)*cos(f*x+e)^2*sin(f*x+e)+(1155*A*c^3+6237*A*c^2*d+6633*A*c*d^2+2431*A*d^3+2079*B*c^3+6633*B*c^2*d+7293*B*c*d^2+2499*B*d^3)*sin(f*x+e)+(385*A*d^3+1155*B*c*d^2+735*B*d^3)*cos(f*x+e)^4+(-2079*A*c^2*d-3861*A*c*d^2-1892*A*d^3-693*B*c^3-3861*B*c^2*d-5676*B*c*d^2-2478*B*d^3)*cos(f*x+e)^2+5775*A*c^3+14553*A*c^2*d+14157*A*c*d^2+4499*A*d^3+4851*B*c^3+14157*B*c^2*d+13497*B*c*d^2+4431*B*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
294,1,207,274,1.435000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{2} \left(\sin \left(f x +e \right)-1\right) \left(\left(-45 A \,d^{2}-90 B c d -85 B \,d^{2}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(105 A \,c^{2}+378 A c d +201 A \,d^{2}+189 B \,c^{2}+402 B c d +221 B \,d^{2}\right) \sin \left(f x +e \right)+35 B \left(\cos^{4}\left(f x +e \right)\right) d^{2}+\left(-126 A c d -117 A \,d^{2}-63 B \,c^{2}-234 B c d -172 B \,d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+525 A \,c^{2}+882 A c d +429 A \,d^{2}+441 B \,c^{2}+858 B c d +409 B \,d^{2}\right)}{315 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/315*(1+sin(f*x+e))*a^2*(sin(f*x+e)-1)*((-45*A*d^2-90*B*c*d-85*B*d^2)*sin(f*x+e)*cos(f*x+e)^2+(105*A*c^2+378*A*c*d+201*A*d^2+189*B*c^2+402*B*c*d+221*B*d^2)*sin(f*x+e)+35*B*cos(f*x+e)^4*d^2+(-126*A*c*d-117*A*d^2-63*B*c^2-234*B*c*d-172*B*d^2)*cos(f*x+e)^2+525*A*c^2+882*A*c*d+429*A*d^2+441*B*c^2+858*B*c*d+409*B*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
295,1,150,149,1.283000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{2} \left(\sin \left(f x +e \right)-1\right) \left(15 B d \left(\sin^{3}\left(f x +e \right)\right)+21 A d \left(\sin^{2}\left(f x +e \right)\right)+21 B c \left(\sin^{2}\left(f x +e \right)\right)+39 B \left(\sin^{2}\left(f x +e \right)\right) d +35 A \sin \left(f x +e \right) c +63 A \sin \left(f x +e \right) d +63 B \sin \left(f x +e \right) c +52 B \sin \left(f x +e \right) d +175 A c +126 A d +126 B c +104 B d \right)}{105 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/105*(1+sin(f*x+e))*a^2*(sin(f*x+e)-1)*(15*B*d*sin(f*x+e)^3+21*A*d*sin(f*x+e)^2+21*B*c*sin(f*x+e)^2+39*B*sin(f*x+e)^2*d+35*A*sin(f*x+e)*c+63*A*sin(f*x+e)*d+63*B*sin(f*x+e)*c+52*B*sin(f*x+e)*d+175*A*c+126*A*d+126*B*c+104*B*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
296,1,77,89,1.085000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{2} \left(\sin \left(f x +e \right)-1\right) \left(\sin \left(f x +e \right) \left(5 A +9 B \right)-3 B \left(\cos^{2}\left(f x +e \right)\right)+25 A +21 B \right)}{15 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/15*(1+sin(f*x+e))*a^2*(sin(f*x+e)-1)*(sin(f*x+e)*(5*A+9*B)-3*B*cos(f*x+e)^2+25*A+21*B)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
297,1,291,131,1.734000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(3 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c d -3 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} d^{2}-3 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{2}+3 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c d +B \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d -3 A \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a d +3 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a c -6 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a d \right)}{3 d^{2} \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/3*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(3*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c*d-3*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*d^2-3*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^2+3*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c*d+B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*d-3*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*d+3*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c-6*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*d)/d^2/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
298,1,592,173,2.315000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{a \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-\sin \left(f x +e \right) d \left(A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d +3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,d^{2}-3 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{2}-3 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d +2 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,d^{2}+2 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c +2 B \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, d \right)-A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{2} d -3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c \,d^{2}+3 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{3}+3 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{2} d -2 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c \,d^{2}+A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c d -A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, d^{2}-3 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c^{2}-B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c d \right)}{d^{2} \left(c +d \right) \left(c +d \sin \left(f x +e \right)\right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"a*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-sin(f*x+e)*d*(A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d+3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*d^2-3*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2-3*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d+2*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*d^2+2*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c+2*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*d)-A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2*d-3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d^2+3*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^3+3*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2*d-2*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d^2+A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c*d-A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*d^2-3*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c^2-B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c*d)/d^2/(c+d)/(c+d*sin(f*x+e))/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
299,1,895,197,2.825000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\frac{\left(-2 \sin \left(f x +e \right) \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c d \left(A c d +7 A \,d^{2}+3 B \,c^{2}+9 B c d +12 B \,d^{2}\right)+\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{2} \left(A c d +7 A \,d^{2}+3 B \,c^{2}+9 B c d +12 B \,d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)-A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{3} d -7 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d^{2}-A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{3}-7 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{4}+A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{2}+7 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{3}-3 a^{2} \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) B \,c^{4}-9 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{3} d -15 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d^{2}-9 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{3}-12 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{4}-5 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{2} d -7 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{2}+4 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{3}+A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d -8 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{2}-9 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{3}+3 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{3}+12 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d +5 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{2}-4 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{3}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(1+\sin \left(f x +e \right)\right)}{4 \sqrt{a \left(c +d \right) d}\, \left(c +d \sin \left(f x +e \right)\right)^{2} \left(c +d \right)^{2} d^{2} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/4*(-2*sin(f*x+e)*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d*(A*c*d+7*A*d^2+3*B*c^2+9*B*c*d+12*B*d^2)+arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^2*(A*c*d+7*A*d^2+3*B*c^2+9*B*c*d+12*B*d^2)*cos(f*x+e)^2-A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^3*d-7*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d^2-A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^3-7*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^4+A*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^2+7*A*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^3-3*a^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*B*c^4-9*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^3*d-15*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d^2-9*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^3-12*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^4-5*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c^2*d-7*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^2+4*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^3+A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d-8*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^2-9*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^3+3*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^3+12*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d+5*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^2-4*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^3)*(-a*(sin(f*x+e)-1))^(1/2)*(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/d^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
300,1,374,506,1.395000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{3} \left(\sin \left(f x +e \right)-1\right) \left(\left(4095 A \,d^{3}+12285 B c \,d^{2}+11970 B \,d^{3}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-19305 A \,c^{2} d -55770 A c \,d^{2}-31265 A \,d^{3}-6435 B \,c^{3}-55770 B \,c^{2} d -93795 B c \,d^{2}-44860 B \,d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(42042 A \,c^{3}+167310 A \,c^{2} d +181038 A c \,d^{2}+64090 A \,d^{3}+55770 B \,c^{3}+181038 B \,c^{2} d +192270 B c \,d^{2}+66362 B \,d^{3}\right) \sin \left(f x +e \right)-3465 B \,d^{3} \left(\cos^{6}\left(f x +e \right)\right)+\left(15015 A c \,d^{2}+14560 A \,d^{3}+15015 B \,c^{2} d +43680 B c \,d^{2}+28700 B \,d^{3}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-9009 A \,c^{3}-77220 A \,c^{2} d -123981 A c \,d^{2}-56810 A \,d^{3}-25740 B \,c^{3}-123981 B \,c^{2} d -170430 B c \,d^{2}-72109 B \,d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)+138138 A \,c^{3}+373230 A \,c^{2} d +359502 A c \,d^{2}+116090 A \,d^{3}+124410 B \,c^{3}+359502 B \,c^{2} d +348270 B c \,d^{2}+113818 B \,d^{3}\right)}{45045 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/45045*(1+sin(f*x+e))*a^3*(sin(f*x+e)-1)*((4095*A*d^3+12285*B*c*d^2+11970*B*d^3)*sin(f*x+e)*cos(f*x+e)^4+(-19305*A*c^2*d-55770*A*c*d^2-31265*A*d^3-6435*B*c^3-55770*B*c^2*d-93795*B*c*d^2-44860*B*d^3)*cos(f*x+e)^2*sin(f*x+e)+(42042*A*c^3+167310*A*c^2*d+181038*A*c*d^2+64090*A*d^3+55770*B*c^3+181038*B*c^2*d+192270*B*c*d^2+66362*B*d^3)*sin(f*x+e)-3465*B*d^3*cos(f*x+e)^6+(15015*A*c*d^2+14560*A*d^3+15015*B*c^2*d+43680*B*c*d^2+28700*B*d^3)*cos(f*x+e)^4+(-9009*A*c^3-77220*A*c^2*d-123981*A*c*d^2-56810*A*d^3-25740*B*c^3-123981*B*c^2*d-170430*B*c*d^2-72109*B*d^3)*cos(f*x+e)^2+138138*A*c^3+373230*A*c^2*d+359502*A*c*d^2+116090*A*d^3+124410*B*c^3+359502*B*c^2*d+348270*B*c*d^2+113818*B*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
301,1,257,405,1.427000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{3} \left(\sin \left(f x +e \right)-1\right) \left(315 B \,d^{2} \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-990 A c d -1430 A \,d^{2}-495 B \,c^{2}-2860 B c d -2405 B \,d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(3234 A \,c^{2}+8580 A c d +4642 A \,d^{2}+4290 B \,c^{2}+9284 B c d +4930 B \,d^{2}\right) \sin \left(f x +e \right)+\left(385 A \,d^{2}+770 B c d +1120 B \,d^{2}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-693 A \,c^{2}-3960 A c d -3179 A \,d^{2}-1980 B \,c^{2}-6358 B c d -4370 B \,d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+10626 A \,c^{2}+19140 A c d +9218 A \,d^{2}+9570 B \,c^{2}+18436 B c d +8930 B \,d^{2}\right)}{3465 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/3465*(1+sin(f*x+e))*a^3*(sin(f*x+e)-1)*(315*B*d^2*sin(f*x+e)*cos(f*x+e)^4+(-990*A*c*d-1430*A*d^2-495*B*c^2-2860*B*c*d-2405*B*d^2)*cos(f*x+e)^2*sin(f*x+e)+(3234*A*c^2+8580*A*c*d+4642*A*d^2+4290*B*c^2+9284*B*c*d+4930*B*d^2)*sin(f*x+e)+(385*A*d^2+770*B*c*d+1120*B*d^2)*cos(f*x+e)^4+(-693*A*c^2-3960*A*c*d-3179*A*d^2-1980*B*c^2-6358*B*c*d-4370*B*d^2)*cos(f*x+e)^2+10626*A*c^2+19140*A*c*d+9218*A*d^2+9570*B*c^2+18436*B*c*d+8930*B*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
302,1,152,192,1.394000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{3} \left(\sin \left(f x +e \right)-1\right) \left(\left(-45 A d -45 B c -130 B d \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(294 A c +390 A d +390 B c +422 B d \right) \sin \left(f x +e \right)+35 B d \left(\cos^{4}\left(f x +e \right)\right)+\left(-63 A c -180 A d -180 B c -289 B d \right) \left(\cos^{2}\left(f x +e \right)\right)+966 A c +870 A d +870 B c +838 B d \right)}{315 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/315*(1+sin(f*x+e))*a^3*(sin(f*x+e)-1)*((-45*A*d-45*B*c-130*B*d)*sin(f*x+e)*cos(f*x+e)^2+(294*A*c+390*A*d+390*B*c+422*B*d)*sin(f*x+e)+35*B*d*cos(f*x+e)^4+(-63*A*c-180*A*d-180*B*c-289*B*d)*cos(f*x+e)^2+966*A*c+870*A*d+870*B*c+838*B*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
303,1,99,122,1.241000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{3} \left(\sin \left(f x +e \right)-1\right) \left(-15 B \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(98 A +130 B \right) \sin \left(f x +e \right)+\left(-21 A -60 B \right) \left(\cos^{2}\left(f x +e \right)\right)+322 A +290 B \right)}{105 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/105*(1+sin(f*x+e))*a^3*(sin(f*x+e)-1)*(-15*B*cos(f*x+e)^2*sin(f*x+e)+(98*A+130*B)*sin(f*x+e)+(-21*A-60*B)*cos(f*x+e)^2+322*A+290*B)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
304,1,543,192,2.052000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-3 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{a \left(c +d \right) d}\, d^{2}+5 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a \,d^{2}-15 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} c^{2} d +30 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} c \,d^{2}-15 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} d^{3}-5 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a c d +20 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a \,d^{2}+15 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} c^{3}-30 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} c^{2} d +15 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{3} c \,d^{2}+15 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{2} c d -45 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{2} d^{2}-15 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{2} c^{2}+45 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{2} c d -60 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{2} d^{2}\right)}{15 d^{3} \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/15*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-3*B*(a-a*sin(f*x+e))^(5/2)*(a*(c+d)*d)^(1/2)*d^2+5*A*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*a*d^2-15*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*c^2*d+30*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*c*d^2-15*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*d^3-5*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*a*c*d+20*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*a*d^2+15*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*c^3-30*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*c^2*d+15*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^3*c*d^2+15*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^2*c*d-45*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^2*d^2-15*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^2*c^2+45*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^2*c*d-60*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^2*d^2)/d^3/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
305,1,932,241,2.545000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{a \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) d \left(9 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d +6 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{2}-15 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{3}-15 a^{2} \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) B \,c^{3}+21 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{2}-6 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} d^{3}+2 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c d +2 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{2}-6 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c d -6 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{2}+12 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2}-6 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c d -18 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{2}\right)+9 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{3} d +6 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d^{2}-15 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{3}+2 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{2} d +2 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{2}-15 a^{2} \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) B \,c^{4}+21 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{2} d^{2}-6 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c \,d^{3}-9 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d -3 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{3}+15 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{3}-12 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d -15 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{2}\right)}{3 d^{3} \left(c +d \right) \left(c +d \sin \left(f x +e \right)\right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/3*a*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*d*(9*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d+6*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^2-15*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^3-15*a^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*B*c^3+21*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^2-6*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^3+2*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d+2*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^2-6*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d-6*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^2+12*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2-6*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d-18*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^2)+9*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^3*d+6*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d^2-15*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^3+2*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c^2*d+2*B*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^2-15*a^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*B*c^4+21*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d^2-6*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^3-9*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d-3*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^3+15*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^3-12*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d-15*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^2)/d^3/(c+d)/(c+d*sin(f*x+e))/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
306,1,1587,280,2.970000," ","int((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","-\frac{a \left(16 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sin \left(f x +e \right) a \,c^{3} d +32 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sin \left(f x +e \right) a \,c^{2} d^{2}+16 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sin \left(f x +e \right) a c \,d^{3}-15 a^{2} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) B \,c^{5}-3 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d^{2}-11 A \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{4}-4 B \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{4}+6 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c^{3} d^{2}+20 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c^{2} d^{3}+38 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c \,d^{4}-30 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c^{4} d -60 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c^{3} d^{2}-14 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c^{2} d^{3}+40 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sin \left(f x +e \right) a^{2} c \,d^{4}-7 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} c \,d^{4}+8 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \left(\sin^{2}\left(f x +e \right)\right) a \,d^{4}+3 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} c^{2} d^{3}+10 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} c \,d^{4}-15 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} c^{3} d^{2}-30 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} c^{2} d^{3}-2 B \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{2} d^{2}-7 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{3} d^{2}+20 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{2} d^{3}+3 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{4} d +10 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{3} d^{2}+19 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{2} d^{3}+8 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \left(\sin^{2}\left(f x +e \right)\right) a \,c^{2} d^{2}+16 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \left(\sin^{2}\left(f x +e \right)\right) a c \,d^{3}-30 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{2} c^{4} d -13 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{3}+29 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{3} d -3 A \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{3} d -13 A \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d^{2}+3 A \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{3}+19 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} d^{5}+6 A \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{3}+20 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2} d^{5}-9 B \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{3} d +13 A \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{4}+15 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{4}+4 B \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,d^{4}+5 A \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{2} d^{2}+15 B \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{3}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(1+\sin \left(f x +e \right)\right)}{4 \sqrt{a \left(c +d \right) d}\, \left(c +d \sin \left(f x +e \right)\right)^{2} \left(c +d \right)^{2} d^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4*a*(16*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)*a*c^3*d+32*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)*a*c^2*d^2+16*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)*a*c*d^3+8*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)^2*a*c^2*d^2+16*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)^2*a*c*d^3-3*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d^2-11*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*d^4-4*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*d^4-15*a^2*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*B*c^5-7*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^3*d^2+20*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^2*d^3-2*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c^2*d^2-13*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^3+3*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*c^2*d^3+10*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*c*d^4-15*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*c^3*d^2-30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*c^2*d^3-7*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*c*d^4+6*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c^3*d^2+20*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c^2*d^3+38*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c*d^4+8*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)^2*a*d^4+29*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^3*d-30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c^4*d-60*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c^3*d^2-14*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c^2*d^3+40*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c*d^4-3*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^3*d-13*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d^2+3*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^3+6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^3+3*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^4*d+10*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^3*d^2+19*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^2*d^3-9*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c^3*d+13*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^4+15*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^4+4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*d^4+19*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*d^5+20*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*d^5+5*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c^2*d^2+15*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^3-30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^4*d)*(-a*(sin(f*x+e)-1))^(1/2)*(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/d^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
307,1,610,259,1.949000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(105 A \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{3}-315 A \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{2} d +315 A \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c \,d^{2}-105 A \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d^{3}-105 B \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{3}+315 B \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{2} d -315 B \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c \,d^{2}+105 B \,a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d^{3}-30 B \,d^{3} \left(a -a \sin \left(f x +e \right)\right)^{\frac{7}{2}}+42 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} a \,d^{3}+126 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} a c \,d^{2}+84 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} a \,d^{3}-210 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2} c \,d^{2}-70 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2} d^{3}-210 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2} c^{2} d -210 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2} c \,d^{2}-140 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2} d^{3}+630 A \,c^{2} d \,a^{3} \sqrt{a -a \sin \left(f x +e \right)}+210 A \,a^{3} d^{3} \sqrt{a -a \sin \left(f x +e \right)}+210 B \,c^{3} a^{3} \sqrt{a -a \sin \left(f x +e \right)}+630 B \,a^{3} c \,d^{2} \sqrt{a -a \sin \left(f x +e \right)}\right)}{105 a^{4} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/105*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(105*A*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^3-315*A*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^2*d+315*A*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*d^2-105*A*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^3-105*B*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^3+315*B*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^2*d-315*B*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*d^2+105*B*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^3-30*B*d^3*(a-a*sin(f*x+e))^(7/2)+42*A*(a-a*sin(f*x+e))^(5/2)*a*d^3+126*B*(a-a*sin(f*x+e))^(5/2)*a*c*d^2+84*B*(a-a*sin(f*x+e))^(5/2)*a*d^3-210*A*(a-a*sin(f*x+e))^(3/2)*a^2*c*d^2-70*A*(a-a*sin(f*x+e))^(3/2)*a^2*d^3-210*B*(a-a*sin(f*x+e))^(3/2)*a^2*c^2*d-210*B*(a-a*sin(f*x+e))^(3/2)*a^2*c*d^2-140*B*(a-a*sin(f*x+e))^(3/2)*a^2*d^3+630*A*c^2*d*a^3*(a-a*sin(f*x+e))^(1/2)+210*A*a^3*d^3*(a-a*sin(f*x+e))^(1/2)+210*B*c^3*a^3*(a-a*sin(f*x+e))^(1/2)+630*B*a^3*c*d^2*(a-a*sin(f*x+e))^(1/2))/a^4/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
308,1,396,179,1.756000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(15 A \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{2}-30 A \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c d +15 A \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d^{2}-15 B \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c^{2}+30 B \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c d -15 B \,a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d^{2}+6 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} d^{2}-10 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a \,d^{2}-20 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a c d -10 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a \,d^{2}+60 A \,a^{2} c d \sqrt{a -a \sin \left(f x +e \right)}+30 B \,a^{2} c^{2} \sqrt{a -a \sin \left(f x +e \right)}+30 B \,a^{2} d^{2} \sqrt{a -a \sin \left(f x +e \right)}\right)}{15 a^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/15*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(15*A*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^2-30*A*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*d+15*A*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^2-15*B*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^2+30*B*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*d-15*B*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^2+6*B*(a-a*sin(f*x+e))^(5/2)*d^2-10*A*(a-a*sin(f*x+e))^(3/2)*a*d^2-20*B*(a-a*sin(f*x+e))^(3/2)*a*c*d-10*B*(a-a*sin(f*x+e))^(3/2)*a*d^2+60*A*a^2*c*d*(a-a*sin(f*x+e))^(1/2)+30*B*a^2*c^2*(a-a*sin(f*x+e))^(1/2)+30*B*a^2*d^2*(a-a*sin(f*x+e))^(1/2))/a^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
309,1,232,113,1.527000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(3 A \,a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c -3 A \,a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d -3 B \,a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c +3 B \,a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d -2 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} d +6 A a d \sqrt{a -a \sin \left(f x +e \right)}+6 B a c \sqrt{a -a \sin \left(f x +e \right)}\right)}{3 a^{2} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/3*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(3*A*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c-3*A*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d-3*B*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c+3*B*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d-2*B*(a-a*sin(f*x+e))^(3/2)*d+6*A*a*d*(a-a*sin(f*x+e))^(1/2)+6*B*a*c*(a-a*sin(f*x+e))^(1/2))/a^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
310,1,128,68,1.292000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) A -\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) B +2 \sqrt{a -a \sin \left(f x +e \right)}\, B \right)}{a \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*A-a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*B+2*(a-a*sin(f*x+e))^(1/2)*B)/a/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
311,1,199,113,2.073000," ","int((A+B*sin(f*x+e))/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a \left(c +d \right) d}\, A -2 A \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sqrt{a}\, d -\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a \left(c +d \right) d}\, B +2 B \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sqrt{a}\, c \right)}{\left(c -d \right) \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*(a*(c+d)*d)^(1/2)*A-2*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(1/2)*d-2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*(a*(c+d)*d)^(1/2)*B+2*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(1/2)*c)/(c-d)/(a*(c+d)*d)^(1/2)/a^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
312,1,899,182,2.719000," ","int((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) d \left(3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c d +A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} d^{2}-B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c^{2}-B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c d -2 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} d^{2}-A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c -A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d +B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c +B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d \right)+3 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c^{2} d +A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c \,d^{2}-B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c^{3}-B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c^{2} d -2 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c \,d^{2}+A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c d -A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} d^{2}-A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c^{2}+B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c d +B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d \right)}{a^{\frac{5}{2}} \left(c -d \right)^{2} \left(c +d \right) \left(c +d \sin \left(f x +e \right)\right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)/a^(5/2)*(sin(f*x+e)*d*(3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d+A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*d^2-B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c^2-B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d-2*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*d^2-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d)+3*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c^2*d+A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d^2-B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c^3-B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c^2*d-2*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d^2+A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d-A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^2-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2+B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d)/(c-d)^2/(c+d)/(c+d*sin(f*x+e))/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
313,1,2277,276,3.580000," ","int((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/4*(8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c*d^3+16*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c^2*d^2+6*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c^4*d-8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^3*d-4*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^2*d^2+3*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^5-8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c^3*d-16*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c^2*d^2-8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c*d^3+4*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*c^2*d^2+8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*c*d^3-4*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*c^2*d^2-8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*c*d^3+8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^4*c^3*d+7*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c^2*d^2-3*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c^3*d-6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c*d^3+2*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c^2*d^2-3*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c*d^3+4*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^4+4*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*d^4-4*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^4*d^4+8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^3*d+4*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^2*d^2-B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^2*d^2+B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c*d^3-15*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*c^2*d^3-10*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*c*d^4+3*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*c^3*d^2+6*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*c^2*d^3+19*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*c*d^4-30*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c^3*d^2-20*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c^2*d^3-14*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c*d^4-9*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^3*d+12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c^3*d^2+5*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^4-10*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^3*d^2+38*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c^2*d^3+9*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c*d^3-B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^3*d+8*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)*c*d^4+19*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^3*d^2+4*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^2*d^3-A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*d^4+A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^2*d^2-7*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*d^5-4*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*c^4+4*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*sin(f*x+e)^2*d^5-7*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^2*d^3-A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*d^4+4*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*d^4-15*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^4*d+6*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(9/2)*c^4*d-4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*d^4)/a^(9/2)*(-a*(sin(f*x+e)-1))^(1/2)*(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/(c-d)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
314,1,1030,256,1.868000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(-40 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} d^{3}+360 A c \,d^{2} a^{\frac{5}{2}} \sqrt{a -a \sin \left(f x +e \right)}-120 A \,a^{\frac{5}{2}} d^{3} \sqrt{a -a \sin \left(f x +e \right)}+24 B \,d^{3} \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{a}-120 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} c \,d^{2}+360 B \,c^{2} d \,a^{\frac{5}{2}} \sqrt{a -a \sin \left(f x +e \right)}-360 B \,a^{\frac{5}{2}} c \,d^{2} \sqrt{a -a \sin \left(f x +e \right)}+240 B \,a^{\frac{5}{2}} d^{3} \sqrt{a -a \sin \left(f x +e \right)}+15 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{3}+135 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{2} d -315 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c \,d^{2}+165 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} d^{3}+45 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{3}-315 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{2} d +495 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c \,d^{2}-225 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} d^{3}\right)-40 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} d^{3}+30 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}} c^{3}-90 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}} c^{2} d +450 A c \,d^{2} a^{\frac{5}{2}} \sqrt{a -a \sin \left(f x +e \right)}-150 A \,a^{\frac{5}{2}} d^{3} \sqrt{a -a \sin \left(f x +e \right)}+24 B \,d^{3} \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{a}-120 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} c \,d^{2}-30 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}} c^{3}+450 B \,c^{2} d \,a^{\frac{5}{2}} \sqrt{a -a \sin \left(f x +e \right)}-450 B \,a^{\frac{5}{2}} c \,d^{2} \sqrt{a -a \sin \left(f x +e \right)}+270 B \,a^{\frac{5}{2}} d^{3} \sqrt{a -a \sin \left(f x +e \right)}+15 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{3}+135 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{2} d -315 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c \,d^{2}+165 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} d^{3}+45 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{3}-315 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c^{2} d +495 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c \,d^{2}-225 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} d^{3}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{60 a^{\frac{9}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/60*(sin(f*x+e)*(-40*A*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*d^3+360*A*c*d^2*a^(5/2)*(a-a*sin(f*x+e))^(1/2)-120*A*a^(5/2)*d^3*(a-a*sin(f*x+e))^(1/2)+24*B*d^3*(a-a*sin(f*x+e))^(5/2)*a^(1/2)-120*B*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*c*d^2+360*B*c^2*d*a^(5/2)*(a-a*sin(f*x+e))^(1/2)-360*B*a^(5/2)*c*d^2*(a-a*sin(f*x+e))^(1/2)+240*B*a^(5/2)*d^3*(a-a*sin(f*x+e))^(1/2)+15*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^3+135*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^2*d-315*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c*d^2+165*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*d^3+45*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^3-315*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^2*d+495*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c*d^2-225*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*d^3)-40*A*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*d^3+30*A*(a-a*sin(f*x+e))^(1/2)*a^(5/2)*c^3-90*A*(a-a*sin(f*x+e))^(1/2)*a^(5/2)*c^2*d+450*A*c*d^2*a^(5/2)*(a-a*sin(f*x+e))^(1/2)-150*A*a^(5/2)*d^3*(a-a*sin(f*x+e))^(1/2)+24*B*d^3*(a-a*sin(f*x+e))^(5/2)*a^(1/2)-120*B*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*c*d^2-30*B*(a-a*sin(f*x+e))^(1/2)*a^(5/2)*c^3+450*B*c^2*d*a^(5/2)*(a-a*sin(f*x+e))^(1/2)-450*B*a^(5/2)*c*d^2*(a-a*sin(f*x+e))^(1/2)+270*B*a^(5/2)*d^3*(a-a*sin(f*x+e))^(1/2)+15*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^3+135*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^2*d-315*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c*d^2+165*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*d^3+45*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^3-315*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c^2*d+495*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c*d^2-225*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*d^3)*(-a*(sin(f*x+e)-1))^(1/2)/a^(9/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
315,1,694,180,1.590000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+18 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -21 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}+24 A \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+9 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-42 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +33 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-8 B \,d^{2} \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}+48 B c d \,a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}-24 B \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\right)+3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+18 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -21 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}+6 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}-12 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c d +30 A \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+9 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-42 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +33 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-8 B \,d^{2} \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}-6 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}+60 B c d \,a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}-30 B \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{12 a^{\frac{7}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/12/a^(7/2)*(sin(f*x+e)*(3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+18*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-21*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2+24*A*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+9*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-42*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+33*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-8*B*d^2*(a-a*sin(f*x+e))^(3/2)*a^(1/2)+48*B*c*d*a^(3/2)*(a-a*sin(f*x+e))^(1/2)-24*B*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2))+3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+18*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-21*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2+6*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2-12*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d+30*A*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+9*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-42*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+33*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-8*B*d^2*(a-a*sin(f*x+e))^(3/2)*a^(1/2)-6*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2+60*B*c*d*a^(3/2)*(a-a*sin(f*x+e))^(1/2)-30*B*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2))*(-a*(sin(f*x+e)-1))^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
316,1,389,116,1.321000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c +3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +3 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c -7 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +8 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d \right)+A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c +3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +3 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c -7 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +2 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c -2 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d -2 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c +10 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d \right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{4 a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4/a^(5/2)*(sin(f*x+e)*(A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c+3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+3*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c-7*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+8*B*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d)+A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c+3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+3*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c-7*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+2*A*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c-2*A*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d-2*B*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c+10*B*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d)*(-a*(sin(f*x+e)-1))^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
317,1,176,72,1.091000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \left(A +3 B \right)+A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a +3 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a +2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, A -2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, B \right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{4 a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4/a^(5/2)*(sin(f*x+e)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*(A+3*B)+A*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a+3*B*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a+2*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*A-2*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*B)*(-a*(sin(f*x+e)-1))^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
318,1,624,158,2.007000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x)","-\frac{\left(\sin \left(f x +e \right) \left(8 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{3}{2}} d^{2}-8 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{3}{2}} c d +A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c -5 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +3 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c +B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d \right)+8 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{3}{2}} d^{2}-8 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{3}{2}} c d +A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c -5 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +3 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c +B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +2 A \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c -2 A \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d -2 B \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c +2 B \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d \right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{4 a^{\frac{5}{2}} \sqrt{a \left(c +d \right) d}\, \left(c -d \right)^{2} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4/a^(5/2)*(sin(f*x+e)*(8*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)*d^2-8*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)*c*d+A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c-5*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d)+8*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)*d^2-8*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)*c*d+A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c-5*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c+B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d+2*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c-2*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d-2*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c+2*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d)*(-a*(sin(f*x+e)-1))^(1/2)/(a*(c+d)*d)^(1/2)/(c-d)^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
319,1,2049,259,3.069000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x)","\text{Expression too large to display}"," ",0,"-1/4/a^(5/2)*(-17*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c*d^2+11*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c^2*d-20*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*c*d^3-9*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*d^3+5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c*d^2-6*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d+A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c^3+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c^3-9*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*d^3+5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*d^3+4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^2+8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c^2*d+2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d+4*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^2-8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c^2*d-9*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c*d^2+5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*d^3+13*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c*d^2-8*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*c*d^2+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*c^2*d+A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*c^2*d+8*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a*c*d^2-7*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a*c^2*d-12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*c^3*d+20*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*c^2*d^2+20*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)^2*c*d^3+32*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*c*d^3-12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)^2*c^2*d^2-12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)^2*c*d^3+2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^3+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c^3-4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d+6*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^2+2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^2-6*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^3+A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*c^3-24*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*c^2*d^2+20*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c^2*d^2+2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3-4*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^3-2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3+12*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c*d^3-12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c^3*d-12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c^2*d^2-8*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c*d^3+12*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)^2*d^4-8*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)^2*d^4+12*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*d^4-8*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*sin(f*x+e)*d^4)*(-a*(sin(f*x+e)-1))^(1/2)/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))/(c+d)/(c-d)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
320,1,4707,363,3.972000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"1/4/a^(7/2)*(-a*(sin(f*x+e)-1))^(1/2)*(11*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^2*d^3-2*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^4*d-112*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^3*d^3-6*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^4*d-33*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^3*d^2-57*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^2*d^3-39*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c*d^4+21*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^3*d^2-3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^3*d^2-15*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^2*d^3-21*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c*d^4+9*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^4*d+47*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^3*d^2+63*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^2*d^3+25*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c*d^4-51*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^3*d^2-51*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^2*d^3-18*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c*d^4-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^3*d^2+26*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c*d^4-21*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^4*d+61*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^2*d^3+51*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c*d^4-4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^5+3*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^5+15*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^5*d+2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^5-7*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^4-2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^3*d^2-2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^2*d^3+2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^4+2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^3*d^2+2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^2*d^3-2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^4+11*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d^3-6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^4-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^5-7*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^3*d^2+2*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d^3+B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^4-3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^5+11*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^4*d+25*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3*d^2+13*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d^3-15*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^4*d-21*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3*d^2-9*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d^3-9*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*d^5+13*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*d^5-9*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*d^5+13*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*d^5+13*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^4*d+7*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^3*d^2-4*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^4*d-17*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^3*d^2+A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^3+12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^4-19*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*d^6+12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*d^6-19*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*d^6+12*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*d^6-35*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^4*d^2-42*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^3*d^3-19*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^4-5*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^5+4*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^5+39*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^3*d^3+30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^4*d^2-2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^5-103*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^2*d^4-38*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c*d^5-2*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^5+15*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^5*d+B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d^2+3*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^5-4*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^5-2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4*d-11*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d^2-A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^3+13*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^4+11*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4*d+108*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^2*d^4+11*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^3-6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^4-A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^5-7*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3*d^2+2*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^3-35*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c^2*d^4-42*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c*d^5+15*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c^3*d^3+30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c^2*d^4+39*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c*d^5+63*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c*d^5+2*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^5-35*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^4*d^2-80*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c*d^5+30*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^4*d^2+75*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^3*d^3-7*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^3-3*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^4-5*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^5+4*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^5+60*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^4*d^2+99*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^3*d^3+90*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^2*d^4+24*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c*d^5+B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^4-3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^5-70*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^3*d^3-119*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^2*d^4+17*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^4-9*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^3)/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/(c-d)^4/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
321,1,1438,281,2.466000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(18 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{3}+126 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{3}+30 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{3}-60 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{3}-36 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{3}-612 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}+1092 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}-46 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{3}-90 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d -342 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}-342 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d +1350 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}-2 \sin \left(f x +e \right) \left(9 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+45 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d +171 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}-225 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}+192 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}+15 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+171 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d -675 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}+489 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}+576 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c \,d^{2}-384 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}-64 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{3}\right)+\left(9 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+45 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d +171 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}-225 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}+192 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}+15 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+171 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2} d -675 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c \,d^{2}+489 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}+576 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c \,d^{2}-384 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{3}-64 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)-1836 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c \,d^{2}+396 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2} d -108 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2} d +396 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c \,d^{2}-234 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2} d +378 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c \,d^{2}+90 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2} d -234 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c \,d^{2}-18 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+450 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}-30 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}-978 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{96 a^{\frac{9}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/96/a^(9/2)*((9*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+45*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d+171*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-225*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3+192*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3+15*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+171*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d-675*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2+489*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3+576*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d^2-384*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3-64*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^3)*cos(f*x+e)^2-2*sin(f*x+e)*(9*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+45*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d+171*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-225*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3+192*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3+15*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+171*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d-675*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2+489*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3+576*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d^2-384*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3-64*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^3)-90*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d+18*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^3+126*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^3+30*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^3-60*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^3-36*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^3-612*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3+1092*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^3-46*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^3-342*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-342*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d+1350*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-18*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+450*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-30*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3-978*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-1836*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d^2+396*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2*d-108*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2*d+396*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d^2-234*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2*d+378*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d^2+90*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2*d-234*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d^2)*(-a*(sin(f*x+e)-1))^(1/2)/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
322,1,982,196,2.036000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(2 \sin \left(f x +e \right) \left(3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+10 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +19 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}+5 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+38 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -75 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}+64 B \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\right)+\left(-3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-10 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -19 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-64 B \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}-5 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-38 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +75 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)-6 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2}-20 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c d +26 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{2}+20 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}+24 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c d -44 A \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+6 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+20 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +38 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-10 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2}+52 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c d -42 B \,d^{2} \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}+12 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}-88 B c d \,a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+204 B \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+10 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+76 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -150 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/32*(2*sin(f*x+e)*(3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+10*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+19*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2+5*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+38*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-75*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2+64*B*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2))+(-3*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-10*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-19*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-64*B*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)-5*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-38*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+75*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2)*cos(f*x+e)^2-6*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2-20*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d+26*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^2+20*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2+24*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d-44*A*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+6*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+20*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+38*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-10*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2+52*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d-42*B*d^2*(a-a*sin(f*x+e))^(3/2)*a^(1/2)+12*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2-88*B*c*d*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+204*B*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+10*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+76*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-150*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2)*(-a*(sin(f*x+e)-1))^(1/2)/a^(9/2)/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
323,1,449,132,1.639000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(2 \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(3 A c +5 A d +5 B c +19 B d \right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(3 A c +5 A d +5 B c +19 B d \right) \left(\cos^{2}\left(f x +e \right)\right)+6 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c +10 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d +20 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c +12 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d -6 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c -10 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d +10 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c +38 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d +12 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c -44 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d -10 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c +26 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d \right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/32*(2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*(3*A*c+5*A*d+5*B*c+19*B*d)-2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*(3*A*c+5*A*d+5*B*c+19*B*d)*cos(f*x+e)^2+6*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c+10*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d+20*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c+12*A*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d-6*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c-10*A*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d+10*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c+38*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d+12*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c-44*B*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d-10*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c+26*B*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d)*(-a*(sin(f*x+e)-1))^(1/2)/a^(9/2)/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
324,1,279,107,1.699000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(2 \sin \left(f x +e \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(3 A +5 B \right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(3 A +5 B \right) \left(\cos^{2}\left(f x +e \right)\right)+20 A \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}}-6 A \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+12 B \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}}-10 B \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+6 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}+10 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{32 a^{\frac{11}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/32*(2*sin(f*x+e)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*(3*A+5*B)-2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*(3*A+5*B)*cos(f*x+e)^2+20*A*(a-a*sin(f*x+e))^(1/2)*a^(5/2)-6*A*(a-a*sin(f*x+e))^(3/2)*a^(3/2)+12*B*(a-a*sin(f*x+e))^(1/2)*a^(5/2)-10*B*(a-a*sin(f*x+e))^(3/2)*a^(3/2)+6*A*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3+10*B*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*(-a*(sin(f*x+e)-1))^(1/2)/a^(11/2)/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
325,1,1418,228,2.665000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x)","-\frac{\left(2 \sin \left(f x +e \right) \left(-64 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} d^{3}+64 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c \,d^{2}+3 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-14 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +43 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}+5 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-34 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -3 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}\right)+\left(64 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} d^{3}-64 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c \,d^{2}-3 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+14 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -43 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-5 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}+34 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +3 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)-128 A \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} d^{3}+128 B \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{5}{2}} c \,d^{2}+6 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-28 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d +86 A \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-6 A \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2}+28 A \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c d -22 A \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{2}+20 A \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}-72 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c d +52 A \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} d^{2}+10 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{2}-68 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c d -6 B \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{2}-10 B \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2}+4 B \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c d +6 B \sqrt{a \left(c +d \right) d}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{2}+12 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c^{2}+8 B \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} c d -20 B \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} d^{2}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(f x +e \right)\right) \sqrt{a \left(c +d \right) d}\, \left(c -d \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/32*(2*sin(f*x+e)*(-64*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*d^3+64*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d^2+3*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-14*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+43*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2+5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-34*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2)+(64*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*d^3-64*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d^2-3*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+14*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-43*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2+34*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+3*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2)*cos(f*x+e)^2-128*A*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*d^3+128*B*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)*c*d^2+6*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-28*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d+86*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-6*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2+28*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d-22*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^2+20*A*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2-72*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d+52*A*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^2+10*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2-68*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d-6*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^2-10*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2+4*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d+6*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^2+12*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2+8*B*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d-20*B*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*d^2)*(-a*(sin(f*x+e)-1))^(1/2)/a^(9/2)/(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c-d)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
326,1,4092,358,4.202000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x)","\text{output too large to display}"," ",0,"1/32/a^(9/2)*(-323*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c*d^3+13*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^3*d-320*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^3*d^2+19*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^2*d^2-55*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^2*d^2-301*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c*d^3+101*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^3*d+255*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^2*d^2+187*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c*d^3+35*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^3*d-167*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^2*d^2+207*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^2*d^2+245*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c*d^3+53*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^2*d^2-5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^3*d+101*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c*d^3-93*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c*d^3+43*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^3*d-3*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*c^3*d-480*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^2*d^3-160*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c*d^4+22*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3*d-288*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c*d^4-148*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^4+52*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^4+84*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d+20*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^2-52*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^3-52*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d-32*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^2*d^2+32*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^3-20*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^3*d+84*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^2-12*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^3*d-116*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^2+84*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^3-115*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*d^4+10*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^3*d+22*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d^2-10*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^3-10*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^4-5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^4+86*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*d^4-115*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*d^4+43*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^3*a^2*d^4+76*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^3+43*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*d^4+19*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3*d-93*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d^2-3*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*c^4-230*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a^2*d^4-115*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^3+53*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3*d+101*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^2*d^2+43*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^3+6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^3*d-38*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d^2-6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^3-6*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)*a^2*c^4+32*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^3+448*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c^2*d^3+544*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*c*d^4+224*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^2*d^3+608*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c*d^4-160*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^3*d^2-10*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^2-22*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^3-5*B*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^4-20*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^2+84*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^3+38*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^4-22*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^4-38*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3*d-6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^2+38*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^3-3*A*(a*(c+d)*d)^(1/2)*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^4-32*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^4-480*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c^2*d^3-384*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*c*d^4+224*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c*d^4-160*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*c^2*d^3-160*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^3*d^2+160*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*d^5+160*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c*d^4+320*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*d^5+224*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^3-128*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^2*d^5+160*A*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*d^5-64*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*d^5-20*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4-32*A*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^4-12*B*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4-64*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^3*d^5+6*A*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^4-160*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^3-64*B*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c*d^4+10*B*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^4)*(-a*(sin(f*x+e)-1))^(1/2)/(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))/(c+d)/(c-d)^4/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
327,1,7322,476,5.811000," ","int((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
328,0,0,193,3.868000," ","int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{2} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
329,0,0,189,3.368000," ","int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right) \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
330,0,0,193,1.057000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
331,0,0,193,10.288000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
332,0,0,409,1.285000," ","int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
333,0,0,161,1.237000," ","int((a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \sqrt{a +a \sin \left(f x +e \right)}\, \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
334,0,0,210,0.972000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","F"
335,0,0,257,0.983000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","F"
336,0,0,339,9.533000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","F"
337,0,0,187,7.608000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x)","F"
338,0,0,105,0.018000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
339,0,0,167,4.046000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x)","F"
340,0,0,269,14.319000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c +d \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","F"
341,0,0,440,12.570000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c +d \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","F"
342,0,0,248,1.204000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x)","F"
343,0,0,238,1.134000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x)","F"
344,0,0,238,0.891000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\sqrt{c +d \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","F"
345,0,0,252,0.917000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","F"
346,0,0,246,1.351000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
347,0,0,255,3.466000," ","int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(-1-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(-1-m),x)","F"
348,0,0,120,1.431000," ","int((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(a -a \sin \left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
349,0,0,127,2.750000," ","int((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x)","\int \left(a -a \sin \left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x)","F"
350,0,0,39,6.471000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d-(c-d)*m+(c+(c-d)*m)*sin(f*x+e)),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{-2-m} \left(d -\left(c -d \right) m +\left(c +\left(c -d \right) m \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d-(c-d)*m+(c+(c-d)*m)*sin(f*x+e)),x)","F"
351,0,0,40,6.558000," ","int((a-a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d+(c+d)*m+(c+(c+d)*m)*sin(f*x+e)),x)","\int \left(a -a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{-2-m} \left(d +\left(c +d \right) m +\left(c +\left(c +d \right) m \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a-a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d+(c+d)*m+(c+(c+d)*m)*sin(f*x+e)),x)","F"
352,1,1246,194,0.461000," ","int((a+b*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","-\frac{4 d \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A a b}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,b^{2} c^{3}}{f \,d^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{4 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,b^{2} c^{4}}{f \,d^{3} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{6 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,b^{2} c^{2}}{f d \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{8 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B a b c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{2 c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B \,b^{2}}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}-\frac{4 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B a b \,c^{3}}{f \,d^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{4 B a b \,c^{2}}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{4 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B a b}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{2 d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a^{2} A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right) c}-\frac{4 d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A a b}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{4 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,b^{2} c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{2 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) A \,a^{2} c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{2 b^{2} B}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{2 b^{2} A \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}-\frac{2 d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) B \,a^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{2 A \,b^{2} c^{2}}{f d \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}-\frac{2 c^{3} B \,b^{2}}{f \,d^{2} \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) A \,b^{2}}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}-\frac{4 A a b c}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}-\frac{2 d \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right) B \,a^{2}}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{4 b B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,d^{2}}-\frac{4 b^{2} B \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{3}}-\frac{2 B \,a^{2} c}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}+\frac{2 d \,a^{2} A}{f \left(\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d +c \right) \left(c^{2}-d^{2}\right)}"," ",0,"-4/f*d/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*a*b-2/f/d^2/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*b^2*c^3+4/f/d^3/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*b^2*c^4-6/f/d/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*b^2*c^2-2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*tan(1/2*f*x+1/2*e)*B*a^2+2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*A*b^2*c^2-2/f/d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*c^3*B*b^2+2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*c*tan(1/2*f*x+1/2*e)*A*b^2-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*A*a*b*c+8/f/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*a*b*c-2/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*c^2*tan(1/2*f*x+1/2*e)*B*b^2+4/f/d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*B*a*b*c^2-4/f/d^2/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*a*b*c^3+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*c*tan(1/2*f*x+1/2*e)*B*a*b+2/f*d^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)/c*tan(1/2*f*x+1/2*e)*a^2*A-4/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*tan(1/2*f*x+1/2*e)*A*a*b+4/f/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*b^2*c-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*B*a^2*c+2/f/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*A*a^2*c+2/f*d/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c^2-d^2)*a^2*A-2/f/d^2*b^2*B/(1+tan(1/2*f*x+1/2*e)^2)+2/f/d^2*b^2*A*arctan(tan(1/2*f*x+1/2*e))-2/f*d/(c^2-d^2)^(3/2)*arctan(1/2*(2*c*tan(1/2*f*x+1/2*e)+2*d)/(c^2-d^2)^(1/2))*B*a^2+4/f/d^2*b*B*arctan(tan(1/2*f*x+1/2*e))*a-4/f/d^3*b^2*B*arctan(tan(1/2*f*x+1/2*e))*c","B"
353,1,6776580,787,100.983000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
354,1,3150101,585,159.526000," ","int((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
355,1,99082,387,1.846000," ","int((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
356,1,198381,510,3.294000," ","int((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
357,1,827062,814,19.791000," ","int((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
358,0,0,37,1.284000," ","int((a+b*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"