1,1,96,94,0.278000," ","int(sin(f*x+e)^3*(a+a*sin(f*x+e))^2,x)","\frac{-\frac{a^{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} \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} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-1/5*a^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*a^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*a^2*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
2,1,143,117,0.343000," ","int(sin(f*x+e)^3*(a+a*sin(f*x+e))^3,x)","\frac{a^{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 a^{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} \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} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(a^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*a^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*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)-1/3*a^3*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
3,1,121,47,0.077000," ","int(sin(x)^4/(a+a*sin(x)),x)","-\frac{\tan^{5}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{10}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5-2/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^4-8/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2+1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)-10/3/a/(tan(1/2*x)^2+1)^3-3/a*arctan(tan(1/2*x))-2/a/(tan(1/2*x)+1)","B"
4,1,100,38,0.072000," ","int(sin(x)^3/(a+a*sin(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}+\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+2/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2-1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)+2/a/(tan(1/2*x)^2+1)^2+3/a*arctan(tan(1/2*x))+2/a/(tan(1/2*x)+1)","B"
5,1,40,27,0.070000," ","int(sin(x)^2/(a+a*sin(x)),x)","-\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2/a/(tan(1/2*x)^2+1)-2/a*arctan(tan(1/2*x))-2/a/(tan(1/2*x)+1)","A"
6,1,25,17,0.074000," ","int(sin(x)/(a+a*sin(x)),x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}+\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"2/a*arctan(tan(1/2*x))+2/a/(tan(1/2*x)+1)","A"
7,1,14,12,0.055000," ","int(1/(a+a*sin(x)),x)","-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2/a/(tan(1/2*x)+1)","A"
8,1,24,20,0.079000," ","int(csc(x)/(a+a*sin(x)),x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}+\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a*ln(tan(1/2*x))+2/a/(tan(1/2*x)+1)","A"
9,1,45,26,0.099000," ","int(csc(x)^2/(a+a*sin(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/2/a*tan(1/2*x)-1/2/a/tan(1/2*x)-1/a*ln(tan(1/2*x))-2/a/(tan(1/2*x)+1)","A"
10,1,67,38,0.099000," ","int(csc(x)^3/(a+a*sin(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}-\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}+\frac{1}{2 a \tan \left(\frac{x}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}+\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/8/a*tan(1/2*x)^2-1/2/a*tan(1/2*x)-1/8/a/tan(1/2*x)^2+1/2/a/tan(1/2*x)+3/2/a*ln(tan(1/2*x))+2/a/(tan(1/2*x)+1)","A"
11,1,89,49,0.099000," ","int(csc(x)^4/(a+a*sin(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a}-\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}+\frac{7 \tan \left(\frac{x}{2}\right)}{8 a}-\frac{1}{24 a \tan \left(\frac{x}{2}\right)^{3}}+\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}-\frac{7}{8 a \tan \left(\frac{x}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/24/a*tan(1/2*x)^3-1/8/a*tan(1/2*x)^2+7/8/a*tan(1/2*x)-1/24/a/tan(1/2*x)^3+1/8/a/tan(1/2*x)^2-7/8/a/tan(1/2*x)-3/2/a*ln(tan(1/2*x))-2/a/(tan(1/2*x)+1)","A"
12,1,126,56,0.102000," ","int(sin(x)^4/(a+a*sin(x))^2,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{7 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+4/a^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2-1/a^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)+4/a^2/(tan(1/2*x)^2+1)^2+7/a^2*arctan(tan(1/2*x))-4/3/a^2/(tan(1/2*x)+1)^3+2/a^2/(tan(1/2*x)+1)^2+6/a^2/(tan(1/2*x)+1)","B"
13,1,66,43,0.096000," ","int(sin(x)^3/(a+a*sin(x))^2,x)","-\frac{2}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{4 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}+\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{4}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2/a^2/(tan(1/2*x)^2+1)-4/a^2*arctan(tan(1/2*x))+4/3/a^2/(tan(1/2*x)+1)^3-2/a^2/(tan(1/2*x)+1)^2-4/a^2/(tan(1/2*x)+1)","A"
14,1,51,31,0.099000," ","int(sin(x)^2/(a+a*sin(x))^2,x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"2/a^2*arctan(tan(1/2*x))-4/3/a^2/(tan(1/2*x)+1)^3+2/a^2/(tan(1/2*x)+1)^2+2/a^2/(tan(1/2*x)+1)","A"
15,1,27,29,0.093000," ","int(sin(x)/(a+a*sin(x))^2,x)","\frac{\frac{4}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}}{a^{2}}"," ",0,"4/a^2*(1/3/(tan(1/2*x)+1)^3-1/2/(tan(1/2*x)+1)^2)","A"
16,1,35,29,0.078000," ","int(1/(a+a*sin(x))^2,x)","\frac{\frac{2}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{4}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{\tan \left(\frac{x}{2}\right)+1}}{a^{2}}"," ",0,"2/a^2*(1/(tan(1/2*x)+1)^2-2/3/(tan(1/2*x)+1)^3-1/(tan(1/2*x)+1))","A"
17,1,50,34,0.119000," ","int(csc(x)/(a+a*sin(x))^2,x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}+\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a^2*ln(tan(1/2*x))+4/3/a^2/(tan(1/2*x)+1)^3-2/a^2/(tan(1/2*x)+1)^2+4/a^2/(tan(1/2*x)+1)","A"
18,1,71,41,0.129000," ","int(csc(x)^2/(a+a*sin(x))^2,x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a^{2}}-\frac{1}{2 a^{2} \tan \left(\frac{x}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{6}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/2/a^2*tan(1/2*x)-1/2/a^2/tan(1/2*x)-2/a^2*ln(tan(1/2*x))-4/3/a^2/(tan(1/2*x)+1)^3+2/a^2/(tan(1/2*x)+1)^2-6/a^2/(tan(1/2*x)+1)","A"
19,1,92,54,0.154000," ","int(csc(x)^3/(a+a*sin(x))^2,x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a^{2}}-\frac{1}{8 a^{2} \tan \left(\frac{x}{2}\right)^{2}}+\frac{1}{a^{2} \tan \left(\frac{x}{2}\right)}+\frac{7 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{2}}+\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{8}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/8/a^2*tan(1/2*x)^2-1/a^2*tan(1/2*x)-1/8/a^2/tan(1/2*x)^2+1/a^2/tan(1/2*x)+7/2/a^2*ln(tan(1/2*x))+4/3/a^2/(tan(1/2*x)+1)^3-2/a^2/(tan(1/2*x)+1)^2+8/a^2/(tan(1/2*x)+1)","A"
20,1,115,59,0.145000," ","int(csc(x)^4/(a+a*sin(x))^2,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a^{2}}-\frac{\tan^{2}\left(\frac{x}{2}\right)}{4 a^{2}}+\frac{15 \tan \left(\frac{x}{2}\right)}{8 a^{2}}-\frac{1}{24 a^{2} \tan \left(\frac{x}{2}\right)^{3}}+\frac{1}{4 a^{2} \tan \left(\frac{x}{2}\right)^{2}}-\frac{15}{8 a^{2} \tan \left(\frac{x}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{4}{3 a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{10}{a^{2} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/24/a^2*tan(1/2*x)^3-1/4/a^2*tan(1/2*x)^2+15/8/a^2*tan(1/2*x)-1/24/a^2/tan(1/2*x)^3+1/4/a^2/tan(1/2*x)^2-15/8/a^2/tan(1/2*x)-5/a^2*ln(tan(1/2*x))-4/3/a^2/(tan(1/2*x)+1)^3+2/a^2/(tan(1/2*x)+1)^2-10/a^2/(tan(1/2*x)+1)","A"
21,1,174,87,0.105000," ","int(sin(x)^6/(a+a*sin(x))^3,x)","-\frac{3 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{12 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{28 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{3 \tan \left(\frac{x}{2}\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{40}{3 a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{23 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}-\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{8}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{8}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{20}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-3/a^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5-12/a^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^4-28/a^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2+3/a^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)-40/3/a^3/(tan(1/2*x)^2+1)^3-23/a^3*arctan(tan(1/2*x))-8/5/a^3/(tan(1/2*x)+1)^5+4/a^3/(tan(1/2*x)+1)^4+8/3/a^3/(tan(1/2*x)+1)^3-8/a^3/(tan(1/2*x)+1)^2-20/a^3/(tan(1/2*x)+1)","A"
22,1,152,78,0.138000," ","int(sin(x)^5/(a+a*sin(x))^3,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{13 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}+\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{4}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{6}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{12}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+6/a^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2-1/a^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)+6/a^3/(tan(1/2*x)^2+1)^2+13/a^3*arctan(tan(1/2*x))+8/5/a^3/(tan(1/2*x)+1)^5-4/a^3/(tan(1/2*x)+1)^4-4/3/a^3/(tan(1/2*x)+1)^3+6/a^3/(tan(1/2*x)+1)^2+12/a^3/(tan(1/2*x)+1)","A"
23,1,79,65,0.104000," ","int(sin(x)^4/(a+a*sin(x))^3,x)","-\frac{2}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{6 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}-\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{6}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2/a^3/(tan(1/2*x)^2+1)-6/a^3*arctan(tan(1/2*x))-8/5/a^3/(tan(1/2*x)+1)^5+4/a^3/(tan(1/2*x)+1)^4-4/a^3/(tan(1/2*x)+1)^2-6/a^3/(tan(1/2*x)+1)","A"
24,1,77,53,0.105000," ","int(sin(x)^3/(a+a*sin(x))^3,x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}-\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"2/a^3*arctan(tan(1/2*x))-4/a^3/(tan(1/2*x)+1)^4+8/5/a^3/(tan(1/2*x)+1)^5+4/3/a^3/(tan(1/2*x)+1)^3+2/a^3/(tan(1/2*x)+1)^2+2/a^3/(tan(1/2*x)+1)","A"
25,1,37,44,0.093000," ","int(sin(x)^2/(a+a*sin(x))^3,x)","\frac{-\frac{8}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{8}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}}{a^{3}}"," ",0,"8/a^3*(-1/5/(tan(1/2*x)+1)^5+1/2/(tan(1/2*x)+1)^4-1/3/(tan(1/2*x)+1)^3)","A"
26,1,45,44,0.094000," ","int(sin(x)/(a+a*sin(x))^3,x)","\frac{\frac{8}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{4}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}}{a^{3}}"," ",0,"4/a^3*(2/5/(tan(1/2*x)+1)^5+1/(tan(1/2*x)+1)^3-1/2/(tan(1/2*x)+1)^2-1/(tan(1/2*x)+1)^4)","A"
27,1,57,44,0.082000," ","int(1/(a+a*sin(x))^3,x)","\frac{\frac{4}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{8}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{16}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2}{\tan \left(\frac{x}{2}\right)+1}+\frac{4}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}}{a^{3}}"," ",0,"2/a^3*(2/(tan(1/2*x)+1)^4-4/5/(tan(1/2*x)+1)^5-8/3/(tan(1/2*x)+1)^3-1/(tan(1/2*x)+1)+2/(tan(1/2*x)+1)^2)","A"
28,1,76,52,0.121000," ","int(csc(x)/(a+a*sin(x))^3,x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}+\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{20}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{6}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/a^3*ln(tan(1/2*x))+8/5/a^3/(tan(1/2*x)+1)^5-4/a^3/(tan(1/2*x)+1)^4+20/3/a^3/(tan(1/2*x)+1)^3-6/a^3/(tan(1/2*x)+1)^2+6/a^3/(tan(1/2*x)+1)","A"
29,1,97,59,0.141000," ","int(csc(x)^2/(a+a*sin(x))^3,x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a^{3}}-\frac{1}{2 a^{3} \tan \left(\frac{x}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}-\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{8}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{8}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{12}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/2/a^3*tan(1/2*x)-1/2/a^3/tan(1/2*x)-3/a^3*ln(tan(1/2*x))-8/5/a^3/(tan(1/2*x)+1)^5+4/a^3/(tan(1/2*x)+1)^4-8/a^3/(tan(1/2*x)+1)^3+8/a^3/(tan(1/2*x)+1)^2-12/a^3/(tan(1/2*x)+1)","A"
30,1,119,74,0.158000," ","int(csc(x)^3/(a+a*sin(x))^3,x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a^{3}}-\frac{3 \tan \left(\frac{x}{2}\right)}{2 a^{3}}-\frac{1}{8 a^{3} \tan \left(\frac{x}{2}\right)^{2}}+\frac{3}{2 a^{3} \tan \left(\frac{x}{2}\right)}+\frac{13 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{3}}+\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}+\frac{28}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{10}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}+\frac{20}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/8/a^3*tan(1/2*x)^2-3/2/a^3*tan(1/2*x)-1/8/a^3/tan(1/2*x)^2+3/2/a^3/tan(1/2*x)+13/2/a^3*ln(tan(1/2*x))+8/5/a^3/(tan(1/2*x)+1)^5-4/a^3/(tan(1/2*x)+1)^4+28/3/a^3/(tan(1/2*x)+1)^3-10/a^3/(tan(1/2*x)+1)^2+20/a^3/(tan(1/2*x)+1)","A"
31,1,141,89,0.154000," ","int(csc(x)^4/(a+a*sin(x))^3,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8 a^{3}}+\frac{27 \tan \left(\frac{x}{2}\right)}{8 a^{3}}-\frac{1}{24 a^{3} \tan \left(\frac{x}{2}\right)^{3}}+\frac{3}{8 a^{3} \tan \left(\frac{x}{2}\right)^{2}}-\frac{27}{8 a^{3} \tan \left(\frac{x}{2}\right)}-\frac{23 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{3}}-\frac{8}{5 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{32}{3 a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}+\frac{12}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{30}{a^{3} \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/24/a^3*tan(1/2*x)^3-3/8/a^3*tan(1/2*x)^2+27/8/a^3*tan(1/2*x)-1/24/a^3/tan(1/2*x)^3+3/8/a^3/tan(1/2*x)^2-27/8/a^3/tan(1/2*x)-23/2/a^3*ln(tan(1/2*x))-8/5/a^3/(tan(1/2*x)+1)^5+4/a^3/(tan(1/2*x)+1)^4-32/3/a^3/(tan(1/2*x)+1)^3+12/a^3/(tan(1/2*x)+1)^2-30/a^3/(tan(1/2*x)+1)","A"
32,1,83,138,0.803000," ","int(sin(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right) \left(35 \left(\sin^{4}\left(d x +c \right)\right)+40 \left(\sin^{3}\left(d x +c \right)\right)+48 \left(\sin^{2}\left(d x +c \right)\right)+64 \sin \left(d x +c \right)+128\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*a*(sin(d*x+c)-1)*(35*sin(d*x+c)^4+40*sin(d*x+c)^3+48*sin(d*x+c)^2+64*sin(d*x+c)+128)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
33,1,73,106,0.675000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right) \left(5 \left(\sin^{3}\left(d x +c \right)\right)+6 \left(\sin^{2}\left(d x +c \right)\right)+8 \sin \left(d x +c \right)+16\right)}{35 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/35*(1+sin(d*x+c))*a*(sin(d*x+c)-1)*(5*sin(d*x+c)^3+6*sin(d*x+c)^2+8*sin(d*x+c)+16)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
34,1,63,74,0.698000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right) \left(3 \left(\sin^{2}\left(d x +c \right)\right)+4 \sin \left(d x +c \right)+8\right)}{15 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/15*(1+sin(d*x+c))*a*(sin(d*x+c)-1)*(3*sin(d*x+c)^2+4*sin(d*x+c)+8)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
35,1,51,48,0.628000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right) \left(\sin \left(d x +c \right)+2\right)}{3 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/3*(1+sin(d*x+c))*a*(sin(d*x+c)-1)*(sin(d*x+c)+2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
36,1,43,24,0.486000," ","int((a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)}{\cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2*(1+sin(d*x+c))*a*(sin(d*x+c)-1)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
37,1,68,31,0.494000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right)}{\cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a^(1/2)*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
38,1,104,56,0.768000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}+\arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{2} \sin \left(d x +c \right)\right)}{\sin \left(d x +c \right) a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*((a-a*sin(d*x+c))^(1/2)*a^(3/2)+arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^2*sin(d*x+c))/sin(d*x+c)/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
39,1,132,86,0.918000," ","int(csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sin \left(d x +c \right) a^{\frac{3}{2}}+3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+2 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{4 \sin \left(d x +c \right)^{2} a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(3*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)*a^(3/2)+3*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+2*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^2/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
40,1,158,118,0.782000," ","int(csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(15 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right)+15 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+10 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sin \left(d x +c \right) a^{\frac{3}{2}}+8 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{24 \sin \left(d x +c \right)^{3} a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(15*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)*sin(d*x+c)^2+15*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+10*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)*a^(3/2)+8*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^3/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
41,1,67,32,0.730000," ","int(csc(d*x+c)*(a-a*sin(d*x+c))^(1/2),x)","\frac{2 \left(\sin \left(d x +c \right)-1\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \sqrt{a}\, \arctanh \left(\frac{\sqrt{a \left(1+\sin \left(d x +c \right)\right)}}{\sqrt{a}}\right)}{\cos \left(d x +c \right) \sqrt{a -a \sin \left(d x +c \right)}\, d}"," ",0,"2*(sin(d*x+c)-1)*(a*(1+sin(d*x+c)))^(1/2)*a^(1/2)*arctanh((a*(1+sin(d*x+c)))^(1/2)/a^(1/2))/cos(d*x+c)/(a-a*sin(d*x+c))^(1/2)/d","B"
42,1,70,33,0.542000," ","int(csc(d*x+c)*(a*sin(d*x+c)-a)^(1/2),x)","\frac{2 \left(\sin \left(d x +c \right)-1\right) \sqrt{-a \left(1+\sin \left(d x +c \right)\right)}\, \sqrt{a}\, \arctan \left(\frac{\sqrt{-a \left(1+\sin \left(d x +c \right)\right)}}{\sqrt{a}}\right)}{\cos \left(d x +c \right) \sqrt{a \sin \left(d x +c \right)-a}\, d}"," ",0,"2*(sin(d*x+c)-1)*(-a*(1+sin(d*x+c)))^(1/2)*a^(1/2)*arctan((-a*(1+sin(d*x+c)))^(1/2)/a^(1/2))/cos(d*x+c)/(a*sin(d*x+c)-a)^(1/2)/d","B"
43,1,69,34,0.491000," ","int(csc(d*x+c)*(-a-a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\, \arctan \left(\frac{\sqrt{a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right)}{\cos \left(d x +c \right) \sqrt{-a -a \sin \left(d x +c \right)}\, d}"," ",0,"-2*(1+sin(d*x+c))*(a*(sin(d*x+c)-1))^(1/2)*a^(1/2)*arctan((a*(sin(d*x+c)-1))^(1/2)/a^(1/2))/cos(d*x+c)/(-a-a*sin(d*x+c))^(1/2)/d","A"
44,1,85,142,0.630000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right) \left(35 \left(\sin^{4}\left(d x +c \right)\right)+85 \left(\sin^{3}\left(d x +c \right)\right)+102 \left(\sin^{2}\left(d x +c \right)\right)+136 \sin \left(d x +c \right)+272\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)*(35*sin(d*x+c)^4+85*sin(d*x+c)^3+102*sin(d*x+c)^2+136*sin(d*x+c)+272)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
45,1,75,100,0.610000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right) \left(15 \left(\sin^{3}\left(d x +c \right)\right)+39 \left(\sin^{2}\left(d x +c \right)\right)+52 \sin \left(d x +c \right)+104\right)}{105 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/105*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)*(15*sin(d*x+c)^3+39*sin(d*x+c)^2+52*sin(d*x+c)+104)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
46,1,63,74,0.767000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right) \left(\sin^{2}\left(d x +c \right)+3 \sin \left(d x +c \right)+6\right)}{5 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/5*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)*(sin(d*x+c)^2+3*sin(d*x+c)+6)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
47,1,53,51,0.582000," ","int((a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right) \left(\sin \left(d x +c \right)+5\right)}{3 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/3*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)*(sin(d*x+c)+5)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
48,1,84,58,0.643000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a \left(\sqrt{a -a \sin \left(d x +c \right)}+\sqrt{a}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)}{\cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a*((a-a*sin(d*x+c))^(1/2)+a^(1/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
49,1,103,58,0.744000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\, \left(3 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a \sin \left(d x +c \right)+\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)}{\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a^(1/2)*(3*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a*sin(d*x+c)+(a-a*sin(d*x+c))^(1/2)*a^(1/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
50,1,126,90,0.934000," ","int(csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(7 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-7 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-9 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}\right)}{4 \sin \left(d x +c \right)^{2} a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(7*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)-7*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^2-9*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2))/sin(d*x+c)^2/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
51,1,144,124,0.785000," ","int(csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(33 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}-88 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+33 a^{5} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right)+63 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}\right)}{24 a^{\frac{7}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*(33*(-a*(sin(d*x+c)-1))^(5/2)*a^(5/2)-88*(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+33*a^5*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3+63*(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
52,1,95,179,0.618000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right) \left(63 \left(\sin^{5}\left(d x +c \right)\right)+224 \left(\sin^{4}\left(d x +c \right)\right)+355 \left(\sin^{3}\left(d x +c \right)\right)+426 \left(\sin^{2}\left(d x +c \right)\right)+568 \sin \left(d x +c \right)+1136\right)}{693 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/693*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)*(63*sin(d*x+c)^5+224*sin(d*x+c)^4+355*sin(d*x+c)^3+426*sin(d*x+c)^2+568*sin(d*x+c)+1136)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
53,1,85,126,0.707000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right) \left(35 \left(\sin^{4}\left(d x +c \right)\right)+130 \left(\sin^{3}\left(d x +c \right)\right)+219 \left(\sin^{2}\left(d x +c \right)\right)+292 \sin \left(d x +c \right)+584\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)*(35*sin(d*x+c)^4+130*sin(d*x+c)^3+219*sin(d*x+c)^2+292*sin(d*x+c)+584)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
54,1,75,100,0.612000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right) \left(3 \left(\sin^{3}\left(d x +c \right)\right)+12 \left(\sin^{2}\left(d x +c \right)\right)+23 \sin \left(d x +c \right)+46\right)}{21 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/21*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)*(3*sin(d*x+c)^3+12*sin(d*x+c)^2+23*sin(d*x+c)+46)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
55,1,65,77,0.575000," ","int((a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right) \left(3 \left(\sin^{2}\left(d x +c \right)\right)+14 \sin \left(d x +c \right)+43\right)}{15 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/15*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)*(3*sin(d*x+c)^2+14*sin(d*x+c)+43)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
56,1,103,84,0.820000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a \left(3 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)-\left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}+9 a \sqrt{a -a \sin \left(d x +c \right)}\right)}{3 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a*(3*a^(3/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))-(a-a*sin(d*x+c))^(3/2)+9*a*(a-a*sin(d*x+c))^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
57,1,123,84,0.958000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}} \left(\sin \left(d x +c \right) \left(2 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}+5 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a \right)+\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)}{\sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)*(sin(d*x+c)*(2*(a-a*sin(d*x+c))^(1/2)*a^(1/2)+5*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a)+(a-a*sin(d*x+c))^(1/2)*a^(1/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
58,1,126,90,0.786000," ","int(csc(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\, \left(-19 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+11 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}-13 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{4 \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*a^(1/2)*(-19*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+11*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)-13*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
59,1,144,124,0.812000," ","int(csc(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(75 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+75 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(d x +c \right)\right)-184 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}+117 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}\right)}{24 \sin \left(d x +c \right)^{3} a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(75*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)+75*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^3-184*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)+117*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2))/sin(d*x+c)^3/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
60,1,162,158,0.836000," ","int(csc(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(1047 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{11}{2}}-2303 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{9}{2}}+1793 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{7}{2}}-489 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{5}{2}}+489 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{6} \left(\sin^{4}\left(d x +c \right)\right)\right)}{192 a^{\frac{7}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/192*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(1047*(-a*(sin(d*x+c)-1))^(1/2)*a^(11/2)-2303*(-a*(sin(d*x+c)-1))^(3/2)*a^(9/2)+1793*(-a*(sin(d*x+c)-1))^(5/2)*a^(7/2)-489*(-a*(sin(d*x+c)-1))^(7/2)*a^(5/2)+489*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^6*sin(d*x+c)^4)/a^(7/2)/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
61,1,130,118,0.937000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(15 a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-6 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}+10 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a -30 a^{2} \sqrt{a -a \sin \left(d x +c \right)}\right)}{15 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/15*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(15*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-6*(a-a*sin(d*x+c))^(5/2)+10*(a-a*sin(d*x+c))^(3/2)*a-30*a^2*(a-a*sin(d*x+c))^(1/2))/a^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
62,1,96,88,0.766000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(3 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-2 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}\right)}{3 a^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(3*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-2*(a-a*sin(d*x+c))^(3/2))/a^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
63,1,94,61,0.793000," ","int(sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-2 \sqrt{a -a \sin \left(d x +c \right)}\right)}{a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-2*(a-a*sin(d*x+c))^(1/2))/a/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
64,1,75,38,0.634000," ","int(1/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{\sqrt{a}\, \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
65,1,96,69,0.781000," ","int(csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-2 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)}{\sqrt{a}\, \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-2*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))/a^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
66,1,133,92,0.811000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) a^{3} \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-\arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)+\sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}\right)}{a^{\frac{7}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*(sin(d*x+c)*a^3*(2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))+(a-a*sin(d*x+c))^(1/2)*a^(5/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
67,1,162,121,1.002000," ","int(csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(7 a^{5} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right)+\left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}-4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} \left(\sin^{2}\left(d x +c \right)\right)\right)}{4 a^{\frac{11}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(11/2)*(7*a^5*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2+(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2)-4*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^5*sin(d*x+c)^2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
68,1,183,156,0.724000," ","int(sin(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(\sin \left(d x +c \right) \left(-8 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a}-80 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}+75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right)-8 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a}-90 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}+75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{20 a^{\frac{9}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/20*(sin(d*x+c)*(-8*(a-a*sin(d*x+c))^(5/2)*a^(1/2)-80*(a-a*sin(d*x+c))^(1/2)*a^(5/2)+75*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)-8*(a-a*sin(d*x+c))^(5/2)*a^(1/2)-90*(a-a*sin(d*x+c))^(1/2)*a^(5/2)+75*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*(-a*(sin(d*x+c)-1))^(1/2)/a^(9/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
69,1,183,122,0.684000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(\sin \left(d x +c \right) \left(33 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-8 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}-24 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)+33 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-8 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}-30 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{12 a^{\frac{7}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/12*(sin(d*x+c)*(33*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-8*(a-a*sin(d*x+c))^(3/2)*a^(1/2)-24*(a-a*sin(d*x+c))^(1/2)*a^(3/2))+33*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-8*(a-a*sin(d*x+c))^(3/2)*a^(1/2)-30*(a-a*sin(d*x+c))^(1/2)*a^(3/2))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
70,1,143,88,0.604000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(\sin \left(d x +c \right) \left(-7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +8 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)-7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +10 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4/a^(5/2)*(sin(d*x+c)*(-7*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+8*(a-a*sin(d*x+c))^(1/2)*a^(1/2))-7*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+10*(a-a*sin(d*x+c))^(1/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
71,1,123,62,0.724000," ","int(sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sin \left(d x +c \right)+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a -2 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a*sin(d*x+c)+3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a-2*(a-a*sin(d*x+c))^(1/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/a^(5/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
72,1,125,62,0.549000," ","int(1/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \sin \left(d x +c \right)+2 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{7}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4/a^(7/2)*(2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*sin(d*x+c)+2*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)*(-a*(sin(d*x+c)-1))^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
73,1,172,93,0.800000," ","int(csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(\sin \left(d x +c \right) a^{3} \left(5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-8 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)+2 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}+5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}-8 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{3}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{9}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4/a^(9/2)*(sin(d*x+c)*a^3*(5*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-8*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))+2*(a-a*sin(d*x+c))^(1/2)*a^(5/2)+5*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3-8*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^3)*(-a*(sin(d*x+c)-1))^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
74,1,219,119,0.683000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a +9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sin \left(d x +c \right)-12 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a +6 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\, \sin \left(d x +c \right)-12 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a \sin \left(d x +c \right)+4 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4/a^(5/2)*(9*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^2*a+9*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a*sin(d*x+c)-12*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a+6*(-a*(sin(d*x+c)-1))^(1/2)*a^(1/2)*sin(d*x+c)-12*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a*sin(d*x+c)+4*(-a*(sin(d*x+c)-1))^(1/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
75,1,299,157,0.926000," ","int(csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(13 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+2 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right)+13 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}-19 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sin \left(d x +c \right) a^{\frac{3}{2}}-5 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\, \sin \left(d x +c \right)-19 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}-5 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{4 a^{\frac{7}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(13*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+2*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)*sin(d*x+c)^2+13*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2-19*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+3*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)*a^(3/2)-5*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)*sin(d*x+c)-19*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+3*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)-5*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
76,1,323,190,0.944000," ","int(sin(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(\sin \left(d x +c \right) \left(384 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a}+640 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+7680 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}-8490 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right)+\left(-192 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a}-320 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-3840 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}+4245 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \left(\cos^{2}\left(d x +c \right)\right)+384 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a}-470 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+9780 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}-8490 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{480 a^{\frac{11}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/480/a^(11/2)*(sin(d*x+c)*(384*(a-a*sin(d*x+c))^(5/2)*a^(1/2)+640*(a-a*sin(d*x+c))^(3/2)*a^(3/2)+7680*(a-a*sin(d*x+c))^(1/2)*a^(5/2)-8490*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)+(-192*(a-a*sin(d*x+c))^(5/2)*a^(1/2)-320*(a-a*sin(d*x+c))^(3/2)*a^(3/2)-3840*(a-a*sin(d*x+c))^(1/2)*a^(5/2)+4245*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*cos(d*x+c)^2+384*(a-a*sin(d*x+c))^(5/2)*a^(1/2)-470*(a-a*sin(d*x+c))^(3/2)*a^(3/2)+9780*(a-a*sin(d*x+c))^(1/2)*a^(5/2)-8490*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
77,1,269,156,0.968000," ","int(sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(\sin \left(d x +c \right) \left(128 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}+768 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}-978 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right)+\left(-64 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}-384 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}+489 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-46 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}+1092 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}-978 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{96 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/96/a^(9/2)*(sin(d*x+c)*(128*(a-a*sin(d*x+c))^(3/2)*a^(1/2)+768*(a-a*sin(d*x+c))^(1/2)*a^(3/2)-978*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)+(-64*(a-a*sin(d*x+c))^(3/2)*a^(1/2)-384*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+489*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)*cos(d*x+c)^2-46*(a-a*sin(d*x+c))^(3/2)*a^(1/2)+1092*(a-a*sin(d*x+c))^(1/2)*a^(3/2)-978*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
78,1,233,122,1.012000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(\sin \left(d x +c \right) \left(150 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-128 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)+\left(-75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+64 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right)+150 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+42 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}-204 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/32/a^(9/2)*(sin(d*x+c)*(150*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-128*(a-a*sin(d*x+c))^(1/2)*a^(3/2))+(-75*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2+64*(a-a*sin(d*x+c))^(1/2)*a^(3/2))*cos(d*x+c)^2+150*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2+42*(a-a*sin(d*x+c))^(3/2)*a^(1/2)-204*(a-a*sin(d*x+c))^(1/2)*a^(3/2))*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
79,1,193,88,0.818000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(-19 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a^{2} \left(\cos^{2}\left(d x +c \right)\right)+38 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \sin \left(d x +c \right)+38 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-44 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}+26 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/32/a^(9/2)*(-19*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*cos(d*x+c)^2+38*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*sin(d*x+c)+38*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-44*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+26*(a-a*sin(d*x+c))^(3/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
80,1,193,88,0.997000," ","int(sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(5 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a^{3} \left(\cos^{2}\left(d x +c \right)\right)-10 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \sin \left(d x +c \right)+10 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-12 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{5}{2}}-10 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{11}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/32/a^(11/2)*(5*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a^3*cos(d*x+c)^2-10*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*sin(d*x+c)+10*(a-a*sin(d*x+c))^(3/2)*a^(3/2)-12*(a-a*sin(d*x+c))^(1/2)*a^(5/2)-10*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
81,1,195,88,0.849000," ","int(1/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(\sin \left(d x +c \right) \left(6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+6 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)-3 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a^{2} \left(\cos^{2}\left(d x +c \right)\right)+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+14 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/32/a^(9/2)*(sin(d*x+c)*(6*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+6*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)-3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*cos(d*x+c)^2+14*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+6*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2)*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
82,1,262,119,0.921000," ","int(csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(2 \sin \left(d x +c \right) a^{5} \left(43 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-64 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)-a^{5} \left(43 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-64 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right) \left(\cos^{2}\left(d x +c \right)\right)+52 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{9}{2}}-22 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+86 a^{5} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-128 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{5}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{15}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/32/a^(15/2)*(2*sin(d*x+c)*a^5*(43*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-64*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))-a^5*(43*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-64*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))*cos(d*x+c)^2+52*(a-a*sin(d*x+c))^(1/2)*a^(9/2)-22*(a-a*sin(d*x+c))^(3/2)*a^(7/2)+86*a^5*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-128*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^5)*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
83,1,356,145,1.120000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(115 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+32 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right)+230 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}-160 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+148 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sin \left(d x +c \right) a^{\frac{3}{2}}-38 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\, \sin \left(d x +c \right)+115 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \sin \left(d x +c \right)-320 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+32 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}-160 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{2} \sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/32*(115*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+32*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)*sin(d*x+c)^2+230*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2-160*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+148*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)*a^(3/2)-38*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)*sin(d*x+c)+115*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^2*sin(d*x+c)-320*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+32*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)-160*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^2*sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(9/2)/(1+sin(d*x+c))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
84,1,404,189,1.283000," ","int(csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(-219 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{4}\left(d x +c \right)\right) a^{2}+312 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{4}\left(d x +c \right)\right) a^{2}-438 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}+126 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\, \left(\sin^{2}\left(d x +c \right)\right)+624 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right) a^{2}-219 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+144 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\, \sin \left(d x +c \right)-172 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right)+312 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+72 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}-112 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sin \left(d x +c \right) a^{\frac{3}{2}}-56 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{32 a^{\frac{9}{2}} \left(1+\sin \left(d x +c \right)\right) \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/32/a^(9/2)*(-219*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^4*a^2+312*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^4*a^2-438*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2+126*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)*sin(d*x+c)^2+624*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3*a^2-219*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+144*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)*sin(d*x+c)-172*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)*sin(d*x+c)^2+312*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+72*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)-112*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)*a^(3/2)-56*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))*(-a*(sin(d*x+c)-1))^(1/2)/(1+sin(d*x+c))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","B"
85,1,320,31,0.316000," ","int((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)^(1/2),x)","\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\sqrt{\sin}\left(f x +e \right)\right) \left(\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right)+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}+1\right)+4 \arctan \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}-1\right)+\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right)\right) \sqrt{2}}{2 f \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/2/f*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)^(1/2)*(ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)+1)+4*arctan((-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*2^(1/2)-1)+ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)))*2^(1/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
86,1,271,32,0.225000," ","int((a-a*sin(f*x+e))^(1/2)/(-sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}\right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)+\sin \left(f x +e \right)-\cos \left(f x +e \right)+1}\right)\right) \sqrt{2}}{2 f \sqrt{-\sin \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/2/f*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1))-ln(-(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)/(2^(1/2)*(-(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)+sin(f*x+e)-cos(f*x+e)+1)))/(-sin(f*x+e))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))*2^(1/2)","B"
87,1,52,15,0.129000," ","int(1/sin(x)^(1/2)/(1+sin(x))^(1/2),x)","-\frac{2 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(1-\cos \left(x \right)+\sin \left(x \right)\right) \left(\sqrt{\sin}\left(x \right)\right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)}{\sqrt{1+\sin \left(x \right)}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"-2*(-(-1+cos(x))/sin(x))^(1/2)*(1-cos(x)+sin(x))*sin(x)^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))/(1+sin(x))^(1/2)/(-1+cos(x))","B"
88,1,54,31,0.161000," ","int(1/sin(x)^(1/2)/(a+a*sin(x))^(1/2),x)","\frac{2 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(-1+\cos \left(x \right)-\sin \left(x \right)\right) \left(\sqrt{\sin}\left(x \right)\right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)}{\sqrt{a \left(1+\sin \left(x \right)\right)}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"2*(-(-1+cos(x))/sin(x))^(1/2)*(-1+cos(x)-sin(x))*sin(x)^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))/(a*(1+sin(x)))^(1/2)/(-1+cos(x))","A"
89,1,52,24,0.160000," ","int(1/(1-sin(x))^(1/2)/sin(x)^(1/2),x)","-\frac{2 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(-1+\cos \left(x \right)+\sin \left(x \right)\right) \left(\sqrt{\sin}\left(x \right)\right) \arctanh \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)}{\sqrt{1-\sin \left(x \right)}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"-2*(-(-1+cos(x))/sin(x))^(1/2)*(-1+cos(x)+sin(x))*sin(x)^(1/2)*arctanh((-(-1+cos(x))/sin(x))^(1/2))/(1-sin(x))^(1/2)/(-1+cos(x))","B"
90,1,53,31,0.152000," ","int(1/sin(x)^(1/2)/(a-a*sin(x))^(1/2),x)","-\frac{2 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(-1+\cos \left(x \right)+\sin \left(x \right)\right) \left(\sqrt{\sin}\left(x \right)\right) \arctanh \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)}{\sqrt{-a \left(-1+\sin \left(x \right)\right)}\, \left(-1+\cos \left(x \right)\right)}"," ",0,"-2*(-(-1+cos(x))/sin(x))^(1/2)*(-1+cos(x)+sin(x))*sin(x)^(1/2)*arctanh((-(-1+cos(x))/sin(x))^(1/2))/(-a*(-1+sin(x)))^(1/2)/(-1+cos(x))","A"
91,0,0,156,0.775000," ","int(sin(d*x+c)^(1/3)/(a+a*sin(d*x+c))^2,x)","\int \frac{\sin^{\frac{1}{3}}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(sin(d*x+c)^(1/3)/(a+a*sin(d*x+c))^2,x)","F"
92,0,0,133,0.651000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(2/3),x)","\int \left(\sin^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(2/3),x)","F"
93,0,0,102,0.649000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x)","\int \left(\sin^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x)","F"
94,0,0,76,0.160000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^(2/3),x)","\int \sin \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(sin(d*x+c)*(a+a*sin(d*x+c))^(2/3),x)","F"
95,0,0,52,0.006000," ","int((a+a*sin(d*x+c))^(2/3),x)","\int \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((a+a*sin(d*x+c))^(2/3),x)","F"
96,0,0,61,0.210000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^(2/3),x)","\int \csc \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(csc(d*x+c)*(a+a*sin(d*x+c))^(2/3),x)","F"
97,0,0,61,0.178000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(2/3),x)","F"
98,0,0,134,0.593000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(4/3),x)","\int \left(\sin^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sin(d*x+c)^3*(a+a*sin(d*x+c))^(4/3),x)","F"
99,0,0,103,0.602000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x)","\int \left(\sin^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sin(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x)","F"
100,0,0,77,0.156000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^(4/3),x)","\int \sin \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(sin(d*x+c)*(a+a*sin(d*x+c))^(4/3),x)","F"
101,0,0,53,0.006000," ","int((a+a*sin(d*x+c))^(4/3),x)","\int \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((a+a*sin(d*x+c))^(4/3),x)","F"
102,0,0,62,0.204000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^(4/3),x)","\int \csc \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(csc(d*x+c)*(a+a*sin(d*x+c))^(4/3),x)","F"
103,0,0,62,0.178000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(csc(d*x+c)^2*(a+a*sin(d*x+c))^(4/3),x)","F"
104,0,0,133,0.830000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{\sin^{3}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/3),x)","F"
105,0,0,102,0.489000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{\sin^{2}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x)","F"
106,0,0,76,0.342000," ","int(sin(d*x+c)/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{\sin \left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sin(d*x+c)/(a+a*sin(d*x+c))^(1/3),x)","F"
107,0,0,52,0.005000," ","int(1/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{1}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+a*sin(d*x+c))^(1/3),x)","F"
108,0,0,61,0.235000," ","int(csc(d*x+c)/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{\csc \left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(csc(d*x+c)/(a+a*sin(d*x+c))^(1/3),x)","F"
109,0,0,61,0.226000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x)","\int \frac{\csc^{2}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/3),x)","F"
110,0,0,136,0.857000," ","int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{\sin^{3}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sin(d*x+c)^3/(a+a*sin(d*x+c))^(4/3),x)","F"
111,0,0,105,0.433000," ","int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{\sin^{2}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sin(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x)","F"
112,0,0,79,0.170000," ","int(sin(d*x+c)/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{\sin \left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sin(d*x+c)/(a+a*sin(d*x+c))^(4/3),x)","F"
113,0,0,55,0.005000," ","int(1/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{1}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+a*sin(d*x+c))^(4/3),x)","F"
114,0,0,64,0.204000," ","int(csc(d*x+c)/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{\csc \left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(csc(d*x+c)/(a+a*sin(d*x+c))^(4/3),x)","F"
115,0,0,64,0.207000," ","int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x)","\int \frac{\csc^{2}\left(d x +c \right)}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(csc(d*x+c)^2/(a+a*sin(d*x+c))^(4/3),x)","F"
116,0,0,90,0.240000," ","int(sin(f*x+e)^n*(1+sin(f*x+e))^(3/2),x)","\int \left(\sin^{n}\left(f x +e \right)\right) \left(1+\sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sin(f*x+e)^n*(1+sin(f*x+e))^(3/2),x)","F"
117,0,0,39,0.166000," ","int(sin(f*x+e)^n*(1+sin(f*x+e))^(1/2),x)","\int \left(\sin^{n}\left(f x +e \right)\right) \sqrt{1+\sin \left(f x +e \right)}\, dx"," ",0,"int(sin(f*x+e)^n*(1+sin(f*x+e))^(1/2),x)","F"
118,0,0,48,0.156000," ","int(sin(f*x+e)^n/(1+sin(f*x+e))^(1/2),x)","\int \frac{\sin^{n}\left(f x +e \right)}{\sqrt{1+\sin \left(f x +e \right)}}\, dx"," ",0,"int(sin(f*x+e)^n/(1+sin(f*x+e))^(1/2),x)","F"
119,0,0,48,0.155000," ","int(sin(f*x+e)^n/(1+sin(f*x+e))^(3/2),x)","\int \frac{\sin^{n}\left(f x +e \right)}{\left(1+\sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sin(f*x+e)^n/(1+sin(f*x+e))^(3/2),x)","F"
120,0,0,100,0.216000," ","int(sin(f*x+e)^n*(a+a*sin(f*x+e))^(3/2),x)","\int \left(\sin^{n}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(sin(f*x+e)^n*(a+a*sin(f*x+e))^(3/2),x)","F"
121,0,0,42,0.221000," ","int(sin(f*x+e)^n*(a+a*sin(f*x+e))^(1/2),x)","\int \left(\sin^{n}\left(f x +e \right)\right) \sqrt{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int(sin(f*x+e)^n*(a+a*sin(f*x+e))^(1/2),x)","F"
122,0,0,50,0.205000," ","int(sin(f*x+e)^n/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\sin^{n}\left(f x +e \right)}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int(sin(f*x+e)^n/(a+a*sin(f*x+e))^(1/2),x)","F"
123,0,0,53,0.204000," ","int(sin(f*x+e)^n/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\sin^{n}\left(f x +e \right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(sin(f*x+e)^n/(a+a*sin(f*x+e))^(3/2),x)","F"
124,0,0,124,0.220000," ","int((d*sin(f*x+e))^n*(1+sin(f*x+e))^(3/2),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(1+\sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(1+sin(f*x+e))^(3/2),x)","F"
125,0,0,68,0.188000," ","int((d*sin(f*x+e))^n*(1+sin(f*x+e))^(1/2),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \sqrt{1+\sin \left(f x +e \right)}\, dx"," ",0,"int((d*sin(f*x+e))^n*(1+sin(f*x+e))^(1/2),x)","F"
126,0,0,68,0.181000," ","int((d*sin(f*x+e))^n/(1+sin(f*x+e))^(1/2),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n}}{\sqrt{1+\sin \left(f x +e \right)}}\, dx"," ",0,"int((d*sin(f*x+e))^n/(1+sin(f*x+e))^(1/2),x)","F"
127,0,0,68,0.191000," ","int((d*sin(f*x+e))^n/(1+sin(f*x+e))^(3/2),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n}}{\left(1+\sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*sin(f*x+e))^n/(1+sin(f*x+e))^(3/2),x)","F"
128,0,0,125,0.246000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2),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}}\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2),x)","F"
129,0,0,62,0.244000," ","int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2),x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \sqrt{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2),x)","F"
130,0,0,70,0.258000," ","int((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","F"
131,0,0,73,0.215000," ","int((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\left(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((d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","F"
132,0,0,57,0.855000," ","int(sin(f*x+e)^n*(1+sin(f*x+e))^m,x)","\int \left(\sin^{n}\left(f x +e \right)\right) \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sin(f*x+e)^n*(1+sin(f*x+e))^m,x)","F"
133,0,0,56,1.055000," ","int((1-sin(f*x+e))^m*(-sin(f*x+e))^n,x)","\int \left(1-\sin \left(f x +e \right)\right)^{m} \left(-\sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((1-sin(f*x+e))^m*(-sin(f*x+e))^n,x)","F"
134,0,0,77,0.966000," ","int((d*sin(f*x+e))^n*(1+sin(f*x+e))^m,x)","\int \left(d \sin \left(f x +e \right)\right)^{n} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sin(f*x+e))^n*(1+sin(f*x+e))^m,x)","F"
135,0,0,78,0.979000," ","int((1-sin(f*x+e))^m*(d*sin(f*x+e))^n,x)","\int \left(1-\sin \left(f x +e \right)\right)^{m} \left(d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((1-sin(f*x+e))^m*(d*sin(f*x+e))^n,x)","F"
136,0,0,73,1.013000," ","int(sin(f*x+e)^n*(a+a*sin(f*x+e))^m,x)","\int \left(\sin^{n}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sin(f*x+e)^n*(a+a*sin(f*x+e))^m,x)","F"
137,0,0,73,1.168000," ","int((-sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x)","\int \left(-\sin \left(f x +e \right)\right)^{n} \left(a -a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x)","F"
138,0,0,93,1.063000," ","int((d*sin(f*x+e))^n*(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)^{m}\, dx"," ",0,"int((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x)","F"
139,0,0,95,1.054000," ","int((d*sin(f*x+e))^n*(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)^{m}\, dx"," ",0,"int((d*sin(f*x+e))^n*(a-a*sin(f*x+e))^m,x)","F"
140,0,0,282,3.039000," ","int(sin(d*x+c)^4*(a+a*sin(d*x+c))^n,x)","\int \left(\sin^{4}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^4*(a+a*sin(d*x+c))^n,x)","F"
141,0,0,203,2.210000," ","int(sin(d*x+c)^3*(a+a*sin(d*x+c))^n,x)","\int \left(\sin^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^3*(a+a*sin(d*x+c))^n,x)","F"
142,0,0,144,1.817000," ","int(sin(d*x+c)^2*(a+a*sin(d*x+c))^n,x)","\int \left(\sin^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^2*(a+a*sin(d*x+c))^n,x)","F"
143,0,0,97,1.526000," ","int(sin(d*x+c)*(a+a*sin(d*x+c))^n,x)","\int \sin \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)*(a+a*sin(d*x+c))^n,x)","F"
144,0,0,62,0.006000," ","int((a+a*sin(d*x+c))^n,x)","\int \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(d*x+c))^n,x)","F"
145,0,0,71,1.275000," ","int(csc(d*x+c)*(a+a*sin(d*x+c))^n,x)","\int \csc \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)*(a+a*sin(d*x+c))^n,x)","F"
146,0,0,71,0.602000," ","int(csc(d*x+c)^2*(a+a*sin(d*x+c))^n,x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^2*(a+a*sin(d*x+c))^n,x)","F"
147,0,0,46,0.468000," ","int((1+sin(d*x+c))^n,x)","\int \left(1+\sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((1+sin(d*x+c))^n,x)","F"
148,0,0,47,0.527000," ","int((1-sin(d*x+c))^n,x)","\int \left(1-\sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((1-sin(d*x+c))^n,x)","F"
149,1,60,69,0.225000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e)),x)","\frac{b \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 \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(b*(-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*a*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
150,1,49,49,0.158000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e)),x)","\frac{-\frac{b \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{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)}{f}"," ",0,"1/f*(-1/3*b*(2+sin(f*x+e)^2)*cos(f*x+e)+a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
151,1,39,35,0.049000," ","int(sin(f*x+e)*(a+b*sin(f*x+e)),x)","\frac{b \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-\cos \left(f x +e \right) a}{f}"," ",0,"1/f*(b*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-cos(f*x+e)*a)","A"
152,1,17,16,0.009000," ","int(a+b*sin(f*x+e),x)","a x -\frac{b \cos \left(f x +e \right)}{f}"," ",0,"a*x-b*cos(f*x+e)/f","A"
153,1,32,17,0.109000," ","int(csc(f*x+e)*(a+b*sin(f*x+e)),x)","b x +\frac{a \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{b e}{f}"," ",0,"b*x+1/f*a*ln(csc(f*x+e)-cot(f*x+e))+1/f*b*e","A"
154,1,35,26,0.167000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e)),x)","-\frac{a \cot \left(f x +e \right)}{f}+\frac{b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"-a*cot(f*x+e)/f+1/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
155,1,54,44,0.288000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e)),x)","-\frac{a \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{a \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{b \cot \left(f x +e \right)}{f}"," ",0,"-1/2*a*cot(f*x+e)*csc(f*x+e)/f+1/2/f*a*ln(csc(f*x+e)-cot(f*x+e))-b*cot(f*x+e)/f","A"
156,1,74,58,0.339000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e)),x)","-\frac{2 a \cot \left(f x +e \right)}{3 f}-\frac{a \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}-\frac{b \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}"," ",0,"-2/3*a*cot(f*x+e)/f-1/3/f*a*cot(f*x+e)*csc(f*x+e)^2-1/2*b*cot(f*x+e)*csc(f*x+e)/f+1/2/f*b*ln(csc(f*x+e)-cot(f*x+e))","A"
157,1,95,102,0.283000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e))^2,x)","\frac{-\frac{b^{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 b \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} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-1/5*b^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+2*a*b*(-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*a^2*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
158,1,89,93,0.210000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e))^2,x)","\frac{b^{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 b \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+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)}{f}"," ",0,"1/f*(b^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*b*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
159,1,64,65,0.163000," ","int(sin(f*x+e)*(a+b*sin(f*x+e))^2,x)","\frac{-\frac{b^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 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)-\cos \left(f x +e \right) a^{2}}{f}"," ",0,"1/f*(-1/3*b^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a*b*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-cos(f*x+e)*a^2)","A"
160,1,51,46,0.084000," ","int((a+b*sin(f*x+e))^2,x)","\frac{b^{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 b \cos \left(f x +e \right)+a^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(b^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*b*cos(f*x+e)+a^2*(f*x+e))","A"
161,1,52,35,0.195000," ","int(csc(f*x+e)*(a+b*sin(f*x+e))^2,x)","2 a b x +\frac{a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}-\frac{b^{2} \cos \left(f x +e \right)}{f}+\frac{2 a b e}{f}"," ",0,"2*a*b*x+1/f*a^2*ln(csc(f*x+e)-cot(f*x+e))-b^2*cos(f*x+e)/f+2/f*a*b*e","A"
162,1,52,34,0.250000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e))^2,x)","b^{2} x -\frac{a^{2} \cot \left(f x +e \right)}{f}+\frac{2 a b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{b^{2} e}{f}"," ",0,"b^2*x-a^2*cot(f*x+e)/f+2/f*a*b*ln(csc(f*x+e)-cot(f*x+e))+1/f*b^2*e","A"
163,1,82,55,0.370000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e))^2,x)","-\frac{a^{2} \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{2 a b \cot \left(f x +e \right)}{f}+\frac{b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"-1/2*a^2*cot(f*x+e)*csc(f*x+e)/f+1/2/f*a^2*ln(csc(f*x+e)-cot(f*x+e))-2*a*b*cot(f*x+e)/f+1/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","A"
164,1,93,78,0.402000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e))^2,x)","-\frac{2 a^{2} \cot \left(f x +e \right)}{3 f}-\frac{a^{2} \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}-\frac{a b \cot \left(f x +e \right) \csc \left(f x +e \right)}{f}+\frac{a b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}-\frac{b^{2} \cot \left(f x +e \right)}{f}"," ",0,"-2/3*a^2*cot(f*x+e)/f-1/3*a^2*cot(f*x+e)*csc(f*x+e)^2/f-a*b*cot(f*x+e)*csc(f*x+e)/f+1/f*a*b*ln(csc(f*x+e)-cot(f*x+e))-1/f*b^2*cot(f*x+e)","A"
165,1,146,102,0.428000," ","int(csc(f*x+e)^5*(a+b*sin(f*x+e))^2,x)","-\frac{a^{2} \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}-\frac{3 a^{2} \cot \left(f x +e \right) \csc \left(f x +e \right)}{8 f}+\frac{3 a^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}-\frac{4 a b \cot \left(f x +e \right)}{3 f}-\frac{2 a b \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}-\frac{b^{2} \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}"," ",0,"-1/4*a^2*cot(f*x+e)*csc(f*x+e)^3/f-3/8*a^2*cot(f*x+e)*csc(f*x+e)/f+3/8/f*a^2*ln(csc(f*x+e)-cot(f*x+e))-4/3*a*b*cot(f*x+e)/f-2/3/f*a*b*cot(f*x+e)*csc(f*x+e)^2-1/2/f*b^2*cot(f*x+e)*csc(f*x+e)+1/2/f*b^2*ln(csc(f*x+e)-cot(f*x+e))","A"
166,1,145,159,0.352000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e))^3,x)","\frac{b^{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 a \,b^{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^{2} b \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} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(b^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*a*b^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*a^2*b*(-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*a^3*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
167,1,124,148,0.273000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e))^3,x)","\frac{-\frac{b^{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 \,b^{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} b \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+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)}{f}"," ",0,"1/f*(-1/5*b^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*a*b^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*b*(2+sin(f*x+e)^2)*cos(f*x+e)+a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
168,1,104,111,0.227000," ","int(sin(f*x+e)*(a+b*sin(f*x+e))^3,x)","\frac{b^{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 \,b^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a^{2} 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^{3} \cos \left(f x +e \right)}{f}"," ",0,"1/f*(b^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*b^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^2*b*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*cos(f*x+e))","A"
169,1,76,82,0.161000," ","int((a+b*sin(f*x+e))^3,x)","\frac{-\frac{b^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 a \,b^{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^{2} b \cos \left(f x +e \right)+\left(f x +e \right) a^{3}}{f}"," ",0,"1/f*(-1/3*b^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a*b^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^2*b*cos(f*x+e)+(f*x+e)*a^3)","A"
170,1,92,68,0.207000," ","int(csc(f*x+e)*(a+b*sin(f*x+e))^3,x)","\frac{a^{3} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+3 a^{2} b x +\frac{3 a^{2} b e}{f}-\frac{3 a \,b^{2} \cos \left(f x +e \right)}{f}-\frac{b^{3} \sin \left(f x +e \right) \cos \left(f x +e \right)}{2 f}+\frac{b^{3} x}{2}+\frac{b^{3} e}{2 f}"," ",0,"1/f*a^3*ln(csc(f*x+e)-cot(f*x+e))+3*a^2*b*x+3/f*a^2*b*e-3*a*b^2*cos(f*x+e)/f-1/2/f*b^3*sin(f*x+e)*cos(f*x+e)+1/2*b^3*x+1/2/f*b^3*e","A"
171,1,72,68,0.266000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e))^3,x)","3 a \,b^{2} x -\frac{a^{3} \cot \left(f x +e \right)}{f}-\frac{b^{3} \cos \left(f x +e \right)}{f}+\frac{3 a^{2} b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+\frac{3 a \,b^{2} e}{f}"," ",0,"3*a*b^2*x-1/f*a^3*cot(f*x+e)-1/f*b^3*cos(f*x+e)+3/f*a^2*b*ln(csc(f*x+e)-cot(f*x+e))+3/f*a*b^2*e","A"
172,1,99,73,0.365000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e))^3,x)","-\frac{a^{3} \csc \left(f x +e \right) \cot \left(f x +e \right)}{2 f}+\frac{a^{3} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{3 a^{2} b \cot \left(f x +e \right)}{f}+\frac{3 a \,b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}+b^{3} x +\frac{b^{3} e}{f}"," ",0,"-1/2/f*a^3*csc(f*x+e)*cot(f*x+e)+1/2/f*a^3*ln(csc(f*x+e)-cot(f*x+e))-3*a^2*b*cot(f*x+e)/f+3/f*a*b^2*ln(csc(f*x+e)-cot(f*x+e))+b^3*x+1/f*b^3*e","A"
173,1,122,101,0.396000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e))^3,x)","-\frac{2 a^{3} \cot \left(f x +e \right)}{3 f}-\frac{a^{3} \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{3 f}-\frac{3 a^{2} b \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{3 a^{2} b \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{3 a \,b^{2} \cot \left(f x +e \right)}{f}+\frac{b^{3} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{f}"," ",0,"-2/3/f*a^3*cot(f*x+e)-1/3/f*a^3*cot(f*x+e)*csc(f*x+e)^2-3/2*a^2*b*cot(f*x+e)*csc(f*x+e)/f+3/2/f*a^2*b*ln(csc(f*x+e)-cot(f*x+e))-3/f*a*b^2*cot(f*x+e)+1/f*b^3*ln(csc(f*x+e)-cot(f*x+e))","A"
174,1,166,126,0.478000," ","int(csc(f*x+e)^5*(a+b*sin(f*x+e))^3,x)","-\frac{a^{3} \cot \left(f x +e \right) \left(\csc^{3}\left(f x +e \right)\right)}{4 f}-\frac{3 a^{3} \csc \left(f x +e \right) \cot \left(f x +e \right)}{8 f}+\frac{3 a^{3} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{8 f}-\frac{2 a^{2} b \cot \left(f x +e \right)}{f}-\frac{a^{2} b \cot \left(f x +e \right) \left(\csc^{2}\left(f x +e \right)\right)}{f}-\frac{3 a \,b^{2} \cot \left(f x +e \right) \csc \left(f x +e \right)}{2 f}+\frac{3 a \,b^{2} \ln \left(\csc \left(f x +e \right)-\cot \left(f x +e \right)\right)}{2 f}-\frac{b^{3} \cot \left(f x +e \right)}{f}"," ",0,"-1/4/f*a^3*cot(f*x+e)*csc(f*x+e)^3-3/8/f*a^3*csc(f*x+e)*cot(f*x+e)+3/8/f*a^3*ln(csc(f*x+e)-cot(f*x+e))-2*a^2*b*cot(f*x+e)/f-a^2*b*cot(f*x+e)*csc(f*x+e)^2/f-3/2/f*a*b^2*cot(f*x+e)*csc(f*x+e)+3/2/f*a*b^2*ln(csc(f*x+e)-cot(f*x+e))-1/f*b^3*cot(f*x+e)","A"
175,1,116,127,0.220000," ","int((a+b*sin(f*x+e))^4,x)","\frac{b^{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{4 a \,b^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+6 a^{2} b^{2} \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-4 a^{3} b \cos \left(f x +e \right)+a^{4} \left(f x +e \right)}{f}"," ",0,"1/f*(b^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)-4/3*a*b^3*(2+sin(f*x+e)^2)*cos(f*x+e)+6*a^2*b^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4*a^3*b*cos(f*x+e)+a^4*(f*x+e))","A"
176,1,213,96,0.076000," ","int(sin(x)^4/(a+b*sin(x)),x)","-\frac{a \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 a^{2} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right) a^{2}}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{a \tan \left(\frac{x}{2}\right)}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 a^{2}}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4}{3 b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a^{3}}{b^{4}}-\frac{\arctan \left(\tan \left(\frac{x}{2}\right)\right) a}{b^{2}}+\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/b^2/(tan(1/2*x)^2+1)^3*a*tan(1/2*x)^5-2/b^3/(tan(1/2*x)^2+1)^3*a^2*tan(1/2*x)^4-4/b^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2*a^2-4/b/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2+1/b^2/(tan(1/2*x)^2+1)^3*a*tan(1/2*x)-2/b^3/(tan(1/2*x)^2+1)^3*a^2-4/3/b/(tan(1/2*x)^2+1)^3-2/b^4*arctan(tan(1/2*x))*a^3-1/b^2*arctan(tan(1/2*x))*a+2*a^4/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
177,1,142,72,0.072000," ","int(sin(x)^3/(a+b*sin(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right) a}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 a}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{b^{3}}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{3} \sqrt{a^{2}-b^{2}}}+\frac{x}{2 b}"," ",0,"1/b/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+2/b^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2*a-1/b/(tan(1/2*x)^2+1)^2*tan(1/2*x)+2/b^2/(tan(1/2*x)^2+1)^2*a+2/b^3*arctan(tan(1/2*x))*a^2-2*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+1/2*x/b","A"
178,1,72,55,0.068000," ","int(sin(x)^2/(a+b*sin(x)),x)","-\frac{2}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a}{b^{2}}+\frac{2 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/b/(tan(1/2*x)^2+1)-2/b^2*arctan(tan(1/2*x))*a+2*a^2/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
179,1,54,44,0.059000," ","int(sin(x)/(a+b*sin(x)),x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b \sqrt{a^{2}-b^{2}}}"," ",0,"2/b*arctan(tan(1/2*x))-2*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
180,1,39,34,0.048000," ","int(1/(a+b*sin(x)),x)","\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}"," ",0,"2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
181,1,53,47,0.097000," ","int(csc(x)/(a+b*sin(x)),x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \sqrt{a^{2}-b^{2}}}"," ",0,"1/a*ln(tan(1/2*x))-2*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
182,1,77,56,0.105000," ","int(csc(x)^2/(a+b*sin(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a*tan(1/2*x)-1/2/a/tan(1/2*x)-1/a^2*b*ln(tan(1/2*x))+2*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
183,1,112,74,0.119000," ","int(csc(x)^3/(a+b*sin(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}-\frac{\tan \left(\frac{x}{2}\right) b}{2 a^{2}}-\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}+\frac{b}{2 a^{2} \tan \left(\frac{x}{2}\right)}-\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/a*tan(1/2*x)^2-1/2/a^2*tan(1/2*x)*b-1/8/a/tan(1/2*x)^2+1/2/a*ln(tan(1/2*x))+1/a^3*ln(tan(1/2*x))*b^2+1/2*b/a^2/tan(1/2*x)-2*b^3/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
184,1,162,98,0.115000," ","int(csc(x)^4/(a+b*sin(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a}-\frac{\left(\tan^{2}\left(\frac{x}{2}\right)\right) b}{8 a^{2}}+\frac{3 \tan \left(\frac{x}{2}\right)}{8 a}+\frac{b^{2} \tan \left(\frac{x}{2}\right)}{2 a^{3}}-\frac{1}{24 a \tan \left(\frac{x}{2}\right)^{3}}-\frac{3}{8 a \tan \left(\frac{x}{2}\right)}-\frac{b^{2}}{2 a^{3} \tan \left(\frac{x}{2}\right)}+\frac{b}{8 a^{2} \tan \left(\frac{x}{2}\right)^{2}}-\frac{b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{4}}+\frac{2 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/a*tan(1/2*x)^3-1/8/a^2*tan(1/2*x)^2*b+3/8/a*tan(1/2*x)+1/2/a^3*b^2*tan(1/2*x)-1/24/a/tan(1/2*x)^3-3/8/a/tan(1/2*x)-1/2/a^3/tan(1/2*x)*b^2+1/8/a^2*b/tan(1/2*x)^2-1/2/a^2*b*ln(tan(1/2*x))-1/a^4*b^3*ln(tan(1/2*x))+2/a^4*b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
185,1,266,159,0.113000," ","int(sin(x)^4/(a+b*sin(x))^2,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right) a}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{4 a}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{b^{4}}+\frac{2 a^{3} \tan \left(\frac{x}{2}\right)}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 a^{4}}{b^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{6 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{8 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{x}{2 b^{2}}"," ",0,"1/b^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+4/b^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2*a-1/b^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)+4/b^3/(tan(1/2*x)^2+1)^2*a+6/b^4*arctan(tan(1/2*x))*a^2+2*a^3/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)+2*a^4/b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)-6*a^5/b^4/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+8*a^3/b^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+1/2*x/b^2","A"
186,1,196,118,0.106000," ","int(sin(x)^3/(a+b*sin(x))^2,x)","-\frac{2}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{4 a \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{3}}-\frac{2 a^{2} \tan \left(\frac{x}{2}\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3}}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{4 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/b^2/(tan(1/2*x)^2+1)-4/b^3*a*arctan(tan(1/2*x))-2*a^2/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)-2*a^3/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)+4*a^4/b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-6*a^2/b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
187,1,170,81,0.102000," ","int(sin(x)^2/(a+b*sin(x))^2,x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}}+\frac{2 a \tan \left(\frac{x}{2}\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 a^{2}}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/b^2*arctan(tan(1/2*x))+2*a/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)+2*a^2/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)-2*a^3/b^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+4*a/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
188,1,99,60,0.093000," ","int(sin(x)/(a+b*sin(x))^2,x)","\frac{-8 \tan \left(\frac{x}{2}\right) b -8 a}{\left(4 a^{2}-4 b^{2}\right) \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)}-\frac{8 b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(4 a^{2}-4 b^{2}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"4*(-2*tan(1/2*x)*b-2*a)/(4*a^2-4*b^2)/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)-8*b/(4*a^2-4*b^2)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
189,1,98,59,0.084000," ","int(1/(a+b*sin(x))^2,x)","\frac{\frac{2 b^{2} \tan \left(\frac{x}{2}\right)}{a \left(a^{2}-b^{2}\right)}+\frac{2 b}{a^{2}-b^{2}}}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(b^2/a/(a^2-b^2)*tan(1/2*x)+b/(a^2-b^2))/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)+2*a/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
190,1,174,87,0.127000," ","int(csc(x)/(a+b*sin(x))^2,x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{2 b^{3} \tan \left(\frac{x}{2}\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 b^{2}}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/a^2*ln(tan(1/2*x))-2/a^2*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)-2/a*b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)-4*b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+2/a^2*b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
191,1,201,117,0.141000," ","int(csc(x)^2/(a+b*sin(x))^2,x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a^{2}}-\frac{1}{2 a^{2} \tan \left(\frac{x}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}+\frac{2 b^{4} \tan \left(\frac{x}{2}\right)}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{2 b^{3}}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}+\frac{6 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{4 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/2/a^2*tan(1/2*x)-1/2/a^2/tan(1/2*x)-2/a^3*b*ln(tan(1/2*x))+2/a^3*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)+2/a^2*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)+6/a*b^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-4/a^3*b^4/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
192,1,236,158,0.147000," ","int(csc(x)^3/(a+b*sin(x))^2,x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a^{2}}-\frac{\tan \left(\frac{x}{2}\right) b}{a^{3}}-\frac{1}{8 a^{2} \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{2}}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{4}}+\frac{b}{a^{3} \tan \left(\frac{x}{2}\right)}-\frac{2 b^{5} \tan \left(\frac{x}{2}\right)}{a^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 b^{4}}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right) \left(a^{2}-b^{2}\right)}-\frac{8 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{6 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/8/a^2*tan(1/2*x)^2-1/a^3*tan(1/2*x)*b-1/8/a^2/tan(1/2*x)^2+1/2/a^2*ln(tan(1/2*x))+3/a^4*ln(tan(1/2*x))*b^2+b/a^3/tan(1/2*x)-2/a^4*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)*tan(1/2*x)-2/a^3*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)/(a^2-b^2)-8/a^2*b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+6/a^4*b^5/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","A"
193,1,712,227,0.128000," ","int(sin(x)^5/(a+b*sin(x))^3,x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{x}{2}\right)\right) a}{b^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{6 a}{b^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{12 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{b^{5}}+\frac{5 a^{6} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{b^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{8 a^{4} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 a^{7} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{3 a^{5} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{18 a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{19 a^{6} \tan \left(\frac{x}{2}\right)}{b^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{28 a^{4} \tan \left(\frac{x}{2}\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 a^{7}}{b^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{9 a^{5}}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{12 a^{7} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{5} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{29 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{20 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{x}{2 b^{3}}"," ",0,"1/b^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+6/b^4/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2*a-1/b^3/(tan(1/2*x)^2+1)^2*tan(1/2*x)+6/b^4/(tan(1/2*x)^2+1)^2*a+12/b^5*arctan(tan(1/2*x))*a^2+5*a^6/b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-8*a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+6*a^7/b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+3*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-18*a^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+19*a^6/b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-28*a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+6*a^7/b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-9*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-12*a^7/b^5/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+29*a^5/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-20*a^3/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+1/2*x/b^3","B"
194,1,634,167,0.120000," ","int(sin(x)^4/(a+b*sin(x))^3,x)","-\frac{2}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{6 a \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{4}}-\frac{3 a^{5} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 a^{3} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a^{6} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{14 a^{2} b \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{13 a^{5} \tan \left(\frac{x}{2}\right)}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{22 a^{3} \tan \left(\frac{x}{2}\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a^{6}}{b^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 a^{4}}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{15 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{12 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"-2/b^3/(tan(1/2*x)^2+1)-6/b^4*a*arctan(tan(1/2*x))-3*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+6*a^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-4*a^6/b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+14*a^2*b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-13*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+22*a^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-4*a^6/b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)+7*a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)+6*a^6/b^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-15*a^4/b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+12*a^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
195,1,612,134,0.119000," ","int(sin(x)^3/(a+b*sin(x))^3,x)","\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b^{3}}+\frac{a^{4} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 b \,a^{2} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 a^{5} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 b^{2} a \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 a^{4} \tan \left(\frac{x}{2}\right)}{b \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{16 b \,a^{2} \tan \left(\frac{x}{2}\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 a^{5}}{b^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{5 a^{3}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{5 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{6 b a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"2/b^3*arctan(tan(1/2*x))+a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-4*b*a^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+2*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-a^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-10*b^2*a/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+7*a^4/b/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-16*b*a^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+2*a^5/b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-5*a^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-2*a^5/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+5*a^3/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-6*b*a/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
196,1,265,108,0.108000," ","int(sin(x)^2/(a+b*sin(x))^3,x)","\frac{\frac{8 \left(a^{2}+2 b^{2}\right) a \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{8 a^{4}-16 a^{2} b^{2}+8 b^{4}}+\frac{3 b \left(a^{2}+2 b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{4}-2 a^{2} b^{2}+b^{4}}-\frac{a \left(a^{2}-10 b^{2}\right) \tan \left(\frac{x}{2}\right)}{a^{4}-2 a^{2} b^{2}+b^{4}}+\frac{3 a^{2} b}{a^{4}-2 a^{2} b^{2}+b^{4}}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2}}+\frac{a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"8*(1/8*(a^2+2*b^2)*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+3/8*b*(a^2+2*b^2)/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-1/8*a*(a^2-10*b^2)/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+3/8*a^2*b/(a^4-2*a^2*b^2+b^4))/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2+a^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
197,1,221,93,0.106000," ","int(sin(x)/(a+b*sin(x))^3,x)","\frac{-\frac{3 a^{2} b \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a^{4}-2 a^{2} b^{2}+b^{4}}-\frac{\left(2 a^{4}+5 a^{2} b^{2}+2 b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}-\frac{\left(5 a^{2}+4 b^{2}\right) b \tan \left(\frac{x}{2}\right)}{a^{4}-2 a^{2} b^{2}+b^{4}}-\frac{\left(2 a^{2}+b^{2}\right) a}{a^{4}-2 a^{2} b^{2}+b^{4}}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2}}-\frac{3 b a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"4*(-3/4*a^2*b/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-1/4*(2*a^4+5*a^2*b^2+2*b^4)/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*x)^2-1/4*(5*a^2+4*b^2)*b/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-1/4*(2*a^2+b^2)*a/(a^4-2*a^2*b^2+b^4))/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2-3*b*a/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
198,1,300,92,0.096000," ","int(1/(a+b*sin(x))^3,x)","\frac{\frac{b^{2} \left(5 a^{2}-2 b^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}+\frac{b \left(4 a^{4}+7 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{b^{2} \left(11 a^{2}-2 b^{2}\right) \tan \left(\frac{x}{2}\right)}{a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 b \left(4 a^{2}-b^{2}\right)}{2 a^{4}-4 a^{2} b^{2}+2 b^{4}}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2}}+\frac{2 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{\arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"2*(1/2*b^2*(5*a^2-2*b^2)/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*x)^3+1/2*b*(4*a^4+7*a^2*b^2-2*b^4)/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*x)^2+1/2*b^2*(11*a^2-2*b^2)/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+1/2*b*(4*a^2-b^2)/(a^4-2*a^2*b^2+b^4))/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2+2*a^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+1/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
199,1,614,135,0.142000," ","int(csc(x)/(a+b*sin(x))^3,x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{3}}-\frac{7 b^{3} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 b^{5} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 b^{2} a \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{9 b^{4} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 b^{6} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{17 b^{3} \tan \left(\frac{x}{2}\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{8 b^{5} \tan \left(\frac{x}{2}\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 a \,b^{2}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{3 b^{4}}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 b a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{5 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"1/a^3*ln(tan(1/2*x))-7*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+4/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-6*b^2*a/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-9/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+6/a^3*b^6/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-17*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+8/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-6*a*b^2/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)+3/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-6*b*a/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+5/a*b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-2/a^3*b^5/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
200,1,641,175,0.162000," ","int(csc(x)^2/(a+b*sin(x))^3,x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a^{3}}-\frac{1}{2 a^{3} \tan \left(\frac{x}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{4}}+\frac{9 b^{4} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 b^{6} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{8 b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{11 b^{5} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 b^{7} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{23 b^{4} \tan \left(\frac{x}{2}\right)}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{14 b^{6} \tan \left(\frac{x}{2}\right)}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{8 b^{3}}{\left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{5 b^{5}}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{12 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{15 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{6 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a^3*tan(1/2*x)-1/2/a^3/tan(1/2*x)-3/a^4*b*ln(tan(1/2*x))+9/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-6/a^3*b^6/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+8*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+11/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-10/a^4*b^7/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+23/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-14/a^3*b^6/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+8*b^3/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-5/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)+12/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))*b^2-15/a^2*b^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+6/a^4*b^6/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
201,1,686,225,0.167000," ","int(csc(x)^3/(a+b*sin(x))^3,x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a^{3}}-\frac{3 \tan \left(\frac{x}{2}\right) b}{2 a^{4}}-\frac{1}{8 a^{3} \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{3}}+\frac{6 \ln \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{5}}+\frac{3 b}{2 a^{4} \tan \left(\frac{x}{2}\right)}-\frac{11 b^{5} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{8 b^{7} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{a^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 b^{4} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{13 b^{6} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{14 b^{8} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{5} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{29 b^{5} \tan \left(\frac{x}{2}\right)}{a^{2} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{20 b^{7} \tan \left(\frac{x}{2}\right)}{a^{4} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 b^{4}}{a \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 b^{6}}{a^{3} \left(\left(\tan^{2}\left(\frac{x}{2}\right)\right) a +2 \tan \left(\frac{x}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{20 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{29 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{12 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a^{5} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/a^3*tan(1/2*x)^2-3/2/a^4*tan(1/2*x)*b-1/8/a^3/tan(1/2*x)^2+1/2/a^3*ln(tan(1/2*x))+6/a^5*ln(tan(1/2*x))*b^2+3/2*b/a^4/tan(1/2*x)-11/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3+8/a^4*b^7/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^3-10/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-13/a^3*b^6/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2+14/a^5*b^8/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)^2-29/a^2*b^5/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)+20/a^4*b^7/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*x)-10/a*b^4/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)+7/a^3*b^6/(tan(1/2*x)^2*a+2*tan(1/2*x)*b+a)^2/(a^4-2*a^2*b^2+b^4)-20/a*b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+29/a^3*b^5/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))-12/a^5*b^7/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
202,1,1733,171,0.207000," ","int(1/(a+b*sin(d*x+c))^4,x)","\frac{9 b^{2} a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{6 b^{4} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{2 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{6 b \,a^{4} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{27 b^{3} a^{2} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{12 b^{5} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{4 b^{7} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a^{2} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{36 a^{3} b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{14 a \,b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{8 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{8 b^{8} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{12 a^{4} b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{40 a^{2} b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{6 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{4 b^{7} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a^{2} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{27 b^{2} a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{4 b^{4} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} a \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{6 b \,a^{4}}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}-\frac{5 b^{3} a^{2}}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{2 b^{5}}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right)}+\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right) \sqrt{a^{2}-b^{2}}}+\frac{3 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"9/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^2*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5-6/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^4*a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^6/a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5+6/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b*a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4+27/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^3*a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4-12/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4+4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^7/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4+36/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*a^3*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3+14/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*a*b^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3-8/3/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3/a*b^6/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3+8/3/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3/a^3*b^8/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3+12/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*a^4*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2+40/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*a^2*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2-6/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2+4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3/a^2*b^7/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2+27/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^2*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)-4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^4*a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^6/a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)+6/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*a^4-5/3/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*a^2+2/3/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^3*b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)+2/d*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/d*a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
203,1,460,222,1.166000," ","int(sin(f*x+e)*(a+b*sin(f*x+e))^(1/2),x)","\frac{\frac{2 \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b}{3}-\frac{2 \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}}{3}-\frac{2 \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}}{3}+\frac{2 \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}}{3}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right) b^{3}}{3}+\frac{2 \left(\sin^{2}\left(f x +e \right)\right) a \,b^{2}}{3}-\frac{2 \sin \left(f x +e \right) b^{3}}{3}-\frac{2 a \,b^{2}}{3}}{b^{2} \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"2/3*(((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^3-((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3+((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^2+sin(f*x+e)^3*b^3+sin(f*x+e)^2*a*b^2-sin(f*x+e)*b^3-a*b^2)/b^2/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","B"
204,1,239,91,1.423000," ","int((a+b*sin(f*x+e))^(1/2),x)","-\frac{2 \left(a -b \right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \left(\EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a +\EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b -a \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)-\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b \right)}{b \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"-2/b*(a-b)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*(EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a+EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b-a*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b)/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","B"
205,1,169,186,1.209000," ","int(csc(f*x+e)*(a+b*sin(f*x+e))^(1/2),x)","\frac{2 \left(a -b \right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \left(\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)-\EllipticPi \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"2*(a-b)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*(EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-EllipticPi(((a+b*sin(f*x+e))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2)))/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
206,1,457,299,1.348000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e))^(1/2),x)","-\frac{a \,b^{2} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(f x +e \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(f x +e \right)}{a +b}+\frac{b}{a +b}}\, \left(\EllipticE \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-\EllipticE \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\EllipticF \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\EllipticF \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\EllipticPi \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+\EllipticPi \left(\sqrt{\frac{b \sin \left(f x +e \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}\right) \sin \left(f x +e \right)+a^{2} b \left(\cos^{2}\left(f x +e \right)\right)}{a b \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"-(a*b^2*sin(f*x+e)*cos(f*x+e)^2-(b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(f*x+e)-b/(a-b))^(1/2)*(-b/(a+b)*sin(f*x+e)+b/(a+b))^(1/2)*(EllipticE((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3-EllipticE((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-EllipticF((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b+EllipticF((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-EllipticPi((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^2+EllipticPi((b/(a-b)*sin(f*x+e)+1/(a-b)*a)^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^3)*sin(f*x+e)+a^2*b*cos(f*x+e)^2)/a/b/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
207,1,202,190,1.061000," ","int(sin(f*x+e)/(a+b*sin(f*x+e))^(1/2),x)","-\frac{2 \left(a -b \right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \left(\EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a +\EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b -\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b \right)}{b^{2} \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"-2*(a-b)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*(EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a+EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b-EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b)/b^2/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
208,1,126,91,0.709000," ","int(1/(a+b*sin(f*x+e))^(1/2),x)","\frac{2 \left(a -b \right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{b \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"2*(a-b)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))/b/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
209,1,135,92,0.986000," ","int(csc(f*x+e)/(a+b*sin(f*x+e))^(1/2),x)","-\frac{2 \left(a -b \right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(f x +e \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{a \cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"-2*(a-b)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(-(sin(f*x+e)-1)*b/(a+b))^(1/2)*(-(1+sin(f*x+e))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(f*x+e))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))/a/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
210,1,412,306,2.923000," ","int(csc(f*x+e)^2/(a+b*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{\sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{a \sin \left(f x +e \right)}-\frac{b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{a \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{b^{2} \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(f x +e \right)\right)}{a +b}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(f x +e \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{a^{2} \sqrt{-\left(-b \sin \left(f x +e \right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \sin \left(f x +e \right)}\, f}"," ",0,"(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*(-1/a*(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)/sin(f*x+e)-1/a*b*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(f*x+e))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))+1/a^2*b^2*(a/b-1)*((a+b*sin(f*x+e))/(a-b))^(1/2)*(b*(1-sin(f*x+e))/(a+b))^(1/2)*((-sin(f*x+e)-1)*b/(a-b))^(1/2)/(-(-b*sin(f*x+e)-a)*cos(f*x+e)^2)^(1/2)*EllipticPi(((a+b*sin(f*x+e))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2)))/cos(f*x+e)/(a+b*sin(f*x+e))^(1/2)/f","A"
211,1,9823,343,0.761000," ","int(sin(d*x+c)^(1/2)*(a+b*sin(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
212,1,318,101,0.295000," ","int(1/sin(d*x+c)^(1/2)/(a+b*sin(d*x+c))^(1/2),x)","-\frac{\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(d x +c \right)-b \sin \left(d x +c \right)+a \cos \left(d x +c \right)-a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(d x +c \right)-b \sin \left(d x +c \right)+a \cos \left(d x +c \right)-a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(d x +c \right)}}\, \sqrt{\frac{a \left(\cos \left(d x +c \right)-1\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(d x +c \right)-b \sin \left(d x +c \right)+a \cos \left(d x +c \right)-a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(d x +c \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \left(\sin^{\frac{3}{2}}\left(d x +c \right)\right) \sqrt{2}\, \left(b +\sqrt{-a^{2}+b^{2}}\right)}{d \sqrt{a +b \sin \left(d x +c \right)}\, \left(\cos \left(d x +c \right)-1\right) a}"," ",0,"-1/d/(a+b*sin(d*x+c))^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(d*x+c)-b*sin(d*x+c)+a*cos(d*x+c)-a)/(b+(-a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*(((-a^2+b^2)^(1/2)*sin(d*x+c)-b*sin(d*x+c)+a*cos(d*x+c)-a)/(-a^2+b^2)^(1/2)/sin(d*x+c))^(1/2)*(a*(cos(d*x+c)-1)/(b+(-a^2+b^2)^(1/2))/sin(d*x+c))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(d*x+c)-b*sin(d*x+c)+a*cos(d*x+c)-a)/(b+(-a^2+b^2)^(1/2))/sin(d*x+c))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*sin(d*x+c)^(3/2)*2^(1/2)/(cos(d*x+c)-1)*(b+(-a^2+b^2)^(1/2))/a","B"
213,0,0,258,5.107000," ","int((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^3,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(a +b \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^3,x)","F"
214,0,0,182,7.288000," ","int((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^2,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(a +b \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*sin(f*x+e))^m*(a+b*sin(f*x+e))^2,x)","F"
215,0,0,127,1.872000," ","int((d*sin(f*x+e))^m*(a+b*sin(f*x+e)),x)","\int \left(d \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))^m*(a+b*sin(f*x+e)),x)","F"
216,0,0,177,0.753000," ","int((d*sin(f*x+e))^m/(a+b*sin(f*x+e)),x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{m}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((d*sin(f*x+e))^m/(a+b*sin(f*x+e)),x)","F"
217,0,0,276,1.463000," ","int((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{m}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^2,x)","F"
218,0,0,368,1.773000," ","int((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^3,x)","\int \frac{\left(d \sin \left(f x +e \right)\right)^{m}}{\left(a +b \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*sin(f*x+e))^m/(a+b*sin(f*x+e))^3,x)","F"
219,0,0,135,10.978000," ","int(sin(d*x+c)^(-1-a^2/(a^2+b^2))*(a+b*sin(d*x+c))^2,x)","\int \left(\sin^{-1-\frac{a^{2}}{a^{2}+b^{2}}}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(sin(d*x+c)^(-1-a^2/(a^2+b^2))*(a+b*sin(d*x+c))^2,x)","F"
220,0,0,63,0.756000," ","int((1+2*sin(d*x+c))^2/sin(d*x+c)^(6/5),x)","\int \frac{\left(1+2 \sin \left(d x +c \right)\right)^{2}}{\sin \left(d x +c \right)^{\frac{6}{5}}}\, dx"," ",0,"int((1+2*sin(d*x+c))^2/sin(d*x+c)^(6/5),x)","F"
221,0,0,23,1.189000," ","int(sin(d*x+c)^m*(a+b*sin(d*x+c))^n,x)","\int \left(\sin^{m}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^m*(a+b*sin(d*x+c))^n,x)","F"
222,0,0,323,0.784000," ","int(sin(d*x+c)^3*(a+b*sin(d*x+c))^n,x)","\int \left(\sin^{3}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^3*(a+b*sin(d*x+c))^n,x)","F"
223,0,0,246,0.730000," ","int(sin(d*x+c)^2*(a+b*sin(d*x+c))^n,x)","\int \left(\sin^{2}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^2*(a+b*sin(d*x+c))^n,x)","F"
224,0,0,192,0.225000," ","int(sin(d*x+c)*(a+b*sin(d*x+c))^n,x)","\int \sin \left(d x +c \right) \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)*(a+b*sin(d*x+c))^n,x)","F"
225,0,0,90,0.008000," ","int((a+b*sin(d*x+c))^n,x)","\int \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*sin(d*x+c))^n,x)","F"
226,0,0,21,1.372000," ","int(csc(d*x+c)*(a+b*sin(d*x+c))^n,x)","\int \csc \left(d x +c \right) \left(a +b \sin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)*(a+b*sin(d*x+c))^n,x)","F"
227,1,149,106,0.283000," ","int((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^4,x)","\frac{-\frac{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 \,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{2 a \,c^{4} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+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)+3 a \,c^{4} \cos \left(f x +e \right)+a \,c^{4} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/5*a*c^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-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)-2/3*a*c^4*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a*c^4*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*a*c^4*cos(f*x+e)+a*c^4*(f*x+e))","A"
228,1,89,75,0.230000," ","int((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^3,x)","\frac{-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 \,c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 a \,c^{3} \cos \left(f x +e \right)+a \,c^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-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*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a*c^3*cos(f*x+e)+a*c^3*(f*x+e))","A"
229,1,77,46,0.165000," ","int((a+a*sin(f*x+e))*(c-c*sin(f*x+e))^2,x)","\frac{-\frac{a \,c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{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)+a \,c^{2} \cos \left(f x +e \right)+a \,c^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/3*a*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)-a*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a*c^2*cos(f*x+e)+a*c^2*(f*x+e))","A"
230,1,40,25,0.048000," ","int((a+a*sin(f*x+e))*(c-c*sin(f*x+e)),x)","\frac{-c 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 \left(f x +e \right)}{f}"," ",0,"1/f*(-c*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a*c*(f*x+e))","A"
231,1,43,33,0.181000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","-\frac{4 a}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2 a \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f c}"," ",0,"-4/f*a/c/(tan(1/2*f*x+1/2*e)-1)-2/f*a/c*arctan(tan(1/2*f*x+1/2*e))","A"
232,1,56,28,0.223000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","\frac{2 a \left(-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{4}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{2}}"," ",0,"2/f*a/c^2*(-1/(tan(1/2*f*x+1/2*e)-1)-4/3/(tan(1/2*f*x+1/2*e)-1)^3-2/(tan(1/2*f*x+1/2*e)-1)^2)","A"
233,1,86,56,0.254000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","\frac{2 a \left(-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{14}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{3}{\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/(tan(1/2*f*x+1/2*e)-1)-14/3/(tan(1/2*f*x+1/2*e)-1)^3-8/5/(tan(1/2*f*x+1/2*e)-1)^5-4/(tan(1/2*f*x+1/2*e)-1)^4-3/(tan(1/2*f*x+1/2*e)-1)^2)","A"
234,1,116,86,0.225000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","\frac{2 a \left(-\frac{14}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{28}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{68}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{16}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{4}}"," ",0,"2/f*a/c^4*(-14/(tan(1/2*f*x+1/2*e)-1)^4-1/(tan(1/2*f*x+1/2*e)-1)-28/3/(tan(1/2*f*x+1/2*e)-1)^3-68/5/(tan(1/2*f*x+1/2*e)-1)^5-16/7/(tan(1/2*f*x+1/2*e)-1)^7-8/(tan(1/2*f*x+1/2*e)-1)^6-4/(tan(1/2*f*x+1/2*e)-1)^2)","A"
235,1,146,118,0.274000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^5,x)","\frac{2 a \left(-\frac{5}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{32}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{46}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{32}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{16}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{236}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{248}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{148}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}\right)}{f \,c^{5}}"," ",0,"2/f*a/c^5*(-5/(tan(1/2*f*x+1/2*e)-1)^2-32/(tan(1/2*f*x+1/2*e)-1)^4-1/(tan(1/2*f*x+1/2*e)-1)-46/3/(tan(1/2*f*x+1/2*e)-1)^3-32/9/(tan(1/2*f*x+1/2*e)-1)^9-16/(tan(1/2*f*x+1/2*e)-1)^8-236/5/(tan(1/2*f*x+1/2*e)-1)^5-248/7/(tan(1/2*f*x+1/2*e)-1)^7-148/3/(tan(1/2*f*x+1/2*e)-1)^6)","A"
236,1,255,140,0.399000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^5,x)","\frac{\frac{c^{5} a^{2} \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 c^{5} a^{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{c^{5} a^{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}-5 c^{5} a^{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{5 c^{5} a^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+c^{5} 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)+3 c^{5} a^{2} \cos \left(f x +e \right)+c^{5} a^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(1/7*c^5*a^2*(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*c^5*a^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*c^5*a^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-5*c^5*a^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)-5/3*c^5*a^2*(2+sin(f*x+e)^2)*cos(f*x+e)+c^5*a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*c^5*a^2*cos(f*x+e)+c^5*a^2*(f*x+e))","A"
237,1,211,108,0.343000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^4,x)","\frac{c^{4} a^{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{2 c^{4} a^{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}-c^{4} a^{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{4 c^{4} a^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-c^{4} 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)+2 c^{4} a^{2} \cos \left(f x +e \right)+c^{4} a^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(c^4*a^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)+2/5*c^4*a^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-c^4*a^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)-4/3*c^4*a^2*(2+sin(f*x+e)^2)*cos(f*x+e)-c^4*a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*c^4*a^2*cos(f*x+e)+c^4*a^2*(f*x+e))","A"
238,1,159,77,0.286000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^3,x)","\frac{\frac{c^{3} a^{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}+c^{3} a^{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 c^{3} a^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 c^{3} 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)+c^{3} a^{2} \cos \left(f x +e \right)+a^{2} c^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(1/5*c^3*a^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+c^3*a^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*c^3*a^2*(2+sin(f*x+e)^2)*cos(f*x+e)-2*c^3*a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+c^3*a^2*cos(f*x+e)+a^2*c^3*(f*x+e))","B"
239,1,88,58,0.174000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e))^2,x)","\frac{c^{2} a^{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^{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)+a^{2} c^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(c^2*a^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^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*c^2*(f*x+e))","A"
240,1,78,46,0.165000," ","int((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x)","\frac{\frac{a^{2} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-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} c \cos \left(f x +e \right)+a^{2} c \left(f x +e \right)}{f}"," ",0,"1/f*(1/3*a^2*c*(2+sin(f*x+e)^2)*cos(f*x+e)-a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*c*cos(f*x+e)+a^2*c*(f*x+e))","A"
241,1,73,57,0.230000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x)","-\frac{8 a^{2}}{f c \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}+\frac{2 a^{2}}{f c \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{6 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f c}"," ",0,"-8/f*a^2/c/(tan(1/2*f*x+1/2*e)-1)+2/f*a^2/c/(1+tan(1/2*f*x+1/2*e)^2)-6/f*a^2/c*arctan(tan(1/2*f*x+1/2*e))","A"
242,1,71,70,0.243000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x)","-\frac{16 a^{2}}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8 a^{2}}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{2 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{2} f}"," ",0,"-16/3*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3-8*a^2/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2+2*a^2/c^2/f*arctan(tan(1/2*f*x+1/2*e))","A"
243,1,88,32,0.273000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x)","\frac{2 a^{2} \left(-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}\right)}{f \,c^{3}}"," ",0,"2/f*a^2/c^3*(-4/(tan(1/2*f*x+1/2*e)-1)^2-1/(tan(1/2*f*x+1/2*e)-1)-8/(tan(1/2*f*x+1/2*e)-1)^4-8/(tan(1/2*f*x+1/2*e)-1)^3-16/5/(tan(1/2*f*x+1/2*e)-1)^5)","B"
244,1,118,63,0.273000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x)","\frac{2 a^{2} \left(-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{5}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{14}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{32}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{16}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{128}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{24}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}\right)}{f \,c^{4}}"," ",0,"2/f*a^2/c^4*(-1/(tan(1/2*f*x+1/2*e)-1)-5/(tan(1/2*f*x+1/2*e)-1)^2-14/(tan(1/2*f*x+1/2*e)-1)^3-32/7/(tan(1/2*f*x+1/2*e)-1)^7-16/(tan(1/2*f*x+1/2*e)-1)^6-128/5/(tan(1/2*f*x+1/2*e)-1)^5-24/(tan(1/2*f*x+1/2*e)-1)^4)","A"
245,1,148,92,0.296000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x)","\frac{2 a^{2} \left(-\frac{50}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{64}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{272}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{6}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{64}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{480}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{404}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{32}{\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*(-50/(tan(1/2*f*x+1/2*e)-1)^4-64/9/(tan(1/2*f*x+1/2*e)-1)^9-272/3/(tan(1/2*f*x+1/2*e)-1)^6-6/(tan(1/2*f*x+1/2*e)-1)^2-1/(tan(1/2*f*x+1/2*e)-1)-64/3/(tan(1/2*f*x+1/2*e)-1)^3-480/7/(tan(1/2*f*x+1/2*e)-1)^7-404/5/(tan(1/2*f*x+1/2*e)-1)^5-32/(tan(1/2*f*x+1/2*e)-1)^8)","A"
246,1,178,124,0.295000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^6,x)","\frac{2 a^{2} \left(-\frac{512}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{7}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{30}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{128}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{2376}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{88}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{932}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{292}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{288}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{64}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}\right)}{f \,c^{6}}"," ",0,"2/f*a^2/c^6*(-512/3/(tan(1/2*f*x+1/2*e)-1)^9-7/(tan(1/2*f*x+1/2*e)-1)^2-1/(tan(1/2*f*x+1/2*e)-1)-30/(tan(1/2*f*x+1/2*e)-1)^3-128/11/(tan(1/2*f*x+1/2*e)-1)^11-2376/7/(tan(1/2*f*x+1/2*e)-1)^7-88/(tan(1/2*f*x+1/2*e)-1)^4-932/5/(tan(1/2*f*x+1/2*e)-1)^5-292/(tan(1/2*f*x+1/2*e)-1)^6-288/(tan(1/2*f*x+1/2*e)-1)^8-64/(tan(1/2*f*x+1/2*e)-1)^10)","A"
247,1,297,166,0.410000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^6,x)","\frac{-\frac{c^{6} a^{3} \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 c^{6} a^{3} \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 c^{6} a^{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{6 c^{6} a^{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}-6 c^{6} 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)-\frac{8 c^{6} a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 c^{6} a^{3} \cos \left(f x +e \right)+c^{6} a^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/9*c^6*a^3*(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*c^6*a^3*(-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*c^6*a^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)+6/5*c^6*a^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-6*c^6*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)-8/3*c^6*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*c^6*a^3*cos(f*x+e)+c^6*a^3*(f*x+e))","A"
248,1,276,133,0.429000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^5,x)","\frac{-c^{5} a^{3} \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 c^{5} a^{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}+2 c^{5} a^{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{6 c^{5} a^{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 c^{5} a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-2 c^{5} 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)+2 c^{5} a^{3} \cos \left(f x +e \right)+c^{5} a^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-c^5*a^3*(-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*c^5*a^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)+2*c^5*a^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)+6/5*c^5*a^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-2*c^5*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)-2*c^5*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+2*c^5*a^3*cos(f*x+e)+c^5*a^3*(f*x+e))","B"
249,1,255,102,0.421000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^4,x)","\frac{-\frac{c^{4} a^{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}-c^{4} a^{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 c^{4} a^{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 c^{4} 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)-c^{4} a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 c^{4} 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)+c^{4} a^{3} \cos \left(f x +e \right)+c^{4} a^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/7*c^4*a^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)-c^4*a^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*c^4*a^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*c^4*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)-c^4*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)-3*c^4*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+c^4*a^3*cos(f*x+e)+c^4*a^3*(f*x+e))","B"
250,1,140,83,0.242000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^3,x)","\frac{-c^{3} a^{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 c^{3} 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 c^{3} 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)+c^{3} a^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-c^3*a^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*c^3*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*c^3*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+c^3*a^3*(f*x+e))","A"
251,1,160,77,0.293000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^2,x)","\frac{-\frac{c^{2} a^{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}+c^{2} 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)+\frac{2 c^{2} a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 c^{2} 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)-c^{2} a^{3} \cos \left(f x +e \right)+c^{2} a^{3} \left(f x +e \right)}{f}"," ",0,"1/f*(-1/5*c^2*a^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+c^2*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)+2/3*c^2*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)-2*c^2*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-c^2*a^3*cos(f*x+e)+c^2*a^3*(f*x+e))","B"
252,1,89,74,0.241000," ","int((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e)),x)","\frac{-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{2 a^{3} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a^{3} c \cos \left(f x +e \right)+a^{3} c \left(f x +e \right)}{f}"," ",0,"1/f*(-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)+2/3*a^3*c*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a^3*c*cos(f*x+e)+a^3*c*(f*x+e))","A"
253,1,181,88,0.270000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x)","-\frac{16 a^{3}}{c f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{a^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{8 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{c f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{8 a^{3}}{c f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{15 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c f}"," ",0,"-16*a^3/c/f/(tan(1/2*f*x+1/2*e)-1)-a^3/c/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3+8*a^3/c/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2+a^3/c/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+8*a^3/c/f/(1+tan(1/2*f*x+1/2*e)^2)^2-15*a^3/c/f*arctan(tan(1/2*f*x+1/2*e))","B"
254,1,121,88,0.282000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x)","-\frac{32 a^{3}}{3 c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{16 a^{3}}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}+\frac{8 a^{3}}{c^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2 a^{3}}{c^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{10 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{2} f}"," ",0,"-32/3*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^3-16*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)^2+8*a^3/c^2/f/(tan(1/2*f*x+1/2*e)-1)-2*a^3/c^2/f/(1+tan(1/2*f*x+1/2*e)^2)+10*a^3/c^2/f*arctan(tan(1/2*f*x+1/2*e))","A"
255,1,143,102,0.314000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x)","-\frac{64 a^{3}}{5 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{32 a^{3}}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{80 a^{3}}{3 c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{8 a^{3}}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{4 a^{3}}{c^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{c^{3} f}"," ",0,"-64/5*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^5-32*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^4-80/3*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^3-8*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)^2-4*a^3/c^3/f/(tan(1/2*f*x+1/2*e)-1)-2*a^3/c^3/f*arctan(tan(1/2*f*x+1/2*e))","A"
256,1,118,32,0.280000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x)","\frac{2 a^{3} \left(-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{20}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{48}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{40}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{6}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{32}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{64}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}\right)}{f \,c^{4}}"," ",0,"2/f*a^3/c^4*(-1/(tan(1/2*f*x+1/2*e)-1)-20/(tan(1/2*f*x+1/2*e)-1)^3-48/(tan(1/2*f*x+1/2*e)-1)^5-40/(tan(1/2*f*x+1/2*e)-1)^4-6/(tan(1/2*f*x+1/2*e)-1)^2-32/(tan(1/2*f*x+1/2*e)-1)^6-64/7/(tan(1/2*f*x+1/2*e)-1)^7)","B"
257,1,148,65,0.338000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x)","\frac{2 a^{3} \left(-\frac{7}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{76}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{128}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{64}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{496}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{86}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{136}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{928}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}\right)}{f \,c^{5}}"," ",0,"2/f*a^3/c^5*(-7/(tan(1/2*f*x+1/2*e)-1)^2-76/(tan(1/2*f*x+1/2*e)-1)^4-128/9/(tan(1/2*f*x+1/2*e)-1)^9-1/(tan(1/2*f*x+1/2*e)-1)-64/(tan(1/2*f*x+1/2*e)-1)^8-496/3/(tan(1/2*f*x+1/2*e)-1)^6-86/3/(tan(1/2*f*x+1/2*e)-1)^3-136/(tan(1/2*f*x+1/2*e)-1)^5-928/7/(tan(1/2*f*x+1/2*e)-1)^7)","B"
258,1,178,95,0.319000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x)","\frac{2 a^{3} \left(-\frac{256}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{3008}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{128}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{116}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{292}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{544}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{126}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{1480}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{4272}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}\right)}{f \,c^{6}}"," ",0,"2/f*a^3/c^6*(-256/11/(tan(1/2*f*x+1/2*e)-1)^11-3008/9/(tan(1/2*f*x+1/2*e)-1)^9-128/(tan(1/2*f*x+1/2*e)-1)^10-1/(tan(1/2*f*x+1/2*e)-1)-116/3/(tan(1/2*f*x+1/2*e)-1)^3-292/(tan(1/2*f*x+1/2*e)-1)^5-544/(tan(1/2*f*x+1/2*e)-1)^8-126/(tan(1/2*f*x+1/2*e)-1)^4-1480/3/(tan(1/2*f*x+1/2*e)-1)^6-4272/7/(tan(1/2*f*x+1/2*e)-1)^7-8/(tan(1/2*f*x+1/2*e)-1)^2)","A"
259,1,208,124,0.372000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^7,x)","\frac{2 a^{3} \left(-\frac{8832}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{50}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{2352}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{9}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{512}{13 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{13}}-\frac{6752}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{192}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{1148}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{1600}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{540}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{256}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{12}}-\frac{13112}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}\right)}{f \,c^{7}}"," ",0,"2/f*a^3/c^7*(-8832/11/(tan(1/2*f*x+1/2*e)-1)^11-50/(tan(1/2*f*x+1/2*e)-1)^3-2352/(tan(1/2*f*x+1/2*e)-1)^8-9/(tan(1/2*f*x+1/2*e)-1)^2-512/13/(tan(1/2*f*x+1/2*e)-1)^13-6752/3/(tan(1/2*f*x+1/2*e)-1)^9-1/(tan(1/2*f*x+1/2*e)-1)-192/(tan(1/2*f*x+1/2*e)-1)^4-1148/(tan(1/2*f*x+1/2*e)-1)^6-1600/(tan(1/2*f*x+1/2*e)-1)^10-540/(tan(1/2*f*x+1/2*e)-1)^5-256/(tan(1/2*f*x+1/2*e)-1)^12-13112/7/(tan(1/2*f*x+1/2*e)-1)^7)","A"
260,1,238,156,0.449000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^8,x)","\frac{2 a^{3} \left(-\frac{81344}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{32288}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{2304}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{13184}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{12}}-\frac{24320}{13 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{13}}-\frac{84112}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{10}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{47072}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1}-\frac{512}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{14}}-\frac{4536}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{188}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{1024}{15 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{15}}-\frac{276}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{7352}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}\right)}{f \,c^{8}}"," ",0,"2/f*a^3/c^8*(-81344/11/(tan(1/2*f*x+1/2*e)-1)^11-32288/7/(tan(1/2*f*x+1/2*e)-1)^7-2304/(tan(1/2*f*x+1/2*e)-1)^6-13184/3/(tan(1/2*f*x+1/2*e)-1)^12-24320/13/(tan(1/2*f*x+1/2*e)-1)^13-84112/9/(tan(1/2*f*x+1/2*e)-1)^9-10/(tan(1/2*f*x+1/2*e)-1)^2-47072/5/(tan(1/2*f*x+1/2*e)-1)^10-1/(tan(1/2*f*x+1/2*e)-1)-512/(tan(1/2*f*x+1/2*e)-1)^14-4536/5/(tan(1/2*f*x+1/2*e)-1)^5-188/3/(tan(1/2*f*x+1/2*e)-1)^3-1024/15/(tan(1/2*f*x+1/2*e)-1)^15-276/(tan(1/2*f*x+1/2*e)-1)^4-7352/(tan(1/2*f*x+1/2*e)-1)^8)","A"
261,1,219,112,0.322000," ","int((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x)","-\frac{5 c^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{22 c^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{48 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{5 c^{4} \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)^{3}}-\frac{70 c^{4}}{3 f a \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)}{f a}-\frac{32 c^{4}}{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)^3*tan(1/2*f*x+1/2*e)^5-22/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4-48/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2+5/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)-70/3/f*c^4/a/(1+tan(1/2*f*x+1/2*e)^2)^3-35/f*c^4/a*arctan(tan(1/2*f*x+1/2*e))-32/f*c^4/a/(tan(1/2*f*x+1/2*e)+1)","A"
262,1,181,86,0.246000," ","int((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x)","-\frac{c^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{8 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{c^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{8 c^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{15 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f}-\frac{16 c^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-c^3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-8*c^3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2+c^3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)-8*c^3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2-15*c^3/a/f*arctan(tan(1/2*f*x+1/2*e))-16*c^3/a/f/(tan(1/2*f*x+1/2*e)+1)","B"
263,1,73,56,0.210000," ","int((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x)","-\frac{2 c^{2}}{f a \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{6 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f a}-\frac{8 c^{2}}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/f*c^2/a/(1+tan(1/2*f*x+1/2*e)^2)-6/f*c^2/a*arctan(tan(1/2*f*x+1/2*e))-8/f*c^2/a/(tan(1/2*f*x+1/2*e)+1)","A"
264,1,43,32,0.181000," ","int((c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x)","-\frac{2 c \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f a}-\frac{4 c}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/f*c/a*arctan(tan(1/2*f*x+1/2*e))-4/f*c/a/(tan(1/2*f*x+1/2*e)+1)","A"
265,-2,0,16,180.000000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","\int \frac{1}{\left(a +a \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)}\, dx"," ",0,"int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x)","F"
266,1,73,49,0.181000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x)","\frac{-\frac{2}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{1}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{3}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f a \,c^{2}}"," ",0,"2/f/a/c^2*(-1/3/(tan(1/2*f*x+1/2*e)-1)^3-1/2/(tan(1/2*f*x+1/2*e)-1)^2-3/4/(tan(1/2*f*x+1/2*e)-1)-1/4/(tan(1/2*f*x+1/2*e)+1))","A"
267,1,103,79,0.251000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x)","\frac{-\frac{4}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{3}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{5}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{7}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f a \,c^{3}}"," ",0,"2/f/a/c^3*(-2/5/(tan(1/2*f*x+1/2*e)-1)^5-1/(tan(1/2*f*x+1/2*e)-1)^4-3/2/(tan(1/2*f*x+1/2*e)-1)^3-5/4/(tan(1/2*f*x+1/2*e)-1)^2-7/8/(tan(1/2*f*x+1/2*e)-1)-1/8/(tan(1/2*f*x+1/2*e)+1))","A"
268,1,133,110,0.246000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{8}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{38}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{9}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{15}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{17}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{15}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f a \,c^{4}}"," ",0,"2/f/a/c^4*(-4/7/(tan(1/2*f*x+1/2*e)-1)^7-2/(tan(1/2*f*x+1/2*e)-1)^6-19/5/(tan(1/2*f*x+1/2*e)-1)^5-9/2/(tan(1/2*f*x+1/2*e)-1)^4-15/4/(tan(1/2*f*x+1/2*e)-1)^3-17/8/(tan(1/2*f*x+1/2*e)-1)^2-15/16/(tan(1/2*f*x+1/2*e)-1)-1/16/(tan(1/2*f*x+1/2*e)+1))","A"
269,1,267,142,0.306000," ","int((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x)","\frac{7 c^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{46 c^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{96 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{7 c^{5} \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)^{3}}+\frac{142 c^{5}}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{105 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{128 c^{5}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{64 c^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{96 c^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5+46*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4+96*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2-7*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)+142/3*c^5/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^3+105*c^5/a^2/f*arctan(tan(1/2*f*x+1/2*e))-128/3*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3+64*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2+96*c^5/a^2/f/(tan(1/2*f*x+1/2*e)+1)","A"
270,1,229,125,0.291000," ","int((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x)","\frac{c^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{12 c^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{c^{4} \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{12 c^{4}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{35 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{64 c^{4}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{32 c^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{32 c^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3+12*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2-c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+12*c^4/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)^2+35*c^4/a^2/f*arctan(tan(1/2*f*x+1/2*e))-64/3*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3+32*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2+32*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)","A"
271,1,121,86,0.262000," ","int((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x)","\frac{2 c^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{10 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{32 c^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8 c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2*c^3/a^2/f/(1+tan(1/2*f*x+1/2*e)^2)+10*c^3/a^2/f*arctan(tan(1/2*f*x+1/2*e))-32/3*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3+16*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2+8*c^3/a^2/f/(tan(1/2*f*x+1/2*e)+1)","A"
272,1,71,68,0.263000," ","int((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x)","\frac{2 c^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{16 c^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"2*c^2/a^2/f*arctan(tan(1/2*f*x+1/2*e))-16/3*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3+8*c^2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2","A"
273,1,56,27,0.224000," ","int((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","\frac{2 c \left(\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{4}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}\right)}{f \,a^{2}}"," ",0,"2/f*c/a^2*(2/(tan(1/2*f*x+1/2*e)+1)^2-1/(tan(1/2*f*x+1/2*e)+1)-4/3/(tan(1/2*f*x+1/2*e)+1)^3)","B"
274,1,73,48,0.264000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{1}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{3}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{a^{2} c f}"," ",0,"2/f/a^2/c*(-1/4/(tan(1/2*f*x+1/2*e)-1)-1/3/(tan(1/2*f*x+1/2*e)+1)^3+1/2/(tan(1/2*f*x+1/2*e)+1)^2-3/4/(tan(1/2*f*x+1/2*e)+1))","A"
275,-2,0,36,180.000000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x)","\int \frac{1}{\left(a +a \sin \left(f x +e \right)\right)^{2} \left(c -c \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x)","F"
276,1,133,70,0.259000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x)","\frac{-\frac{2}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{1}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{5}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{3}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{11}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{1}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{5}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,c^{3} a^{2}}"," ",0,"2/f/c^3/a^2*(-1/5/(tan(1/2*f*x+1/2*e)-1)^5-1/2/(tan(1/2*f*x+1/2*e)-1)^4-5/6/(tan(1/2*f*x+1/2*e)-1)^3-3/4/(tan(1/2*f*x+1/2*e)-1)^2-11/16/(tan(1/2*f*x+1/2*e)-1)-1/12/(tan(1/2*f*x+1/2*e)+1)^3+1/8/(tan(1/2*f*x+1/2*e)+1)^2-5/16/(tan(1/2*f*x+1/2*e)+1))","A"
277,1,163,103,0.266000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{4}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{5}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{55}{12 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{23}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{13}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{12 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{1}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,c^{4} a^{2}}"," ",0,"2/f/c^4/a^2*(-2/7/(tan(1/2*f*x+1/2*e)-1)^7-1/(tan(1/2*f*x+1/2*e)-1)^6-2/(tan(1/2*f*x+1/2*e)-1)^5-5/2/(tan(1/2*f*x+1/2*e)-1)^4-55/24/(tan(1/2*f*x+1/2*e)-1)^3-23/16/(tan(1/2*f*x+1/2*e)-1)^2-13/16/(tan(1/2*f*x+1/2*e)-1)-1/24/(tan(1/2*f*x+1/2*e)+1)^3+1/16/(tan(1/2*f*x+1/2*e)+1)^2-3/16/(tan(1/2*f*x+1/2*e)+1))","A"
278,1,193,134,0.280000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x)","\frac{-\frac{8}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{68}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{46}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{35}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{59}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{19}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{9}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{57}{32 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{24 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{1}{16 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{7}{32 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,a^{2} c^{5}}"," ",0,"2/f/a^2/c^5*(-4/9/(tan(1/2*f*x+1/2*e)-1)^9-2/(tan(1/2*f*x+1/2*e)-1)^8-34/7/(tan(1/2*f*x+1/2*e)-1)^7-23/3/(tan(1/2*f*x+1/2*e)-1)^6-35/4/(tan(1/2*f*x+1/2*e)-1)^5-59/8/(tan(1/2*f*x+1/2*e)-1)^4-19/4/(tan(1/2*f*x+1/2*e)-1)^3-9/4/(tan(1/2*f*x+1/2*e)-1)^2-57/64/(tan(1/2*f*x+1/2*e)-1)-1/48/(tan(1/2*f*x+1/2*e)+1)^3+1/32/(tan(1/2*f*x+1/2*e)+1)^2-7/64/(tan(1/2*f*x+1/2*e)+1))","A"
279,1,277,149,0.336000," ","int((c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x)","-\frac{c^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{16 c^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{c^{5} \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{16 c^{5}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{63 c^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{256 c^{5}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{128 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{64 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{32 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{64 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-16*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2+c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)-16*c^5/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)^2-63*c^5/a^3/f*arctan(tan(1/2*f*x+1/2*e))-256/5*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5+128*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4-64*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3-32*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2-64*c^5/a^3/f/(tan(1/2*f*x+1/2*e)+1)","A"
280,1,145,118,0.312000," ","int((c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x)","-\frac{2 c^{4}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{14 c^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{128 c^{4}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{64 c^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{128 c^{4}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{16 c^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2*c^4/a^3/f/(1+tan(1/2*f*x+1/2*e)^2)-14*c^4/a^3/f*arctan(tan(1/2*f*x+1/2*e))-128/5*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5+64*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4-128/3*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3-16*c^4/a^3/f/(tan(1/2*f*x+1/2*e)+1)","A"
281,1,143,99,0.297000," ","int((c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x)","-\frac{2 c^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{64 c^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{32 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{80 c^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2*c^3/a^3/f*arctan(tan(1/2*f*x+1/2*e))-64/5*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5+32*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4-80/3*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3+8*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2-4*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)","A"
282,1,88,31,0.273000," ","int((c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x)","\frac{2 c^{2} \left(\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{8}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{16}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}\right)}{f \,a^{3}}"," ",0,"2/f*c^2/a^3*(4/(tan(1/2*f*x+1/2*e)+1)^2+8/(tan(1/2*f*x+1/2*e)+1)^4-1/(tan(1/2*f*x+1/2*e)+1)-8/(tan(1/2*f*x+1/2*e)+1)^3-16/5/(tan(1/2*f*x+1/2*e)+1)^5)","B"
283,1,86,54,0.264000," ","int((c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\frac{2 c \left(\frac{3}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{1}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}-\frac{14}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}\right)}{f \,a^{3}}"," ",0,"2/f*c/a^3*(3/(tan(1/2*f*x+1/2*e)+1)^2+4/(tan(1/2*f*x+1/2*e)+1)^4-1/(tan(1/2*f*x+1/2*e)+1)-14/3/(tan(1/2*f*x+1/2*e)+1)^3-8/5/(tan(1/2*f*x+1/2*e)+1)^5)","A"
284,1,101,77,0.255000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x)","\frac{-\frac{1}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{4}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{3}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{5}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{7}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{a^{3} c f}"," ",0,"2/f/a^3/c*(-1/8/(tan(1/2*f*x+1/2*e)-1)-2/5/(tan(1/2*f*x+1/2*e)+1)^5+1/(tan(1/2*f*x+1/2*e)+1)^4-3/2/(tan(1/2*f*x+1/2*e)+1)^3+5/4/(tan(1/2*f*x+1/2*e)+1)^2-7/8/(tan(1/2*f*x+1/2*e)+1))","A"
285,1,133,69,0.227000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{5}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{2}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{5}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{3}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{11}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,c^{2} a^{3}}"," ",0,"2/f/c^2/a^3*(-1/12/(tan(1/2*f*x+1/2*e)-1)^3-1/8/(tan(1/2*f*x+1/2*e)-1)^2-5/16/(tan(1/2*f*x+1/2*e)-1)-1/5/(tan(1/2*f*x+1/2*e)+1)^5+1/2/(tan(1/2*f*x+1/2*e)+1)^4-5/6/(tan(1/2*f*x+1/2*e)+1)^3+3/4/(tan(1/2*f*x+1/2*e)+1)^2-11/16/(tan(1/2*f*x+1/2*e)+1))","A"
286,-2,0,55,180.000000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x)","\int \frac{1}{\left(a +a \sin \left(f x +e \right)\right)^{3} \left(c -c \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x)","F"
287,1,193,89,0.286000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x)","\frac{-\frac{2}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{1}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{21}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{11}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{11}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{15}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{21}{16 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{10 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{1}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{1}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{1}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{11}{16 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,c^{4} a^{3}}"," ",0,"2/f/c^4/a^3*(-1/7/(tan(1/2*f*x+1/2*e)-1)^7-1/2/(tan(1/2*f*x+1/2*e)-1)^6-21/20/(tan(1/2*f*x+1/2*e)-1)^5-11/8/(tan(1/2*f*x+1/2*e)-1)^4-11/8/(tan(1/2*f*x+1/2*e)-1)^3-15/16/(tan(1/2*f*x+1/2*e)-1)^2-21/32/(tan(1/2*f*x+1/2*e)-1)-1/20/(tan(1/2*f*x+1/2*e)+1)^5+1/8/(tan(1/2*f*x+1/2*e)+1)^4-1/4/(tan(1/2*f*x+1/2*e)+1)^3+1/4/(tan(1/2*f*x+1/2*e)+1)^2-11/32/(tan(1/2*f*x+1/2*e)+1))","B"
288,1,223,121,0.286000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x)","\frac{-\frac{4}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{5}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{49}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{49}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{35}{4 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{49}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{51}{16 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{99}{64 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{20 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{1}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{13}{48 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{9}{32 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{29}{64 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,a^{3} c^{5}}"," ",0,"2/f/a^3/c^5*(-2/9/(tan(1/2*f*x+1/2*e)-1)^9-1/(tan(1/2*f*x+1/2*e)-1)^8-5/2/(tan(1/2*f*x+1/2*e)-1)^7-49/12/(tan(1/2*f*x+1/2*e)-1)^6-49/10/(tan(1/2*f*x+1/2*e)-1)^5-35/8/(tan(1/2*f*x+1/2*e)-1)^4-49/16/(tan(1/2*f*x+1/2*e)-1)^3-51/32/(tan(1/2*f*x+1/2*e)-1)^2-99/128/(tan(1/2*f*x+1/2*e)-1)-1/40/(tan(1/2*f*x+1/2*e)+1)^5+1/16/(tan(1/2*f*x+1/2*e)+1)^4-13/96/(tan(1/2*f*x+1/2*e)+1)^3+9/64/(tan(1/2*f*x+1/2*e)+1)^2-29/128/(tan(1/2*f*x+1/2*e)+1))","A"
289,1,253,155,0.315000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x)","\frac{-\frac{8}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{11}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{10}}-\frac{106}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{9}}-\frac{23}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{8}}-\frac{33}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{7}}-\frac{217}{6 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{6}}-\frac{623}{20 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{5}}-\frac{169}{8 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{4}}-\frac{365}{32 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{3}}-\frac{303}{64 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)^{2}}-\frac{219}{128 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)-1\right)}-\frac{1}{40 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{1}{16 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{7}{48 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{5}{32 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{37}{128 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}}{f \,a^{3} c^{6}}"," ",0,"2/f/a^3/c^6*(-4/11/(tan(1/2*f*x+1/2*e)-1)^11-2/(tan(1/2*f*x+1/2*e)-1)^10-53/9/(tan(1/2*f*x+1/2*e)-1)^9-23/2/(tan(1/2*f*x+1/2*e)-1)^8-33/2/(tan(1/2*f*x+1/2*e)-1)^7-217/12/(tan(1/2*f*x+1/2*e)-1)^6-623/40/(tan(1/2*f*x+1/2*e)-1)^5-169/16/(tan(1/2*f*x+1/2*e)-1)^4-365/64/(tan(1/2*f*x+1/2*e)-1)^3-303/128/(tan(1/2*f*x+1/2*e)-1)^2-219/256/(tan(1/2*f*x+1/2*e)-1)-1/80/(tan(1/2*f*x+1/2*e)+1)^5+1/32/(tan(1/2*f*x+1/2*e)+1)^4-7/96/(tan(1/2*f*x+1/2*e)+1)^3+5/64/(tan(1/2*f*x+1/2*e)+1)^2-37/256/(tan(1/2*f*x+1/2*e)+1))","A"
290,1,79,121,0.714000," ","int((a+a*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(35 \left(\sin^{3}\left(f x +e \right)\right)-165 \left(\sin^{2}\left(f x +e \right)\right)+321 \sin \left(f x +e \right)-319\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^4*(1+sin(f*x+e))^2*a*(35*sin(f*x+e)^3-165*sin(f*x+e)^2+321*sin(f*x+e)-319)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
291,1,69,91,0.876000," ","int((a+a*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(15 \left(\sin^{2}\left(f x +e \right)\right)-54 \sin \left(f x +e \right)+71\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^3*(1+sin(f*x+e))^2*a*(15*sin(f*x+e)^2-54*sin(f*x+e)+71)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
292,1,59,61,0.757000," ","int((a+a*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(3 \sin \left(f x +e \right)-7\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^2*(1+sin(f*x+e))^2*a*(3*sin(f*x+e)-7)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
293,1,47,30,0.540000," ","int((a+a*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}{3 \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))^2*a/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
294,1,94,66,0.716000," ","int((a+a*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(\sqrt{c}\, \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)}\right)}{c \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2*(sin(f*x+e)-1)*(c*(1+sin(f*x+e)))^(1/2)*a*(c^(1/2)*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))/c/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
295,1,120,65,0.632000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","\frac{a \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c \sin \left(f x +e \right)-\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}\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/c^(5/2)*a*(2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c*sin(f*x+e)-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))*(c*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
296,1,189,94,0.815000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{a \left(-\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}+2 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}+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^{3}+4 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, 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) c^{3}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{16 c^{\frac{11}{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/c^(11/2)*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)^2*c^3+2*(c*(1+sin(f*x+e)))^(3/2)*c^(3/2)+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^3+4*(c*(1+sin(f*x+e)))^(1/2)*c^(5/2)-2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^3)*(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","A"
297,1,243,122,1.060000," ","int((a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x)","-\frac{a \left(6 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{\frac{5}{2}}-3 \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^{5}-32 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{7}{2}}+9 \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^{5}-24 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{9}{2}}-9 \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}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{5}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{192 c^{\frac{17}{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/c^(17/2)*a*(6*(c*(1+sin(f*x+e)))^(5/2)*c^(5/2)-3*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^5-32*(c*(1+sin(f*x+e)))^(3/2)*c^(7/2)+9*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^5-24*(c*(1+sin(f*x+e)))^(1/2)*c^(9/2)-9*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+3*2^(1/2)*arctanh(1/2*(c*(1+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)^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
298,1,81,129,0.872000," ","int((a+a*sin(f*x+e))^2*(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(105 \left(\sin^{3}\left(f x +e \right)\right)-455 \left(\sin^{2}\left(f x +e \right)\right)+755 \sin \left(f x +e \right)-533\right)}{1155 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/1155*(sin(f*x+e)-1)*c^4*(1+sin(f*x+e))^3*a^2*(105*sin(f*x+e)^3-455*sin(f*x+e)^2+755*sin(f*x+e)-533)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
299,1,71,97,0.840000," ","int((a+a*sin(f*x+e))^2*(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(35 \left(\sin^{2}\left(f x +e \right)\right)-110 \sin \left(f x +e \right)+107\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))^3*a^2*(35*sin(f*x+e)^2-110*sin(f*x+e)+107)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
300,1,61,65,0.839000," ","int((a+a*sin(f*x+e))^2*(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(5 \sin \left(f x +e \right)-9\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^2*(1+sin(f*x+e))^3*a^2*(5*sin(f*x+e)-9)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
301,1,49,32,0.641000," ","int((a+a*sin(f*x+e))^2*(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}}{5 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/5*(sin(f*x+e)-1)*c*(1+sin(f*x+e))^3*a^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
302,1,112,100,0.924000," ","int((a+a*sin(f*x+e))^2/(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(6 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)-\left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}-6 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c \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^2*(6*c^(3/2)*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)-6*(c*(1+sin(f*x+e)))^(1/2)*c)/c^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
303,1,145,102,0.776000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x)","\frac{a^{2} \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c \sin \left(f x +e \right)-3 \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}\, \sin \left(f x +e \right)+4 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{c^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"a^2*(3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c*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-2*(c*(1+sin(f*x+e)))^(1/2)*c^(1/2)*sin(f*x+e)+4*(c*(1+sin(f*x+e)))^(1/2)*c^(1/2))*(c*(1+sin(f*x+e)))^(1/2)/c^(5/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
304,1,191,103,0.895000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x)","-\frac{a^{2} \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(\sin^{2}\left(f x +e \right)\right) c^{2}-6 \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 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c}+3 \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 \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*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*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*(c*(1+sin(f*x+e)))^(3/2)*c^(1/2)+3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2-12*(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","A"
305,1,245,133,1.016000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(7/2),x)","-\frac{a^{2} \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(\sin^{3}\left(f x +e \right)\right) c^{4}+24 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{7}{2}}-32 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{5}{2}}-6 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{\frac{3}{2}}-9 \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^{4}+9 \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^{4}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{4}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{96 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,"-1/96*a^2*(3*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^4+24*(c*(1+sin(f*x+e)))^(1/2)*c^(7/2)-32*(c*(1+sin(f*x+e)))^(3/2)*c^(5/2)-6*(c*(1+sin(f*x+e)))^(5/2)*c^(3/2)-9*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^4+9*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^4-3*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^(15/2)/(sin(f*x+e)-1)^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
306,1,299,163,1.299000," ","int((a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(9/2),x)","\frac{a^{2} \left(6 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} c^{\frac{5}{2}}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{4}\left(f x +e \right)\right) c^{6}-44 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{\frac{7}{2}}+12 \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^{6}-88 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{9}{2}}-18 \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^{6}+48 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{11}{2}}+12 \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^{6}-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{6}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{512 c^{\frac{21}{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,"1/512/c^(21/2)*a^2*(6*(c*(1+sin(f*x+e)))^(7/2)*c^(5/2)-3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^4*c^6-44*(c*(1+sin(f*x+e)))^(5/2)*c^(7/2)+12*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^6-88*(c*(1+sin(f*x+e)))^(3/2)*c^(9/2)-18*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^6+48*(c*(1+sin(f*x+e)))^(1/2)*c^(11/2)+12*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^6-3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^6)*(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","A"
307,1,81,129,0.894000," ","int((a+a*sin(f*x+e))^3*(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(231 \left(\sin^{3}\left(f x +e \right)\right)-945 \left(\sin^{2}\left(f x +e \right)\right)+1421 \sin \left(f x +e \right)-835\right)}{3003 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/3003*(sin(f*x+e)-1)*c^4*(1+sin(f*x+e))^4*a^3*(231*sin(f*x+e)^3-945*sin(f*x+e)^2+1421*sin(f*x+e)-835)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
308,1,71,97,0.759000," ","int((a+a*sin(f*x+e))^3*(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(63 \left(\sin^{2}\left(f x +e \right)\right)-182 \sin \left(f x +e \right)+151\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^3*(1+sin(f*x+e))^4*a^3*(63*sin(f*x+e)^2-182*sin(f*x+e)+151)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
309,1,61,65,0.832000," ","int((a+a*sin(f*x+e))^3*(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(7 \sin \left(f x +e \right)-11\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^2*(1+sin(f*x+e))^4*a^3*(7*sin(f*x+e)-11)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
310,1,49,32,0.729000," ","int((a+a*sin(f*x+e))^3*(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}}{7 \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/7*(sin(f*x+e)-1)*c*(1+sin(f*x+e))^4*a^3/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
311,1,129,132,1.132000," ","int((a+a*sin(f*x+e))^3/(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(60 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)-3 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}-10 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c -60 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^3*(60*c^(5/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))-3*(c*(1+sin(f*x+e)))^(5/2)-10*(c*(1+sin(f*x+e)))^(3/2)*c-60*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"
312,1,189,133,1.017000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x)","\frac{2 a^{3} \left(15 \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}-12 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}} \sin \left(f x +e \right)-\left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c}\, \sin \left(f x +e \right)-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+18 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}}+\left(c \left(1+\sin \left(f x +e \right)\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,"2/3*a^3*(15*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^2-12*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)*sin(f*x+e)-(c*(1+sin(f*x+e)))^(3/2)*c^(1/2)*sin(f*x+e)-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2+18*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)+(c*(1+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"
313,1,239,134,1.168000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x)","-\frac{a^{3} \left(15 \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}-8 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right)-30 \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}+18 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c}+16 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{3}{2}} \sin \left(f x +e \right)+15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}-36 \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)}}{4 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,"-1/4/c^(9/2)*a^3*(15*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^2-8*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)*sin(f*x+e)^2-30*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+18*(c*(1+sin(f*x+e)))^(3/2)*c^(1/2)+16*(c*(1+sin(f*x+e)))^(1/2)*c^(3/2)*sin(f*x+e)+15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2-36*(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","A"
314,1,245,134,1.004000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(7/2),x)","\frac{a^{3} \left(15 \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 \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 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c}+45 \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 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{3}{2}}-15 \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 \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*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*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*(c*(1+sin(f*x+e)))^(5/2)*c^(1/2)+45*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*(c*(1+sin(f*x+e)))^(3/2)*c^(3/2)-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^3+120*(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","A"
315,1,299,164,1.123000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(9/2),x)","-\frac{a^{3} \left(-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{4}\left(f x +e \right)\right) c^{5}+30 c^{\frac{3}{2}} \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}+60 \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^{5}+292 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{\frac{5}{2}}-90 \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^{5}-440 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{7}{2}}+60 \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}+240 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{9}{2}}-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{5}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{768 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,"-1/768/c^(19/2)*a^3*(-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^4*c^5+30*c^(3/2)*(c*(1+sin(f*x+e)))^(7/2)+60*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^5+292*(c*(1+sin(f*x+e)))^(5/2)*c^(5/2)-90*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^5-440*(c*(1+sin(f*x+e)))^(3/2)*c^(7/2)+60*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+240*(c*(1+sin(f*x+e)))^(1/2)*c^(9/2)-15*2^(1/2)*arctanh(1/2*(c*(1+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","A"
316,1,353,194,1.117000," ","int((a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(11/2),x)","\frac{a^{3} \left(15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{5}\left(f x +e \right)\right) c^{7}-30 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{9}{2}} c^{\frac{5}{2}}+280 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} c^{\frac{7}{2}}+1024 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} c^{\frac{9}{2}}-1120 \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} c^{\frac{11}{2}}+480 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, c^{\frac{13}{2}}-75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \left(\sin^{4}\left(f x +e \right)\right) c^{7}+150 \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^{7}-150 \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^{7}+75 \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^{7}-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{7}\right) \sqrt{c \left(1+\sin \left(f x +e \right)\right)}}{5120 c^{\frac{25}{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,"1/5120*a^3*(15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^5*c^7-30*(c*(1+sin(f*x+e)))^(9/2)*c^(5/2)+280*(c*(1+sin(f*x+e)))^(7/2)*c^(7/2)+1024*(c*(1+sin(f*x+e)))^(5/2)*c^(9/2)-1120*(c*(1+sin(f*x+e)))^(3/2)*c^(11/2)+480*(c*(1+sin(f*x+e)))^(1/2)*c^(13/2)-75*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*sin(f*x+e)^4*c^7+150*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^7-150*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^7+75*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^7-15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^7)*(c*(1+sin(f*x+e)))^(1/2)/c^(25/2)/(sin(f*x+e)-1)^4/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
317,1,69,116,0.637000," ","int((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(\sin^{3}\left(f x +e \right)-7 \left(\sin^{2}\left(f x +e \right)\right)+43 \sin \left(f x +e \right)+91\right)}{5 a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2/5*c^4/a*(sin(f*x+e)-1)*(sin(f*x+e)^3-7*sin(f*x+e)^2+43*sin(f*x+e)+91)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
318,1,59,86,0.705000," ","int((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(\sin^{2}\left(f x +e \right)-10 \sin \left(f x +e \right)-23\right)}{3 a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*c^3/a*(sin(f*x+e)-1)*(sin(f*x+e)^2-10*sin(f*x+e)-23)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
319,1,49,56,0.633000," ","int((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(3+\sin \left(f x +e \right)\right)}{a \cos \left(f x +e \right) \sqrt{c -c \sin \left(f x +e \right)}\, f}"," ",0,"2*c^2/a*(sin(f*x+e)-1)*(3+sin(f*x+e))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
320,1,39,27,0.612000," ","int((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)}{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)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
321,1,86,73,0.963000," ","int(1/(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) c \sqrt{c \left(1+\sin \left(f x +e \right)\right)}+2 c^{\frac{3}{2}}\right)}{2 a \,c^{\frac{3}{2}} \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*(c*(1+sin(f*x+e)))^(1/2)+2*c^(3/2))/c^(3/2)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
322,1,134,100,0.822000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x)","-\frac{3 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \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 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c \sqrt{c \left(1+\sin \left(f x +e \right)\right)}-6 c^{\frac{3}{2}} \sin \left(f x +e \right)+2 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*(3*(c*(1+sin(f*x+e)))^(1/2)*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-3*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c*(c*(1+sin(f*x+e)))^(1/2)-6*c^(3/2)*sin(f*x+e)+2*c^(3/2))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
323,1,210,133,1.525000," ","int(1/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x)","-\frac{15 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \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}-30 c^{\frac{5}{2}} \left(\sin^{2}\left(f x +e \right)\right)-30 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \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}+40 c^{\frac{5}{2}} \sin \left(f x +e \right)+15 \sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2}+6 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*(15*(c*(1+sin(f*x+e)))^(1/2)*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^2-30*c^(5/2)*sin(f*x+e)^2-30*(c*(1+sin(f*x+e)))^(1/2)*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+40*c^(5/2)*sin(f*x+e)+15*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^2+6*c^(5/2))/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
324,1,91,156,0.671000," ","int((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(3 \left(\sin^{4}\left(f x +e \right)\right)-28 \left(\sin^{3}\left(f x +e \right)\right)+258 \left(\sin^{2}\left(f x +e \right)\right)+1092 \sin \left(f x +e \right)+723\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^5/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(3*sin(f*x+e)^4-28*sin(f*x+e)^3+258*sin(f*x+e)^2+1092*sin(f*x+e)+723)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
325,1,79,124,0.843000," ","int((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(\sin^{3}\left(f x +e \right)-15 \left(\sin^{2}\left(f x +e \right)\right)-69 \sin \left(f x +e \right)-45\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^4/a^2*(sin(f*x+e)-1)/(1+sin(f*x+e))*(sin(f*x+e)^3-15*sin(f*x+e)^2-69*sin(f*x+e)-45)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
326,1,71,92,0.822000," ","int((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(3 \left(\sin^{2}\left(f x +e \right)\right)+18 \sin \left(f x +e \right)+11\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))*(3*sin(f*x+e)^2+18*sin(f*x+e)+11)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
327,1,61,62,0.914000," ","int((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(3 \sin \left(f x +e \right)+1\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))*(3*sin(f*x+e)+1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
328,1,49,32,0.747000," ","int((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)}{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))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
329,1,109,105,1.251000," ","int(1/(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(10 c^{\frac{7}{2}}+6 c^{\frac{7}{2}} \sin \left(f x +e \right)-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2} \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}\right)}{12 a^{2} c^{\frac{7}{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^(7/2)/(1+sin(f*x+e))*(10*c^(7/2)+6*c^(7/2)*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^2*(c*(1+sin(f*x+e)))^(3/2))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
330,1,157,132,1.246000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x)","-\frac{15 \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 -15 \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 -20 c^{\frac{5}{2}} \sin \left(f x +e \right)-30 c^{\frac{5}{2}} \left(\sin^{2}\left(f x +e \right)\right)+26 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*(15*(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-15*(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-20*c^(5/2)*sin(f*x+e)-30*c^(5/2)*sin(f*x+e)^2+26*c^(5/2))/(1+sin(f*x+e))/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
331,1,233,165,1.187000," ","int(1/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x)","-\frac{105 \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}+70 c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)-210 c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)-210 \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}+322 c^{\frac{7}{2}} \sin \left(f x +e \right)+105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{2} \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}-86 c^{\frac{7}{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*(105*(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+70*c^(7/2)*sin(f*x+e)^2-210*c^(7/2)*sin(f*x+e)^3-210*(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+322*c^(7/2)*sin(f*x+e)+105*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)))^(3/2)-86*c^(7/2))/(1+sin(f*x+e))/(sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
332,1,91,156,0.790000," ","int((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(5 \left(\sin^{4}\left(f x +e \right)\right)-100 \left(\sin^{3}\left(f x +e \right)\right)-690 \left(\sin^{2}\left(f x +e \right)\right)-900 \sin \left(f x +e \right)-363\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*(5*sin(f*x+e)^4-100*sin(f*x+e)^3-690*sin(f*x+e)^2-900*sin(f*x+e)-363)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
333,1,81,124,1.359000," ","int((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(5 \left(\sin^{3}\left(f x +e \right)\right)+45 \left(\sin^{2}\left(f x +e \right)\right)+55 \sin \left(f x +e \right)+23\right)}{5 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,"2/5*c^4/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2*(5*sin(f*x+e)^3+45*sin(f*x+e)^2+55*sin(f*x+e)+23)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
334,1,71,94,0.839000," ","int((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 \left(\sin^{2}\left(f x +e \right)\right)+10 \sin \left(f x +e \right)+7\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*sin(f*x+e)^2+10*sin(f*x+e)+7)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
335,1,61,65,0.816000," ","int((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(5 \sin \left(f x +e \right)-1\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*(5*sin(f*x+e)-1)/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
336,1,49,32,0.656000," ","int((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)}{5 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,"2/5*c/a^3*(sin(f*x+e)-1)/(1+sin(f*x+e))^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
337,1,122,137,1.184000," ","int(1/(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(-30 c^{\frac{11}{2}} \left(\sin^{2}\left(f x +e \right)\right)-80 c^{\frac{11}{2}} \sin \left(f x +e \right)-74 c^{\frac{11}{2}}+15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{c \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c^{3} \left(c \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}\right)}{120 a^{3} c^{\frac{11}{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*(sin(f*x+e)-1)*(-30*c^(11/2)*sin(f*x+e)^2-80*c^(11/2)*sin(f*x+e)-74*c^(11/2)+15*2^(1/2)*arctanh(1/2*(c*(1+sin(f*x+e)))^(1/2)*2^(1/2)/c^(1/2))*c^3*(c*(1+sin(f*x+e)))^(5/2))/a^3/c^(11/2)/(1+sin(f*x+e))^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
338,1,170,164,1.250000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x)","-\frac{105 \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 \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 +42 c^{\frac{7}{2}} \sin \left(f x +e \right)-350 c^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)\right)-210 c^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)+278 c^{\frac{7}{2}}}{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*(105*(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*(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+42*c^(7/2)*sin(f*x+e)-350*c^(7/2)*sin(f*x+e)^2-210*c^(7/2)*sin(f*x+e)^3+278*c^(7/2))/(1+sin(f*x+e))^2/cos(f*x+e)/(c-c*sin(f*x+e))^(1/2)/f","A"
339,1,246,197,1.298000," ","int(1/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x)","-\frac{315 \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) \left(\sin^{2}\left(f x +e \right)\right) c^{2}+1176 c^{\frac{9}{2}} \left(\sin^{2}\left(f x +e \right)\right)-420 c^{\frac{9}{2}} \left(\sin^{3}\left(f x +e \right)\right)-630 c^{\frac{9}{2}} \left(\sin^{4}\left(f x +e \right)\right)-630 \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^{2}+708 c^{\frac{9}{2}} \sin \left(f x +e \right)+315 \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^{2}-514 c^{\frac{9}{2}}}{1280 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,"-1/1280/c^(13/2)/a^3*(315*(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)^2*c^2+1176*c^(9/2)*sin(f*x+e)^2-420*c^(9/2)*sin(f*x+e)^3-630*c^(9/2)*sin(f*x+e)^4-630*(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^2+708*c^(9/2)*sin(f*x+e)+315*(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^2-514*c^(9/2))/(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"
340,1,103,37,0.441000," ","int((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\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)}\, \left(\cos^{6}\left(f x +e \right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+4 \sin \left(f x +e \right)+4\right)}{4 f \cos \left(f x +e \right)^{7}}"," ",0,"1/4/f*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^2+4*sin(f*x+e)+4)/cos(f*x+e)^7","B"
341,1,78,37,0.338000," ","int((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \sin \left(f x +e \right)+2\right)}{3 f \cos \left(f x +e \right)^{5}}"," ",0,"1/3/f*(-c*(sin(f*x+e)-1))^(5/2)*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)+2*sin(f*x+e)+2)/cos(f*x+e)^5","B"
342,1,61,37,0.312000," ","int((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right)+1\right)}{2 f \cos \left(f x +e \right)^{3}}"," ",0,"1/2/f*(-c*(sin(f*x+e)-1))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(cos(f*x+e)^2+sin(f*x+e)+1)/cos(f*x+e)^3","A"
343,1,44,37,0.306000," ","int((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right)}{f \cos \left(f x +e \right)}"," ",0,"1/f*(-c*(sin(f*x+e)-1))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)/cos(f*x+e)","A"
344,1,106,48,0.263000," ","int((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\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*(a*(1+sin(f*x+e)))^(1/2)*(-1+cos(f*x+e)+sin(f*x+e))*(2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(2/(cos(f*x+e)+1)))/(1-cos(f*x+e)+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(1/2)","B"
345,1,68,36,0.272000," ","int((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}{f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/f*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(-1+cos(f*x+e)+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(3/2)/(1-cos(f*x+e)+sin(f*x+e))","A"
346,1,96,37,0.275000," ","int((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-3 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+3\right)}{2 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/2/f*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-3*sin(f*x+e)-2*cos(f*x+e)+3)/(-c*(sin(f*x+e)-1))^(5/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
347,1,120,37,0.299000," ","int((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+3 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right)-7 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+7\right)}{3 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,"-1/3/f*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+3*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)^2-7*sin(f*x+e)-4*cos(f*x+e)+7)/(-c*(sin(f*x+e)-1))^(7/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
348,1,106,77,0.326000," ","int((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(2 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+2 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \sin \left(f x +e \right)+6\right)}{10 f \cos \left(f x +e \right)^{7}}"," ",0,"1/10/f*(-c*(sin(f*x+e)-1))^(7/2)*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(2*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+2*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+6*sin(f*x+e)+6)/cos(f*x+e)^7","A"
349,1,90,77,0.289000," ","int((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{\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}} \left(3 \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right)+5 \sin \left(f x +e \right)+5\right)}{12 f \cos \left(f x +e \right)^{5}}"," ",0,"1/12/f*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(3*cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)+4*cos(f*x+e)^2+5*sin(f*x+e)+5)/cos(f*x+e)^5","A"
350,1,55,77,0.258000," ","int((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(2+\cos^{2}\left(f x +e \right)\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}}}{3 f \cos \left(f x +e \right)^{3}}"," ",0,"1/3/f*(2+cos(f*x+e)^2)*(-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"
351,1,63,37,0.298000," ","int((a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(-1-\left(\cos^{2}\left(f x +e \right)\right)+\sin \left(f x +e \right)\right)}{2 f \cos \left(f x +e \right)^{3}}"," ",0,"-1/2/f*(-c*(sin(f*x+e)-1))^(1/2)*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(-1-cos(f*x+e)^2+sin(f*x+e))/cos(f*x+e)^3","A"
352,1,252,88,0.266000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(\sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \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)-\left(\cos^{2}\left(f x +e \right)\right)-2 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \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)-\sin \left(f x +e \right)+2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+1\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \left(f x +e \right)-2\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/f*(sin(f*x+e)*cos(f*x+e)-2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+4*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2-2*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)+2*ln(2/(cos(f*x+e)+1))-4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+1)*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(1/2)","B"
353,1,375,89,0.241000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(2 \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)-\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 \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)+\left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 \left(\cos^{2}\left(f x +e \right)\right)-2 \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)+\cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 \sin \left(f x +e \right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \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*(2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*sin(f*x+e)*cos(f*x+e)-4*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*cos(f*x+e)^2-2*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)*ln(2/(cos(f*x+e)+1))+2*sin(f*x+e)+4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*ln(2/(cos(f*x+e)+1))-2)*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(3/2)","B"
354,1,90,36,0.228000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \left(f x +e \right)-2\right)}"," ",0,"-1/f*(-1+cos(f*x+e)+sin(f*x+e))*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)/(sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^2-2*sin(f*x+e)+cos(f*x+e)-2)","B"
355,1,141,76,0.257000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right)+3 \sin \left(f x +e \right) \cos \left(f x +e \right)-7 \cos \left(f x +e \right)-10 \sin \left(f x +e \right)+10\right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \left(f x +e \right)-2\right)}"," ",0,"1/6/f*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(cos(f*x+e)^3+cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^2+3*sin(f*x+e)*cos(f*x+e)-7*cos(f*x+e)-10*sin(f*x+e)+10)/(-c*(sin(f*x+e)-1))^(7/2)/(sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^2-2*sin(f*x+e)+cos(f*x+e)-2)","A"
356,1,169,80,0.283000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \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)-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{3}\left(f x +e \right)\right)-7 \sin \left(f x +e \right) \cos \left(f x +e \right)+12 \left(\cos^{2}\left(f x +e \right)\right)+17 \sin \left(f x +e \right)+10 \cos \left(f x +e \right)-17\right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \left(f x +e \right)-2\right)}"," ",0,"-1/6/f*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4-5*cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^3-7*sin(f*x+e)*cos(f*x+e)+12*cos(f*x+e)^2+17*sin(f*x+e)+10*cos(f*x+e)-17)/(-c*(sin(f*x+e)-1))^(9/2)/(sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^2-2*sin(f*x+e)+cos(f*x+e)-2)","B"
357,1,196,80,0.279000," ","int((a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x)","-\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(3 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{5}\left(f x +e \right)\right)+15 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-18 \left(\cos^{4}\left(f x +e \right)\right)-51 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-36 \left(\cos^{3}\left(f x +e \right)\right)-45 \sin \left(f x +e \right) \cos \left(f x +e \right)+96 \left(\cos^{2}\left(f x +e \right)\right)+98 \sin \left(f x +e \right)+53 \cos \left(f x +e \right)-98\right)}{20 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \sin \left(f x +e \right)+\cos \left(f x +e \right)-2\right)}"," ",0,"-1/20/f*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(3*sin(f*x+e)*cos(f*x+e)^4+3*cos(f*x+e)^5+15*sin(f*x+e)*cos(f*x+e)^3-18*cos(f*x+e)^4-51*cos(f*x+e)^2*sin(f*x+e)-36*cos(f*x+e)^3-45*sin(f*x+e)*cos(f*x+e)+96*cos(f*x+e)^2+98*sin(f*x+e)+53*cos(f*x+e)-98)/(-c*(sin(f*x+e)-1))^(11/2)/(sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^2-2*sin(f*x+e)+cos(f*x+e)-2)","B"
358,1,116,116,0.321000," ","int((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(5 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)+11 \sin \left(f x +e \right)+11\right)}{30 f \cos \left(f x +e \right)^{7}}"," ",0,"1/30/f*(-c*(sin(f*x+e)-1))^(7/2)*(a*(1+sin(f*x+e)))^(5/2)*sin(f*x+e)*(5*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+6*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2+11*sin(f*x+e)+11)/cos(f*x+e)^7","A"
359,1,67,116,0.278000," ","int((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(3 \left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right)+8\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}}}{15 f \cos \left(f x +e \right)^{5}}"," ",0,"1/15/f*(3*cos(f*x+e)^4+4*cos(f*x+e)^2+8)*(-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"
360,1,91,77,0.284000," ","int((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x)","\frac{\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}} \left(3 \left(\cos^{4}\left(f x +e \right)\right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right)-5 \sin \left(f x +e \right)+5\right)}{12 f \cos \left(f x +e \right)^{5}}"," ",0,"1/12/f*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(3*cos(f*x+e)^4-cos(f*x+e)^2*sin(f*x+e)+4*cos(f*x+e)^2-5*sin(f*x+e)+5)/cos(f*x+e)^5","A"
361,1,80,37,0.316000," ","int((a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\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}} \left(-\left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2+2 \sin \left(f x +e \right)\right)}{3 f \cos \left(f x +e \right)^{5}}"," ",0,"-1/3/f*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(-cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)-2+2*sin(f*x+e))/cos(f*x+e)^5","B"
362,1,315,127,0.299000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)-6 \sin \left(f x +e \right) \cos \left(f x +e \right)-16 \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)+8 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+5 \left(\cos^{2}\left(f x +e \right)\right)-16 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+5 \sin \left(f x +e \right)-\cos \left(f x +e \right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-5\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) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-1/2/f*(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3-6*sin(f*x+e)*cos(f*x+e)-16*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+5*cos(f*x+e)^2-16*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+5*sin(f*x+e)-cos(f*x+e)+16*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*ln(2/(cos(f*x+e)+1))-5)*(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))^(1/2)","B"
363,1,439,132,0.269000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \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)+4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{3}\left(f x +e \right)+8 \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 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+5 \sin \left(f x +e \right) \cos \left(f x +e \right)+16 \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)-8 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 \left(\cos^{2}\left(f x +e \right)\right)+8 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 \sin \left(f x +e \right)-\cos \left(f x +e \right)-16 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{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/f*(cos(f*x+e)^2*sin(f*x+e)-8*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+4*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^3+8*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+5*sin(f*x+e)*cos(f*x+e)+16*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-6*cos(f*x+e)^2+8*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-6*sin(f*x+e)-cos(f*x+e)-16*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*ln(2/(cos(f*x+e)+1))+6)*(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"
364,1,553,133,0.263000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \sin \left(f x +e \right) \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)+\left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \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 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \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 \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 \left(\cos^{3}\left(f x +e \right)\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 \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 \left(\cos^{2}\left(f x +e \right)\right)-2 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \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 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{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{5}{2}}}"," ",0,"1/f*(sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))-2*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2*sin(f*x+e)+2*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+2*cos(f*x+e)^3-3*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+6*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-4*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+8*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*cos(f*x+e)^2-2*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+4*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)-2*cos(f*x+e)+4*ln(2/(cos(f*x+e)+1))-8*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2)*(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))^(5/2)","B"
365,1,130,36,0.275000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(\cos^{2}\left(f x +e \right)-4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right)}{3 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{7}{2}}}"," ",0,"1/3/f*(-1+cos(f*x+e)+sin(f*x+e))*(cos(f*x+e)^2-4)*(a*(1+sin(f*x+e)))^(5/2)*sin(f*x+e)/(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))^(7/2)","B"
366,1,199,76,0.283000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \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)-5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)+9 \left(\cos^{2}\left(f x +e \right)\right)+14 \sin \left(f x +e \right)+10 \cos \left(f x +e \right)-14\right)}{6 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \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)}"," ",0,"-1/6/f*(a*(1+sin(f*x+e)))^(5/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4-5*cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)+9*cos(f*x+e)^2+14*sin(f*x+e)+10*cos(f*x+e)-14)/(-c*(sin(f*x+e)-1))^(9/2)/(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)","B"
367,1,226,115,0.285000," ","int((a+a*sin(f*x+e))^(5/2)/(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(2 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+2 \left(\cos^{5}\left(f x +e \right)\right)+10 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-12 \left(\cos^{4}\left(f x +e \right)\right)-34 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-24 \left(\cos^{3}\left(f x +e \right)\right)-25 \sin \left(f x +e \right) \cos \left(f x +e \right)+59 \left(\cos^{2}\left(f x +e \right)\right)+62 \sin \left(f x +e \right)+37 \cos \left(f x +e \right)-62\right)}{15 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \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)}"," ",0,"-1/15/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(2*sin(f*x+e)*cos(f*x+e)^4+2*cos(f*x+e)^5+10*sin(f*x+e)*cos(f*x+e)^3-12*cos(f*x+e)^4-34*cos(f*x+e)^2*sin(f*x+e)-24*cos(f*x+e)^3-25*sin(f*x+e)*cos(f*x+e)+59*cos(f*x+e)^2+62*sin(f*x+e)+37*cos(f*x+e)-62)/(-c*(sin(f*x+e)-1))^(11/2)/(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"
368,1,252,122,0.323000," ","int((a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x)","\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(7 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)-7 \left(\cos^{6}\left(f x +e \right)\right)-49 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-42 \left(\cos^{5}\left(f x +e \right)\right)-119 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+168 \left(\cos^{4}\left(f x +e \right)\right)+343 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+224 \left(\cos^{3}\left(f x +e \right)\right)+202 \sin \left(f x +e \right) \cos \left(f x +e \right)-545 \left(\cos^{2}\left(f x +e \right)\right)-444 \sin \left(f x +e \right)-242 \cos \left(f x +e \right)+444\right)}{60 f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}} \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)}"," ",0,"1/60/f*(a*(1+sin(f*x+e)))^(5/2)*sin(f*x+e)*(7*sin(f*x+e)*cos(f*x+e)^5-7*cos(f*x+e)^6-49*sin(f*x+e)*cos(f*x+e)^4-42*cos(f*x+e)^5-119*sin(f*x+e)*cos(f*x+e)^3+168*cos(f*x+e)^4+343*cos(f*x+e)^2*sin(f*x+e)+224*cos(f*x+e)^3+202*sin(f*x+e)*cos(f*x+e)-545*cos(f*x+e)^2-444*sin(f*x+e)-242*cos(f*x+e)+444)/(-c*(sin(f*x+e)-1))^(13/2)/(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)","B"
369,1,143,155,0.370000," ","int((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(35 \left(\cos^{8}\left(f x +e \right)\right)+5 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+40 \left(\cos^{6}\left(f x +e \right)\right)+13 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+48 \left(\cos^{4}\left(f x +e \right)\right)+29 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+64 \left(\cos^{2}\left(f x +e \right)\right)+93 \sin \left(f x +e \right)+93\right)}{280 f \cos \left(f x +e \right)^{9}}"," ",0,"1/280/f*(-c*(sin(f*x+e)-1))^(9/2)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(35*cos(f*x+e)^8+5*cos(f*x+e)^6*sin(f*x+e)+40*cos(f*x+e)^6+13*sin(f*x+e)*cos(f*x+e)^4+48*cos(f*x+e)^4+29*cos(f*x+e)^2*sin(f*x+e)+64*cos(f*x+e)^2+93*sin(f*x+e)+93)/cos(f*x+e)^9","A"
370,1,77,155,0.308000," ","int((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(5 \left(\cos^{6}\left(f x +e \right)\right)+6 \left(\cos^{4}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)+16\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}}}{35 f \cos \left(f x +e \right)^{7}}"," ",0,"1/35/f*(5*cos(f*x+e)^6+6*cos(f*x+e)^4+8*cos(f*x+e)^2+16)*(-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"
371,1,116,116,0.314000," ","int((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x)","-\frac{\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}} \left(-5 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-6 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+11 \sin \left(f x +e \right)-11\right)}{30 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/30/f*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(-5*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4-6*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+11*sin(f*x+e)-11)/cos(f*x+e)^7","A"
372,1,106,77,0.308000," ","int((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(-2 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \sin \left(f x +e \right)-6\right)}{10 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/10/f*(-c*(sin(f*x+e)-1))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(-2*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4-2*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+6*sin(f*x+e)-6)/cos(f*x+e)^7","A"
373,1,103,37,0.342000," ","int((a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(-\left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)+4 \sin \left(f x +e \right)-4\right)}{4 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/4/f*(-c*(sin(f*x+e)-1))^(1/2)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(-cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^2+4*sin(f*x+e)-4)/cos(f*x+e)^7","B"
374,1,367,166,0.315000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\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)+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \left(\cos^{3}\left(f x +e \right)\right)+24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-22 \sin \left(f x +e \right) \cos \left(f x +e \right)-48 \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 \left(\cos^{2}\left(f x +e \right)\right)-48 \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 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 \sin \left(f x +e \right)-6 \cos \left(f x +e \right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16\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) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/3/f*(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4+5*cos(f*x+e)^2*sin(f*x+e)+6*cos(f*x+e)^3+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-22*sin(f*x+e)*cos(f*x+e)-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+17*cos(f*x+e)^2-48*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*ln(2/(cos(f*x+e)+1))+16*sin(f*x+e)-6*cos(f*x+e)+48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-16)*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(1/2)","B"
375,1,491,174,0.289000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\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)+8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 \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 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+9 \left(\cos^{3}\left(f x +e \right)\right)+48 \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 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+25 \sin \left(f x +e \right) \cos \left(f x +e \right)+96 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-33 \left(\cos^{2}\left(f x +e \right)\right)+48 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-34 \sin \left(f x +e \right)-9 \cos \left(f x +e \right)-96 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+48 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+34\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{3}{2}}}"," ",0,"1/2/f*(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4+8*cos(f*x+e)^2*sin(f*x+e)-48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)+24*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+9*cos(f*x+e)^3+48*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+25*sin(f*x+e)*cos(f*x+e)+96*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-33*cos(f*x+e)^2+48*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-34*sin(f*x+e)-9*cos(f*x+e)-96*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+48*ln(2/(cos(f*x+e)+1))+34)*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(3/2)","B"
376,1,618,175,0.300000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+12 \sin \left(f x +e \right) \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)-\left(\cos^{4}\left(f x +e \right)\right)-6 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+12 \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)-11 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-12 \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 \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)-10 \left(\cos^{3}\left(f x +e \right)\right)+18 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-36 \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 \sin \left(f x +e \right) \cos \left(f x +e \right)+24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 \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 \left(\cos^{2}\left(f x +e \right)\right)+12 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 \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 \sin \left(f x +e \right)+10 \cos \left(f x +e \right)-24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-16\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{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/f*(sin(f*x+e)*cos(f*x+e)^3-6*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+12*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^4-6*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+12*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-11*cos(f*x+e)^2*sin(f*x+e)-12*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+24*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-10*cos(f*x+e)^3+18*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-36*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*sin(f*x+e)*cos(f*x+e)+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+17*cos(f*x+e)^2+12*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-24*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+16*sin(f*x+e)+10*cos(f*x+e)-24*ln(2/(cos(f*x+e)+1))+48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-16)*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(5/2)","B"
377,1,748,173,0.294000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\left(-20+20 \sin \left(f x +e \right)+6 \cos \left(f x +e \right)-14 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{4}\left(f x +e \right)\right)-12 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 \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 \sin \left(f x +e \right) \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)-12 \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 \left(\cos^{3}\left(f x +e \right)\right)+28 \left(\cos^{2}\left(f x +e \right)\right)-9 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-24 \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 \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 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-14 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \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 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+18 \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)+3 \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 \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)+24 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\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*(-20-12*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+20*sin(f*x+e)+6*cos(f*x+e)+28*cos(f*x+e)^2-14*sin(f*x+e)*cos(f*x+e)+24*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))*sin(f*x+e)*cos(f*x+e)-12*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-48*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-6*cos(f*x+e)^3-8*cos(f*x+e)^4+48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*ln(2/(cos(f*x+e)+1))+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+12*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-24*cos(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*sin(f*x+e)*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*sin(f*x+e)*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))-9*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+18*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-14*cos(f*x+e)^2*sin(f*x+e)+8*sin(f*x+e)*cos(f*x+e)^3+6*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1)))*(a*(1+sin(f*x+e)))^(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)/(-c*(sin(f*x+e)-1))^(7/2)","B"
378,1,154,36,0.255000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(\cos^{2}\left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right)}{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/f*(-1+cos(f*x+e)+sin(f*x+e))*(cos(f*x+e)^2-2)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)/(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)/(-c*(sin(f*x+e)-1))^(9/2)","B"
379,1,247,76,0.303000," ","int((a+a*sin(f*x+e))^(7/2)/(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(\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\cos^{5}\left(f x +e \right)+5 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-6 \left(\cos^{4}\left(f x +e \right)\right)-22 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-17 \left(\cos^{3}\left(f x +e \right)\right)-10 \sin \left(f x +e \right) \cos \left(f x +e \right)+32 \left(\cos^{2}\left(f x +e \right)\right)+36 \sin \left(f x +e \right)+26 \cos \left(f x +e \right)-36\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)*(sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^5+5*sin(f*x+e)*cos(f*x+e)^3-6*cos(f*x+e)^4-22*cos(f*x+e)^2*sin(f*x+e)-17*cos(f*x+e)^3-10*sin(f*x+e)*cos(f*x+e)+32*cos(f*x+e)^2+36*sin(f*x+e)+26*cos(f*x+e)-36)/(-c*(sin(f*x+e)-1))^(11/2)/(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)","B"
380,1,276,115,0.313000," ","int((a+a*sin(f*x+e))^(7/2)/(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 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)-3 \left(\cos^{6}\left(f x +e \right)\right)-21 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-18 \left(\cos^{5}\left(f x +e \right)\right)-51 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+72 \left(\cos^{4}\left(f x +e \right)\right)+157 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+106 \left(\cos^{3}\left(f x +e \right)\right)+78 \sin \left(f x +e \right) \cos \left(f x +e \right)-235 \left(\cos^{2}\left(f x +e \right)\right)-196 \sin \left(f x +e \right)-118 \cos \left(f x +e \right)+196\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*sin(f*x+e)*cos(f*x+e)^5-3*cos(f*x+e)^6-21*sin(f*x+e)*cos(f*x+e)^4-18*cos(f*x+e)^5-51*sin(f*x+e)*cos(f*x+e)^3+72*cos(f*x+e)^4+157*cos(f*x+e)^2*sin(f*x+e)+106*cos(f*x+e)^3+78*sin(f*x+e)*cos(f*x+e)-235*cos(f*x+e)^2-196*sin(f*x+e)-118*cos(f*x+e)+196)/(-c*(sin(f*x+e)-1))^(13/2)/(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)","B"
381,1,302,154,0.346000," ","int((a+a*sin(f*x+e))^(7/2)/(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(13 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+13 \left(\cos^{7}\left(f x +e \right)\right)+91 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)-104 \left(\cos^{6}\left(f x +e \right)\right)-403 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-312 \left(\cos^{5}\left(f x +e \right)\right)-637 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+1040 \left(\cos^{4}\left(f x +e \right)\right)+1712 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+1075 \left(\cos^{3}\left(f x +e \right)\right)+756 \sin \left(f x +e \right) \cos \left(f x +e \right)-2468 \left(\cos^{2}\left(f x +e \right)\right)-1672 \sin \left(f x +e \right)-916 \cos \left(f x +e \right)+1672\right)}{140 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,"-1/140/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(13*cos(f*x+e)^6*sin(f*x+e)+13*cos(f*x+e)^7+91*sin(f*x+e)*cos(f*x+e)^5-104*cos(f*x+e)^6-403*sin(f*x+e)*cos(f*x+e)^4-312*cos(f*x+e)^5-637*sin(f*x+e)*cos(f*x+e)^3+1040*cos(f*x+e)^4+1712*cos(f*x+e)^2*sin(f*x+e)+1075*cos(f*x+e)^3+756*sin(f*x+e)*cos(f*x+e)-2468*cos(f*x+e)^2-1672*sin(f*x+e)-916*cos(f*x+e)+1672)/(-c*(sin(f*x+e)-1))^(15/2)/(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"
382,1,328,164,0.384000," ","int((a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x)","\frac{\left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(3 \sin \left(f x +e \right) \left(\cos^{7}\left(f x +e \right)\right)-3 \left(\cos^{8}\left(f x +e \right)\right)-27 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-24 \left(\cos^{7}\left(f x +e \right)\right)-93 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)+120 \left(\cos^{6}\left(f x +e \right)\right)+333 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+240 \left(\cos^{5}\left(f x +e \right)\right)+387 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-720 \left(\cos^{4}\left(f x +e \right)\right)-970 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-583 \left(\cos^{3}\left(f x +e \right)\right)-367 \sin \left(f x +e \right) \cos \left(f x +e \right)+1337 \left(\cos^{2}\left(f x +e \right)\right)+769 \sin \left(f x +e \right)+402 \cos \left(f x +e \right)-769\right)}{35 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,"1/35/f*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(3*sin(f*x+e)*cos(f*x+e)^7-3*cos(f*x+e)^8-27*cos(f*x+e)^6*sin(f*x+e)-24*cos(f*x+e)^7-93*sin(f*x+e)*cos(f*x+e)^5+120*cos(f*x+e)^6+333*sin(f*x+e)*cos(f*x+e)^4+240*cos(f*x+e)^5+387*sin(f*x+e)*cos(f*x+e)^3-720*cos(f*x+e)^4-970*cos(f*x+e)^2*sin(f*x+e)-583*cos(f*x+e)^3-367*sin(f*x+e)*cos(f*x+e)+1337*cos(f*x+e)^2+769*sin(f*x+e)+402*cos(f*x+e)-769)/(-c*(sin(f*x+e)-1))^(17/2)/(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"
383,1,320,125,0.292000," ","int((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5 \left(\cos^{2}\left(f x +e \right)\right)+6 \sin \left(f x +e \right) \cos \left(f x +e \right)-16 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 \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)-8 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-\cos \left(f x +e \right)-5 \sin \left(f x +e \right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-5\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}{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) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"-1/2/f*(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)+5*cos(f*x+e)^2+6*sin(f*x+e)*cos(f*x+e)-16*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+8*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+16*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-8*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-cos(f*x+e)-5*sin(f*x+e)+16*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-8*ln(2/(cos(f*x+e)+1))-5)*(-c*(sin(f*x+e)-1))^(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)/(a*(1+sin(f*x+e)))^(1/2)","B"
384,1,261,85,0.273000," ","int((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(\sin \left(f x +e \right) \cos \left(f x +e \right)+4 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+\cos^{2}\left(f x +e \right)-4 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-\sin \left(f x +e \right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-1\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) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"-1/f*(sin(f*x+e)*cos(f*x+e)+4*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+cos(f*x+e)^2-4*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-sin(f*x+e)+4*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*ln(2/(cos(f*x+e)+1))-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)))^(1/2)","B"
385,1,106,45,0.228000," ","int((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\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)}\, \left(\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/f*(1-cos(f*x+e)+sin(f*x+e))*(-c*(sin(f*x+e)-1))^(1/2)*(ln(2/(cos(f*x+e)+1))-2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))/(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))","B"
386,1,92,42,0.250000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \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)\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*(ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-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)","B"
387,1,165,83,0.269000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(\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)-\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)-\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \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)+\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*(sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+ln(-(-1+cos(f*x+e)-sin(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))^(3/2)","A"
388,1,252,122,0.273000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(\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)-\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 \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 \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 \left(\cos^{2}\left(f x +e \right)\right)+3 \sin \left(f x +e \right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2\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*(cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2+3*sin(f*x+e)-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(5/2)","B"
389,1,501,173,0.296000," ","int((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-48 \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 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-9 \left(\cos^{3}\left(f x +e \right)\right)-48 \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 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+25 \sin \left(f x +e \right) \cos \left(f x +e \right)+96 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+33 \left(\cos^{2}\left(f x +e \right)\right)-48 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-34 \sin \left(f x +e \right)+9 \cos \left(f x +e \right)+96 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-34\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{3}{2}}}"," ",0,"-1/2/f*(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4+8*cos(f*x+e)^2*sin(f*x+e)-48*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-9*cos(f*x+e)^3-48*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+25*sin(f*x+e)*cos(f*x+e)+96*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-48*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+33*cos(f*x+e)^2-48*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-34*sin(f*x+e)+9*cos(f*x+e)+96*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-48*ln(2/(cos(f*x+e)+1))-34)*(-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"
390,1,446,131,0.274000," ","int((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \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)-\left(\cos^{3}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 \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)+5 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 \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 \left(\cos^{2}\left(f x +e \right)\right)+4 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 \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 \sin \left(f x +e \right)+\cos \left(f x +e \right)-8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6\right) \left(-c \left(\sin \left(f x +e \right)-1\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(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/f*(cos(f*x+e)^2*sin(f*x+e)+4*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-8*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^3+4*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-8*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+5*sin(f*x+e)*cos(f*x+e)-8*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+16*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+6*cos(f*x+e)^2+4*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-8*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-6*sin(f*x+e)+cos(f*x+e)-8*ln(2/(cos(f*x+e)+1))+16*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-6)*(-c*(sin(f*x+e)-1))^(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)/(a*(1+sin(f*x+e)))^(3/2)","B"
391,1,388,89,0.284000," ","int((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(\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 \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)+\left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \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 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \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 \left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \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 \sin \left(f x +e \right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2\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{3}{2}}}"," ",0,"1/f*(ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-2*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*cos(f*x+e)-2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+4*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2+cos(f*x+e)*ln(2/(cos(f*x+e)+1))-2*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)-2*ln(2/(cos(f*x+e)+1))+4*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2)*(-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)))^(3/2)","B"
392,1,68,37,0.271000," ","int((c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}{f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/f*(1-cos(f*x+e)+sin(f*x+e))*sin(f*x+e)*(-c*(sin(f*x+e)-1))^(1/2)/(a*(1+sin(f*x+e)))^(3/2)/(-1+cos(f*x+e)+sin(f*x+e))","A"
393,1,167,83,0.267000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{\left(\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)-\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)-\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)-\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)}{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*(sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-sin(f*x+e)+ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(1/2)","A"
394,1,115,125,0.243000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(-\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)+\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)+\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}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(-cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+sin(f*x+e))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(3/2)","A"
395,1,229,167,0.273000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(3 \sin \left(f x +e \right) \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 \sin \left(f x +e \right) \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 \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) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 \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)-\left(\cos^{2}\left(f x +e \right)\right)-3 \sin \left(f x +e \right)+1\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*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-3*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+3*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2-3*sin(f*x+e)+1)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
396,1,685,215,0.319000," ","int((c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(-132-192 \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)-132 \sin \left(f x +e \right)+74 \cos \left(f x +e \right)+58 \sin \left(f x +e \right) \cos \left(f x +e \right)+96 \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)-11 \left(\cos^{4}\left(f x +e \right)\right)+48 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-288 \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)+96 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{5}\left(f x +e \right)\right)-73 \left(\cos^{3}\left(f x +e \right)\right)+384 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+143 \left(\cos^{2}\left(f x +e \right)\right)-48 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-192 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-96 \sin \left(f x +e \right) \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)-192 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+96 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-12 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+85 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+144 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-192 \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)+384 \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)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}{2 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,"1/2/f*(-132-96*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-192*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+48*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-132*sin(f*x+e)+74*cos(f*x+e)+143*cos(f*x+e)^2+58*sin(f*x+e)*cos(f*x+e)+96*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+144*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-cos(f*x+e)^5-73*cos(f*x+e)^3-288*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+384*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-11*cos(f*x+e)^4-192*ln(2/(cos(f*x+e)+1))-192*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+96*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-48*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+85*cos(f*x+e)^2*sin(f*x+e)-12*sin(f*x+e)*cos(f*x+e)^3+sin(f*x+e)*cos(f*x+e)^4+96*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-192*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+384*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*(-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"
397,1,633,173,0.308000," ","int((c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+12 \sin \left(f x +e \right) \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 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+\cos^{4}\left(f x +e \right)-12 \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 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-11 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 \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)-12 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+10 \left(\cos^{3}\left(f x +e \right)\right)+36 \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)-18 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 \sin \left(f x +e \right) \cos \left(f x +e \right)-48 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-17 \left(\cos^{2}\left(f x +e \right)\right)+24 \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 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16 \sin \left(f x +e \right)-10 \cos \left(f x +e \right)-48 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+16\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{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/f*(sin(f*x+e)*cos(f*x+e)^3+12*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-6*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+cos(f*x+e)^4-12*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+6*cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))-11*cos(f*x+e)^2*sin(f*x+e)+24*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-12*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)+10*cos(f*x+e)^3+36*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-18*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-6*sin(f*x+e)*cos(f*x+e)-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-17*cos(f*x+e)^2+24*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-12*cos(f*x+e)*ln(2/(cos(f*x+e)+1))+16*sin(f*x+e)-10*cos(f*x+e)-48*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*ln(2/(cos(f*x+e)+1))+16)*(-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"
398,1,567,129,0.259000," ","int((c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \sin \left(f x +e \right) \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)-\left(\cos^{3}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 \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 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \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 \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 \left(\cos^{3}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 \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 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 \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 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 \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 \sin \left(f x +e \right)+2 \cos \left(f x +e \right)-4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+8 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\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(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/f*(sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^3*ln(2/(cos(f*x+e)+1))+2*cos(f*x+e)^3*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2*sin(f*x+e)+2*ln(2/(cos(f*x+e)+1))*sin(f*x+e)*cos(f*x+e)-4*sin(f*x+e)*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*cos(f*x+e)^3+3*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-6*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-4*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+8*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2+2*cos(f*x+e)*ln(2/(cos(f*x+e)+1))-4*cos(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)+2*cos(f*x+e)-4*ln(2/(cos(f*x+e)+1))+8*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2)*(-c*(sin(f*x+e)-1))^(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)/(a*(1+sin(f*x+e)))^(5/2)","B"
399,1,93,36,0.291000," ","int((c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\sin \left(f x +e \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right)}{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{5}{2}}}"," ",0,"-1/f*sin(f*x+e)*(-c*(sin(f*x+e)-1))^(3/2)*(-1+cos(f*x+e)-sin(f*x+e))/(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)))^(5/2)","B"
400,1,92,37,0.280000," ","int((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(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+2 \cos \left(f x +e \right)-3 \sin \left(f x +e \right)-3\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)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+2*cos(f*x+e)-3*sin(f*x+e)-3)/(a*(1+sin(f*x+e)))^(5/2)/(-1+cos(f*x+e)+sin(f*x+e))","B"
401,1,252,122,0.274000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(-\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)+\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 \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 \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 \left(\cos^{2}\left(f x +e \right)\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+3 \sin \left(f x +e \right)+2\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*(-cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*cos(f*x+e)^2+2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*sin(f*x+e)+2)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
402,1,229,164,0.268000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(3 \sin \left(f x +e \right) \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 \sin \left(f x +e \right) \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 \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) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 \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)-\left(\cos^{2}\left(f x +e \right)\right)+3 \sin \left(f x +e \right)+1\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*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-3*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-3*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2+3*sin(f*x+e)+1)*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(3/2)","A"
403,1,134,206,0.281000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(3 \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^{4}\left(f x +e \right)\right)-3 \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 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \sin \left(f x +e \right)\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*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))*cos(f*x+e)^4-3*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+3*cos(f*x+e)^2*sin(f*x+e)+2*sin(f*x+e))*cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
404,0,0,90,1.716000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
405,0,0,72,5.568000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","F"
406,0,0,72,6.569000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","F"
407,0,0,70,1.798000," ","int((a+a*sin(f*x+e))^m*(c-c*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)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x)","F"
408,0,0,64,0.400000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","F"
409,0,0,72,1.126000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","F"
410,0,0,72,1.086000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","F"
411,0,0,154,0.365000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","F"
412,0,0,96,0.301000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","F"
413,0,0,44,0.300000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \sqrt{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","F"
414,0,0,62,0.280000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
415,0,0,66,0.277000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","F"
416,0,0,66,0.247000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","F"
417,0,0,62,0.008000," ","int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
418,0,0,62,0.358000," ","int((c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","\int \frac{\left(c +c \sin \left(f x +e \right)\right)^{m}}{\sqrt{a -a \sin \left(f x +e \right)}}\, dx"," ",0,"int((c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","F"
419,0,0,162,1.021000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-3-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","F"
420,0,0,101,0.793000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-2-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","F"
421,0,0,46,0.606000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","F"
422,0,0,90,0.707000," ","int((a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","F"
423,0,0,92,0.555000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","F"
424,0,0,92,0.806000," ","int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x)","F"
425,1,259,215,0.329000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^4,x)","\frac{-a \,c^{4} \cos \left(f x +e \right)+4 a \,c^{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)-2 a \,c^{2} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+4 a c \,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)-\frac{a \,d^{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 \,c^{4} \left(f x +e \right)-4 a \,c^{3} d \cos \left(f x +e \right)+6 a \,c^{2} 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{4 a c \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a \,d^{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)}{f}"," ",0,"1/f*(-a*c^4*cos(f*x+e)+4*a*c^3*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*c^2*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+4*a*c*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)-1/5*a*d^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a*c^4*(f*x+e)-4*a*c^3*d*cos(f*x+e)+6*a*c^2*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4/3*a*c*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)+a*d^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"
426,1,182,152,0.288000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{-a \,c^{3} \cos \left(f x +e \right)+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)-a c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+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)+a \,c^{3} \left(f x +e \right)-3 a \,c^{2} d \cos \left(f x +e \right)+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)-\frac{a \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(-a*c^3*cos(f*x+e)+3*a*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+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)+a*c^3*(f*x+e)-3*a*c^2*d*cos(f*x+e)+3*a*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a*d^3*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
427,1,115,91,0.188000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{-a \,c^{2} \cos \left(f x +e \right)+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{a \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a \,c^{2} \left(f x +e \right)-2 a c d \cos \left(f x +e \right)+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)}{f}"," ",0,"1/f*(-a*c^2*cos(f*x+e)+2*a*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+a*c^2*(f*x+e)-2*a*c*d*cos(f*x+e)+a*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
428,1,59,44,0.104000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{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)-c a \cos \left(f x +e \right)-d a \cos \left(f x +e \right)+a c \left(f x +e \right)}{f}"," ",0,"1/f*(d*a*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-c*a*cos(f*x+e)-d*a*cos(f*x+e)+a*c*(f*x+e))","A"
429,1,17,16,0.013000," ","int(a+a*sin(f*x+e),x)","a x -\frac{a \cos \left(f x +e \right)}{f}"," ",0,"a*x-a*cos(f*x+e)/f","A"
430,1,119,58,0.200000," ","int((a+a*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) 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)}{f \sqrt{c^{2}-d^{2}}}+\frac{2 a \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))*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))+2/f*a/d*arctan(tan(1/2*f*x+1/2*e))","B"
431,1,147,78,0.238000," ","int((a+a*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)}{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}{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 \arctan \left(\frac{2 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 d}{2 \sqrt{c^{2}-d^{2}}}\right)}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}"," ",0,"-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d/(c+d)/c*tan(1/2*f*x+1/2*e)-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/(c+d)+2/f*a/(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"
432,1,1104,125,0.281000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","-\frac{3 a d c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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 \,d^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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 \,d^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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 \,c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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) 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{3 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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) 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{5 a d c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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 \,d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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 \,d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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{2 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{2 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 \,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 \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}{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) d}{f \left(c^{3}+c^{2} d -c \,d^{2}-d^{3}\right) \sqrt{c^{2}-d^{2}}}"," ",0,"-3/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d/(c^3+c^2*d-c*d^2-d^3)*c*tan(1/2*f*x+1/2*e)^3+2/f*a/(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^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)^3+2/f*a/(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^3+c^2*d-c*d^2-d^3)/c*tan(1/2*f*x+1/2*e)^3-2/f*a/(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+2/f*a/(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*d-3/f*a/(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*d^2+4/f*a/(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*d^3+2/f*a/(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*d^4-5/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*d*c/(c^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)+6/f*a/(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^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)+2/f*a/(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^3+c^2*d-c*d^2-d^3)*tan(1/2*f*x+1/2*e)-2/f*a/(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+2/f*a/(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*d+1/f*a/(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)*d^2+2/f*a/(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))*c-1/f*a/(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))*d","B"
433,1,3104,181,0.317000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^4,x)","\text{output too large to display}"," ",0,"-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^4/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^4/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^5-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^4*tan(1/2*f*x+1/2*e)^4-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^4*tan(1/2*f*x+1/2*e)^2+4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^3*d+2/3/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^2*d^2+2/f*a/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/(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^2+1/f*a/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/(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))*d^2-1/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c*d^3+6/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^4*d^4+10/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^4/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3-4/3/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c*d^5/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2*d^6/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3-8/3/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^3*d^7/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3+8/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^3*tan(1/2*f*x+1/2*e)^2*d-12/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^2*tan(1/2*f*x+1/2*e)^2*d^2+28/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c*tan(1/2*f*x+1/2*e)^2*d^3-6/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/c*tan(1/2*f*x+1/2*e)^2*d^5-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^4-2/3/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*d^4-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/c^2*tan(1/2*f*x+1/2*e)^2*d^6+17/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c*tan(1/2*f*x+1/2*e)^4*d^3-6/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/c*tan(1/2*f*x+1/2*e)^4*d^5-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/c^2*tan(1/2*f*x+1/2*e)^4*d^6-12/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3*d/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3+24/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2*d^2/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c*d^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^3-8/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d*c^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)+19/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^2*c^2/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^5/c/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)-2/f*a/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)/(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*d-4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d*c^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^5+5/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^2*c^2/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^5+4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^3*c/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^5-2/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^5/c/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*tan(1/2*f*x+1/2*e)^5+4/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^3*tan(1/2*f*x+1/2*e)^4*d-10/f*a/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^5+c^4*d-2*c^3*d^2-2*c^2*d^3+c*d^4+d^5)*c^2*tan(1/2*f*x+1/2*e)^4*d^2","B"
434,1,462,304,0.394000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^4,x)","\frac{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} c^{3} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+6 a^{2} c^{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)-\frac{4 a^{2} c \,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} d^{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)-2 a^{2} c^{4} \cos \left(f x +e \right)+8 a^{2} c^{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)-4 a^{2} c^{2} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+8 a^{2} c \,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)-\frac{2 a^{2} d^{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} c^{4} \left(f x +e \right)-4 a^{2} c^{3} d \cos \left(f x +e \right)+6 a^{2} c^{2} 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{4 a^{2} c \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} d^{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)}{f}"," ",0,"1/f*(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*c^3*d*(2+sin(f*x+e)^2)*cos(f*x+e)+6*a^2*c^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)-4/5*a^2*c*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*d^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*a^2*c^4*cos(f*x+e)+8*a^2*c^3*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4*a^2*c^2*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+8*a^2*c*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)-2/5*a^2*d^4*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+a^2*c^4*(f*x+e)-4*a^2*c^3*d*cos(f*x+e)+6*a^2*c^2*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-4/3*a^2*c*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*d^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"
435,1,329,221,0.332000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x)","\frac{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} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 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{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}-2 a^{2} c^{3} \cos \left(f x +e \right)+6 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)-2 a^{2} c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+2 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)+a^{2} c^{3} \left(f x +e \right)-3 a^{2} c^{2} d \cos \left(f x +e \right)+3 a^{2} 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} d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(a^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*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)-1/5*a^2*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-2*a^2*c^3*cos(f*x+e)+6*a^2*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a^2*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*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^2*c^3*(f*x+e)-3*a^2*c^2*d*cos(f*x+e)+3*a^2*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^2*d^3*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
436,1,219,146,0.256000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x)","\frac{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{2 a^{2} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+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)-2 a^{2} c^{2} \cos \left(f x +e \right)+4 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{2 a^{2} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+a^{2} c^{2} \left(f x +e \right)-2 a^{2} c d \cos \left(f x +e \right)+a^{2} 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)}{f}"," ",0,"1/f*(a^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*a^2*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+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)-2*a^2*c^2*cos(f*x+e)+4*a^2*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*a^2*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+a^2*c^2*(f*x+e)-2*a^2*c*d*cos(f*x+e)+a^2*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
437,1,117,86,0.188000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e)),x)","\frac{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{a^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a^{2} c \cos \left(f x +e \right)+2 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)+a^{2} c \left(f x +e \right)-a^{2} d \cos \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a^2*c*cos(f*x+e)+2*a^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*c*(f*x+e)-a^2*d*cos(f*x+e))","A"
438,1,52,41,0.092000," ","int((a+a*sin(f*x+e))^2,x)","\frac{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)-2 \cos \left(f x +e \right) a^{2}+a^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(a^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*cos(f*x+e)*a^2+a^2*(f*x+e))","A"
439,1,228,87,0.247000," ","int((a+a*sin(f*x+e))^2/(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) 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) 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)}{f \sqrt{c^{2}-d^{2}}}-\frac{2 a^{2}}{f d \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) c}{f \,d^{2}}+\frac{4 a^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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))*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))*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))-2/f*a^2/d/(1+tan(1/2*f*x+1/2*e)^2)-2/f*a^2/d^2*arctan(tan(1/2*f*x+1/2*e))*c+4/f*a^2/d*arctan(tan(1/2*f*x+1/2*e))","B"
440,1,389,107,0.294000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x)","\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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)}{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}{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}}{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} \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^{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) 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)}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}+\frac{2 a^{2} \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)-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)+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-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)-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))*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))*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))+2*a^2/f/d^2*arctan(tan(1/2*f*x+1/2*e))","B"
441,1,799,129,0.324000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x)","\frac{a^{2} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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^{2}+2 c d +d^{2}\right)}-\frac{2 a^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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^{2}+2 c d +d^{2}\right) c}-\frac{4 a^{2} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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^{2}+2 c d +d^{2}\right)}-\frac{8 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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^{2}+2 c d +d^{2}\right) c}-\frac{2 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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^{2}+2 c d +d^{2}\right) c^{2}}-\frac{a^{2} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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^{2}+2 c d +d^{2}\right)}-\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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} c \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{a^{2} 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^{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)}{f \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}"," ",0,"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)^3-4*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)*tan(1/2*f*x+1/2*e)^3*d-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)^2/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)^3*d^2-4*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^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)*tan(1/2*f*x+1/2*e)^2*d-8*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*d^2-2*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^2+2*c*d+d^2)/c^2*tan(1/2*f*x+1/2*e)^2*d^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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)-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^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*d-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)^2/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)*d^2-4*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-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)*d+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))","B"
442,1,2425,196,0.363000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x)","\text{Expression too large to display}"," ",0,"-2*a^2/f/(c^4+2*c^3*d-2*c*d^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))*d-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)^3*c^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4-8*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^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)^3*c^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^5+8*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4*d^3+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)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^5*d^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)^3*c^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)+7/3*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*c^2*d+8*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)*d^3+22*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^2*d^3-24*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2*d/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+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)^3/c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4*d^4+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)^3/c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4*d^5-6*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^5*d+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)^3/c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^5*d^4+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)^3*c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4*d-18*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^4*d^2+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)^3/c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)*d^4+14*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)*d^2-18*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)*d-24*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^2*d^2+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)^3/c/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^2*d^4+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)^3/c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^2*d^5+14*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c*d^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+40/3*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c*d^4/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+8*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2*d^5/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+8/3*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^3*d^6/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+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)^3*c^2/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^2*d-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)^3*d^3/(c^4+2*c^3*d-2*c*d^3-d^4)*tan(1/2*f*x+1/2*e)^3+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)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*c*d^2+3*a^2/f/(c^4+2*c^3*d-2*c*d^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))*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)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*c^3+2/3*a^2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^4+2*c^3*d-2*c*d^3-d^4)*d^3","B"
443,1,6466,271,0.413000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
444,1,481,203,0.398000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x)","\frac{-\frac{a^{3} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 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{3 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}+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} 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)-3 a^{3} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+9 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 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}-3 a^{3} c^{3} \cos \left(f x +e \right)+9 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} c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 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)+a^{3} c^{3} \left(f x +e \right)-3 a^{3} c^{2} d \cos \left(f x +e \right)+3 a^{3} 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^{3} d^{3} \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*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*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)-3/5*a^3*c*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+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*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^3*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+9*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*a^3*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-3*a^3*c^3*cos(f*x+e)+9*a^3*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^3*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*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)+a^3*c^3*(f*x+e)-3*a^3*c^2*d*cos(f*x+e)+3*a^3*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^3*d^3*(2+sin(f*x+e)^2)*cos(f*x+e))","B"
445,1,319,154,0.317000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x)","\frac{-\frac{c^{2} a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 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{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 c^{2} 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)-2 a^{3} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 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)-3 c^{2} a^{3} \cos \left(f x +e \right)+6 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)-a^{3} d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+c^{2} a^{3} \left(f x +e \right)-2 a^{3} c d \cos \left(f x +e \right)+a^{3} 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)}{f}"," ",0,"1/f*(-1/3*c^2*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)+2*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)-1/5*a^3*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+3*c^2*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a^3*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*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)-3*c^2*a^3*cos(f*x+e)+6*a^3*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+c^2*a^3*(f*x+e)-2*a^3*c*d*cos(f*x+e)+a^3*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","B"
446,1,178,102,0.251000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e)),x)","\frac{-\frac{a^{3} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+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} 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} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-3 a^{3} c \cos \left(f x +e \right)+3 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)+a^{3} c \left(f x +e \right)-a^{3} d \cos \left(f x +e \right)}{f}"," ",0,"1/f*(-1/3*a^3*c*(2+sin(f*x+e)^2)*cos(f*x+e)+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*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^3*d*(2+sin(f*x+e)^2)*cos(f*x+e)-3*a^3*c*cos(f*x+e)+3*a^3*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^3*c*(f*x+e)-a^3*d*cos(f*x+e))","A"
447,1,74,57,0.184000," ","int((a+a*sin(f*x+e))^3,x)","\frac{-\frac{a^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 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)-3 a^{3} \cos \left(f x +e \right)+\left(f x +e \right) a^{3}}{f}"," ",0,"1/f*(-1/3*a^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^3*cos(f*x+e)+(f*x+e)*a^3)","A"
448,1,480,132,0.258000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x)","-\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) 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) 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) 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)}{f \sqrt{c^{2}-d^{2}}}+\frac{a^{3} \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^{3} \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{6 a^{3} \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^{3} \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^{3} c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 a^{3}}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f \,d^{3}}-\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2}}+\frac{7 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d}"," ",0,"-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))*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))*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))*c+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))+1/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3+2/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c-6/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2-1/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+2/f*a^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)^2*c-6/f*a^3/d/(1+tan(1/2*f*x+1/2*e)^2)^2+2/f*a^3/d^3*arctan(tan(1/2*f*x+1/2*e))*c^2-6/f*a^3/d^2*arctan(tan(1/2*f*x+1/2*e))*c+7/f*a^3/d*arctan(tan(1/2*f*x+1/2*e))","B"
449,1,600,156,0.314000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x)","-\frac{2 a^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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^{3} 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{4 a^{3} 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}}{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{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) 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) 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) 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)}{f \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 a^{3}}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{4 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{3}}+\frac{6 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}"," ",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)+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)-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)-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+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-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)+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))*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))*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))*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))-2*a^3/f/d^2/(1+tan(1/2*f*x+1/2*e)^2)-4*a^3/f/d^3*arctan(tan(1/2*f*x+1/2*e))*c+6*a^3/f/d^2*arctan(tan(1/2*f*x+1/2*e))","B"
450,1,1400,178,0.340000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x)","\frac{a^{3} c^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{5 a^{3} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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^{3} d \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{2 a^{3} d^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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^{3} c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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^{3} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{a^{3} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{7 a^{3} d \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{10 a^{3} d^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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^{3} d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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{7 a^{3} c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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{11 a^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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{16 a^{3} d \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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{2 a^{3} d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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{2 a^{3} 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^{3} 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{5 a^{3} 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^{3} 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^{2}+2 c d +d^{2}\right)}-\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) c^{3}}{f \,d^{3} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\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) c^{2}}{f \,d^{2} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{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}{f d \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{7 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)}{f \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{2 a^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{3}}"," ",0,"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+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)^3-4*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)^3-2*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+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+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^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+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)^2-10*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)^2-2*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+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)+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)-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)-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)+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+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^2-5*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-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)-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))*c^3-4*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))*c^2-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))*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))+2*a^3/f/d^3*arctan(tan(1/2*f*x+1/2*e))","B"
451,1,1924,196,0.378000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x)","-\frac{18 a^{3} d^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{2 a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} c \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{3 a^{3} c \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{18 a^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} c \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{4 a^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} c^{2} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{44 a^{3} c d \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{100 a^{3} d^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} c \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{12 a^{3} d^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} c^{2} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{8 a^{3} d^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} c^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{12 a^{3} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{18 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} c \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{4 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} c^{2} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{38 a^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{2 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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)^{3} c \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{6 a^{3} c \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{22 a^{3} c^{2}}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{2 a^{3} d^{2}}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{3 a^{3} 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{6 a^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{30 a^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{60 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{12 a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{3 a^{3} c^{2} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{6 a^{3} c^{2} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{16 a^{3} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}-\frac{3 a^{3} c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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)^{3} \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right)}+\frac{5 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)}{f \left(c^{3}+3 c^{2} d +3 c \,d^{2}+d^{3}\right) \sqrt{c^{2}-d^{2}}}"," ",0,"-30*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^4*d^2-18*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^3-60*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^2*d^2-12*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)*d^2+3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^5-6*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^4-16*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^2-3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)-3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*c*d-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)^3/c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^5*d^3+3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^4*d-18*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^4*d^3-4*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^4*d^4-44*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c*d/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^3-100/3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c*d^3/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^3-12*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2*d^4/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^3-8/3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^3*d^5/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^3-12*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^2*d-18*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^2*d^3-4*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^2*d^4-38*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)*d-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)^3/c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)*d^3-6*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^5*d-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)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*tan(1/2*f*x+1/2*e)^5*d^2+5*a^3/f/(c^3+3*c^2*d+3*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))-22/3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*c^2-2/3*a^3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^3+3*c^2*d+3*c*d^2+d^3)*d^2","B"
452,1,5149,274,0.418000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
453,1,673,181,0.233000," ","int((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e)),x)","\frac{4 \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,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) d^{4}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2} d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{4}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{24 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2} d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{16 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{4}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c \,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) d^{4}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 c^{2} d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 c \,d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{10 d^{4}}{3 a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{3}}{a f}-\frac{12 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2} d^{2}}{a f}+\frac{12 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{3}}{a f}-\frac{3 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{4}}{a f}-\frac{2 c^{4}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 c^{3} d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{12 c^{2} d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 c \,d^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 d^{4}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"4/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*c*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*d^4-12/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c^2*d^2+8/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c*d^3-2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*d^4-24/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c^2*d^2+16/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c*d^3-8/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*d^4-4/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*c*d^3+1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*d^4-12/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*c^2*d^2+8/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*c*d^3-10/3/a/f/(1+tan(1/2*f*x+1/2*e)^2)^3*d^4+8/a/f*d*arctan(tan(1/2*f*x+1/2*e))*c^3-12/a/f*arctan(tan(1/2*f*x+1/2*e))*c^2*d^2+12/a/f*arctan(tan(1/2*f*x+1/2*e))*c*d^3-3/a/f*arctan(tan(1/2*f*x+1/2*e))*d^4-2/a/f/(tan(1/2*f*x+1/2*e)+1)*c^4+8/a/f/(tan(1/2*f*x+1/2*e)+1)*c^3*d-12/a/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d^2+8/a/f/(tan(1/2*f*x+1/2*e)+1)*c*d^3-2/a/f/(tan(1/2*f*x+1/2*e)+1)*d^4","B"
454,1,364,117,0.263000," ","int((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x)","\frac{\left(\tan^{3}\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)^{2}}-\frac{6 \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)^{2}}+\frac{2 \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)^{2}}-\frac{\tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 c \,d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 d^{3}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a f}-\frac{6 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c \,d^{2}}{a f}+\frac{3 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{3}}{a f}-\frac{2 c^{3}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 c^{2} d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 c \,d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 d^{3}}{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*tan(1/2*f*x+1/2*e)^3*d^3-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c*d^2+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*d^3-1/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)*d^3-6/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*c*d^2+2/a/f/(1+tan(1/2*f*x+1/2*e)^2)^2*d^3+6/a/f*d*arctan(tan(1/2*f*x+1/2*e))*c^2-6/a/f*arctan(tan(1/2*f*x+1/2*e))*c*d^2+3/a/f*arctan(tan(1/2*f*x+1/2*e))*d^3-2/a/f/(tan(1/2*f*x+1/2*e)+1)*c^3+6/a/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d-6/a/f/(tan(1/2*f*x+1/2*e)+1)*c*d^2+2/a/f/(tan(1/2*f*x+1/2*e)+1)*d^3","B"
455,1,140,62,0.245000," ","int((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x)","-\frac{2 d^{2}}{a f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{4 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a f}-\frac{2 \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{a f}-\frac{2 c^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{2 d^{2}}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/a/f*d^2/(1+tan(1/2*f*x+1/2*e)^2)+4/a/f*d*arctan(tan(1/2*f*x+1/2*e))*c-2/a/f*arctan(tan(1/2*f*x+1/2*e))*d^2-2/a/f/(tan(1/2*f*x+1/2*e)+1)*c^2+4/a/f/(tan(1/2*f*x+1/2*e)+1)*c*d-2/a/f/(tan(1/2*f*x+1/2*e)+1)*d^2","B"
456,1,65,35,0.154000," ","int((c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x)","\frac{2 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f}-\frac{2 c}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 d}{a f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"2/a/f*d*arctan(tan(1/2*f*x+1/2*e))-2/a/f/(tan(1/2*f*x+1/2*e)+1)*c+2/a/f/(tan(1/2*f*x+1/2*e)+1)*d","A"
457,1,22,23,0.115000," ","int(1/(a+a*sin(f*x+e)),x)","-\frac{2}{f a \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/f/a/(tan(1/2*f*x+1/2*e)+1)","A"
458,1,87,84,0.291000," ","int(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x)","-\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)}{a f \left(c -d \right) \sqrt{c^{2}-d^{2}}}-\frac{2}{a f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-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))-2/a/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)","A"
459,1,273,145,0.336000," ","int(1/(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 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}}{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 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) c}{a f \left(c -d \right)^{2} \left(c +d \right) \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)}{a f \left(c -d \right)^{2} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2}{a f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-2/a/f*d^3/(c-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*tan(1/2*f*x+1/2*e)-2/a/f*d^2/(c-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)-4/a/f*d/(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))*c-2/a/f*d^2/(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))-2/a/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)","A"
460,1,1224,204,0.332000," ","int(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","-\frac{7 d^{3} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} c \left(c^{2}+2 c d +d^{2}\right)}-\frac{6 d^{2} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{3} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{11 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 d^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} c \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{6} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a f \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)^{2} c^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{17 d^{3} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{6 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right) c}-\frac{6 d^{2} c^{2}}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{3} c}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{d^{4}}{a f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{6 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) c^{2}}{a f \left(c -d \right)^{3} \left(c^{2}+2 c d +d^{2}\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) c}{a f \left(c -d \right)^{3} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{3 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 \left(c -d \right)^{3} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{2}{a f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-7/a/f*d^3/(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*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3-2/a/f*d^4/(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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3+2/a/f*d^5/(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/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^3-6/a/f*d^2/(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*c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2-2/a/f*d^3/(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*c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2-11/a/f*d^4/(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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2-4/a/f*d^5/(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/c/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2+2/a/f*d^6/(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/c^2/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2-17/a/f*d^3/(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/(c^2+2*c*d+d^2)*c*tan(1/2*f*x+1/2*e)-6/a/f*d^4/(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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)+2/a/f*d^5/(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/(c^2+2*c*d+d^2)/c*tan(1/2*f*x+1/2*e)-6/a/f*d^2/(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/(c^2+2*c*d+d^2)*c^2-2/a/f*d^3/(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/(c^2+2*c*d+d^2)*c+1/a/f*d^4/(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/(c^2+2*c*d+d^2)-6/a/f*d/(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))*c^2-6/a/f*d^2/(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))*c-3/a/f*d^3/(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))-2/a/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)","B"
461,1,982,248,0.318000," ","int((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x)","-\frac{40 d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{40 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{5 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{5 d^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{20 d^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{20 d^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 c^{5}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 d^{5}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{10 d^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{2 c^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{8 d^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 c^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 d^{5}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{22 d^{5}}{3 a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{16 d^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{2 d^{5} \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)^{3}}-\frac{20 d^{3} c^{2}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 d^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{20 d^{4} c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 d^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{20 c^{4} d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{40 c^{3} d^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{40 c^{2} d^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{20 c \,d^{4}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{35 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f}+\frac{30 c \,d^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{10 c^{4} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{20 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{3}}{a^{2} f}-\frac{40 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{2} f}+\frac{20 c^{3} d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{40 c^{2} d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{20 c^{3} d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{20 c^{2} d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{10 c \,d^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^5+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*d^5-22/3/a^2/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3-10/a^2/f*d^5*arctan(tan(1/2*f*x+1/2*e))-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^5-8/a^2/f/(tan(1/2*f*x+1/2*e)+1)*d^5+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^5-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*d^5+20/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^4*d-40/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^3*d^2+40/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2*d^3-20/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d^4+35/a^2/f*d^4*arctan(tan(1/2*f*x+1/2*e))*c+30/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c*d^4-10/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^4*d+20/a^2/f*d^2*arctan(tan(1/2*f*x+1/2*e))*c^3-40/a^2/f*d^3*arctan(tan(1/2*f*x+1/2*e))*c^2+20/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*c-6/a^2/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4-16/a^2/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2+2/a^2/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)-20/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*c^2+20/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^3*d^2-40/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d^3+20/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^3*d^2-20/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d^3+10/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^4-2/a^2/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5-40/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c^2+40/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c-5/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*c+5/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*c-20/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c^2+20/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c","B"
462,1,618,185,0.303000," ","int((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x)","\frac{d^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{8 d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{d^{4} \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{8 d^{3} c}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 d^{4}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{12 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{2} f}-\frac{16 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f}+\frac{7 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{2 c^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{12 c^{2} d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{16 c \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 d^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 c^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 c^{3} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{12 c^{2} d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 c \,d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 d^{4}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c^{4}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c^{3} d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 c^{2} d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c \,d^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 d^{4}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"1/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-8/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c+4/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2-1/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)-8/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)^2*c+4/a^2/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2+12/a^2/f*d^2*arctan(tan(1/2*f*x+1/2*e))*c^2-16/a^2/f*d^3*arctan(tan(1/2*f*x+1/2*e))*c+7/a^2/f*d^4*arctan(tan(1/2*f*x+1/2*e))-2*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)+12/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d^2-16/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c*d^3+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)*d^4+2*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2-8/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^3*d+12/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d^2-8/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^3+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*d^4-4/3*c^4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3+16/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^3*d-8/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2*d^2+16/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d^3-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*d^4","B"
463,1,340,114,0.267000," ","int((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x)","-\frac{2 d^{3}}{a^{2} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{6 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{2} f}-\frac{4 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{2 c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4 d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 c^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{6 c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 d^{3}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 c^{2} d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 c \,d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 d^{3}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-2/a^2/f*d^3/(1+tan(1/2*f*x+1/2*e)^2)+6/a^2/f*d^2*arctan(tan(1/2*f*x+1/2*e))*c-4/a^2/f*d^3*arctan(tan(1/2*f*x+1/2*e))-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^3+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c*d^2-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)*d^3+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^3-6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d+6/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^2-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*d^3-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^3+4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2*d-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d^2+4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*d^3","B"
464,1,213,81,0.253000," ","int((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x)","\frac{2 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f}-\frac{2 c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 c^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c d}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 d^{2}}{a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 c^{2}}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 c d}{3 a^{2} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 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*d^2*arctan(tan(1/2*f*x+1/2*e))-2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*c^2+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)*d^2+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2-4/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d+2/a^2/f/(tan(1/2*f*x+1/2*e)+1)^2*d^2-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2+8/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d-4/3/a^2/f/(tan(1/2*f*x+1/2*e)+1)^3*d^2","B"
465,1,70,61,0.217000," ","int((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x)","\frac{-\frac{-2 c +2 d}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(2 c -2 d \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 c}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2}}"," ",0,"2/f/a^2*(-1/2*(-2*c+2*d)/(tan(1/2*f*x+1/2*e)+1)^2-1/3*(2*c-2*d)/(tan(1/2*f*x+1/2*e)+1)^3-c/(tan(1/2*f*x+1/2*e)+1))","A"
466,1,53,51,0.141000," ","int(1/(a+a*sin(f*x+e))^2,x)","\frac{\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{2}}"," ",0,"2/f/a^2*(1/(tan(1/2*f*x+1/2*e)+1)^2-2/3/(tan(1/2*f*x+1/2*e)+1)^3-1/(tan(1/2*f*x+1/2*e)+1))","A"
467,1,175,122,0.310000," ","int(1/(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^{2} f \left(c -d \right)^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 c}{a^{2} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 d}{a^{2} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4}{3 a^{2} f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"2/a^2/f*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))-2/a^2/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*c+4/a^2/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)*d-4/3/a^2/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)^3+2/a^2/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)^2","A"
468,1,361,210,0.319000," ","int(1/(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^{2} f \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}}{a^{2} f \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) c}{a^{2} f \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^{2} f \left(c -d \right)^{3} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{2 c}{a^{2} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 d}{a^{2} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4}{3 a^{2} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"2/a^2/f*d^4/(c-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)/c*tan(1/2*f*x+1/2*e)+2/a^2/f*d^3/(c-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)+6/a^2/f*d^2/(c-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))*c+4/a^2/f*d^3/(c-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))-2/a^2/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*c+6/a^2/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*d-4/3/a^2/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3+2/a^2/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2","A"
469,1,1313,281,0.353000," ","int(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x)","\frac{9 d^{4} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 d^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{6} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} c \left(c^{2}+2 c d +d^{2}\right)}+\frac{8 d^{3} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 d^{4} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{15 d^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{8 d^{6} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} c \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{7} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{2} f \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)^{2} c^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{23 d^{4} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{12 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{6} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right) c}+\frac{8 d^{3} c^{2}}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{4 d^{4} c}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{d^{5}}{a^{2} f \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)^{2} \left(c^{2}+2 c d +d^{2}\right)}+\frac{12 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) c^{2}}{a^{2} f \left(c -d \right)^{4} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{16 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) c}{a^{2} f \left(c -d \right)^{4} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}+\frac{7 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^{2} f \left(c -d \right)^{4} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{2 c}{a^{2} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 d}{a^{2} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{4}{3 a^{2} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{2}{a^{2} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}"," ",0,"9/a^2/f*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+4/a^2/f*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)^3-2/a^2/f*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+8/a^2/f*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)^2+4/a^2/f*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)^2+15/a^2/f*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+8/a^2/f*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)^2-2/a^2/f*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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2+23/a^2/f*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)+12/a^2/f*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^2/f*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)+8/a^2/f*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+4/a^2/f*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-1/a^2/f*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)+12/a^2/f*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))*c^2+16/a^2/f*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))*c+7/a^2/f*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))-2/a^2/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*c+8/a^2/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*d-4/3/a^2/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3+2/a^2/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2","B"
470,1,1340,340,0.286000," ","int((c+d*sin(f*x+e))^6/(a+a*sin(f*x+e))^3,x)","\frac{36 d^{5} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{60 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{72 d^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{6 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{6 d^{5} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{30 d^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{8 d^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c^{6}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 d^{6}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 c^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{4 d^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 c^{6}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{8 d^{6}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{23 d^{6} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 c^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{20 d^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c^{6}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{40 d^{6}}{3 a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{30 d^{4} c^{2}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{3 d^{6} \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)^{3}}-\frac{3 d^{6} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 d^{6} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{28 d^{6} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{36 d^{5} c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 c^{5} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{40 c^{3} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{60 c^{2} d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{36 c \,d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{24 c^{5} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{60 c^{2} d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{24 c \,d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{48 c^{5} d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{24 c^{4} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{32 c^{3} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{24 c^{2} d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{48 c \,d^{5}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{40 c^{4} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{80 c^{3} d^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 c \,d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{24 c^{5} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{60 c^{4} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{80 c^{3} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{90 c^{2} d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{72 c \,d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{40 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{3}}{a^{3} f}-\frac{90 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{3} f}+\frac{78 d^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f}+\frac{40 c^{3} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-60/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c^2+72/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c-6/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*c+6/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*c-30/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c^2+36/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*d^6-16/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^6+8/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*d^6+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^6+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*d^6-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^6-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*d^6-40/3/a^3/f*d^6/(1+tan(1/2*f*x+1/2*e)^2)^3-23/a^3/f*d^6*arctan(tan(1/2*f*x+1/2*e))-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^6-20/a^3/f/(tan(1/2*f*x+1/2*e)+1)*d^6+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^6-12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^5*d+40/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^3*d^3-60/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d^4+36/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^5+24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^5*d-30/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^3*c^2+3/a^3/f*d^6/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)-3/a^3/f*d^6/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5-12/a^3/f*d^6/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4-28/a^3/f*d^6/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2+60/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^2*d^4-24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c*d^5+48/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^5*d-24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^4*d^2+32/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^3*d^3-24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^2*d^4+48/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c*d^5-40/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^4*d^2+80/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^3*d^3-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d^5-24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^5*d+60/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^4*d^2-80/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^3*d^3-90/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d^4+72/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c*d^5+36/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^3*c+40/a^3/f*d^3*arctan(tan(1/2*f*x+1/2*e))*c^3-90/a^3/f*d^4*arctan(tan(1/2*f*x+1/2*e))*c^2+78/a^3/f*d^5*arctan(tan(1/2*f*x+1/2*e))*c+40/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^3*d^3","B"
471,1,924,266,0.292000," ","int((c+d*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x)","\frac{6 d^{5}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{d^{5} \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{6 d^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{d^{5} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{10 d^{4} c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c^{5}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{4 d^{5}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{4 d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 c^{5}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 d^{5}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{13 d^{5} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{12 d^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c^{5}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{10 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{40 c^{2} d^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{20 c^{4} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{40 c^{3} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{40 c^{2} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{20 c \,d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{8 c^{4} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16 c^{3} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{16 c^{2} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{8 c \,d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{10 c^{4} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{20 c^{2} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{20 c \,d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{20 c^{4} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{80 c^{3} d^{2}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{20 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{a^{3} f}-\frac{30 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f}+\frac{20 c^{2} d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{30 c \,d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"6/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*d^5-16/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^5-4/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*d^5+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^5-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*d^5-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^5+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*d^5+6/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^2+13/a^3/f*d^5*arctan(tan(1/2*f*x+1/2*e))-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^5+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)*d^5+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^5-10/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c+40/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2*d^3-20/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^4*d+40/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^3*d^2-40/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^2*d^3+20/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c*d^4+8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^4*d-16/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^3*d^2+16/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^2*d^3-1/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c*d^4-10/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^4*d+20/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d^3-20/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^4+20/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^4*d-80/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^3*d^2+6/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2+20/a^3/f*d^3*arctan(tan(1/2*f*x+1/2*e))*c^2-30/a^3/f*d^4*arctan(tan(1/2*f*x+1/2*e))*c+20/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^2*d^3-30/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c*d^4+1/a^3/f*d^5/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-10/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)^2*c","B"
472,1,593,187,0.288000," ","int((c+d*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x)","-\frac{2 d^{4}}{a^{3} f \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{8 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{a^{3} f}-\frac{6 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 c^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 c \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8 c^{3} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{8 c \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{4 d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 c^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{16 c^{3} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{24 c^{2} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{16 c \,d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{4 d^{4}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 c^{4}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{32 c^{3} d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{48 c^{2} d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{32 c \,d^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{8 d^{4}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16 c^{4}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c^{3} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{16 c^{2} d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{16 c \,d^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"-2/a^3/f*d^4/(1+tan(1/2*f*x+1/2*e)^2)+8/a^3/f*d^3*arctan(tan(1/2*f*x+1/2*e))*c-6/a^3/f*d^4*arctan(tan(1/2*f*x+1/2*e))-2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c^4+8/a^3/f/(tan(1/2*f*x+1/2*e)+1)*c*d^3-6/a^3/f/(tan(1/2*f*x+1/2*e)+1)*d^4+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^4-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^3*d+8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c*d^3-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*d^4+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^4-16/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^3*d+24/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^2*d^2-16/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c*d^3+4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*d^4-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^4+32/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^3*d-48/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^2*d^2+32/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c*d^3-8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*d^4-16/3/a^3/f*c^4/(tan(1/2*f*x+1/2*e)+1)^3+16/a^3/f*c^3/(tan(1/2*f*x+1/2*e)+1)^3*d-16/a^3/f*c^2/(tan(1/2*f*x+1/2*e)+1)^3*d^2+16/3/a^3/f*c/(tan(1/2*f*x+1/2*e)+1)^3*d^3","B"
473,1,438,136,0.252000," ","int((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x)","\frac{2 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f}-\frac{2 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{2 d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{4 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{2 d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 c^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{12 c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{12 c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{4 d^{3}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8 c^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{24 c^{2} d}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{24 c \,d^{2}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{8 d^{3}}{5 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16 c^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{12 c^{2} d}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 c \,d^{2}}{a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{4 d^{3}}{3 a^{3} f \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}"," ",0,"2/a^3/f*d^3*arctan(tan(1/2*f*x+1/2*e))-2*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)*d^3+4*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2-6/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*c^2*d+2/a^3/f/(tan(1/2*f*x+1/2*e)+1)^2*d^3+4*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4-12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c^2*d+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*c*d^2-4/a^3/f/(tan(1/2*f*x+1/2*e)+1)^4*d^3-8/5*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5+24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c^2*d-24/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*c*d^2+8/5/a^3/f/(tan(1/2*f*x+1/2*e)+1)^5*d^3-16/3*c^3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3+12/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c^2*d-8/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*c*d^2+4/3/a^3/f/(tan(1/2*f*x+1/2*e)+1)^3*d^3","B"
474,1,139,119,0.235000," ","int((c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x)","\frac{-\frac{-8 c^{2}+16 c d -8 d^{2}}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 \left(4 c^{2}-8 c d +4 d^{2}\right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(8 c^{2}-12 c d +4 d^{2}\right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 c^{2}}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}+\frac{4 c \left(c -d \right)}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}}{f \,a^{3}}"," ",0,"2/f/a^3*(-1/4*(-8*c^2+16*c*d-8*d^2)/(tan(1/2*f*x+1/2*e)+1)^4-1/5*(4*c^2-8*c*d+4*d^2)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(8*c^2-12*c*d+4*d^2)/(tan(1/2*f*x+1/2*e)+1)^3-c^2/(tan(1/2*f*x+1/2*e)+1)+2*c*(c-d)/(tan(1/2*f*x+1/2*e)+1)^2)","A"
475,1,114,96,0.194000," ","int((c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x)","\frac{-\frac{-4 c +2 d}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 \left(4 c -4 d \right)}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2 \left(8 c -6 d \right)}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{-8 c +8 d}{2 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 c}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}}{f \,a^{3}}"," ",0,"2/f/a^3*(-1/2*(-4*c+2*d)/(tan(1/2*f*x+1/2*e)+1)^2-1/5*(4*c-4*d)/(tan(1/2*f*x+1/2*e)+1)^5-1/3*(8*c-6*d)/(tan(1/2*f*x+1/2*e)+1)^3-1/4*(-8*c+8*d)/(tan(1/2*f*x+1/2*e)+1)^4-c/(tan(1/2*f*x+1/2*e)+1))","A"
476,1,85,77,0.158000," ","int(1/(a+a*sin(f*x+e))^3,x)","\frac{\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{8}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{16}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2}{\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1}+\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}}{f \,a^{3}}"," ",0,"2/f/a^3*(2/(tan(1/2*f*x+1/2*e)+1)^2-4/5/(tan(1/2*f*x+1/2*e)+1)^5-8/3/(tan(1/2*f*x+1/2*e)+1)^3-1/(tan(1/2*f*x+1/2*e)+1)+2/(tan(1/2*f*x+1/2*e)+1)^4)","A"
477,1,325,175,0.327000," ","int(1/(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^{3} f \left(c -d \right)^{3} \sqrt{c^{2}-d^{2}}}+\frac{4 c}{a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{6 d}{a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c}{3 a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{20 d}{3 a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{2 c^{2}}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{6 c d}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{6 d^{2}}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{8}{5 a^{3} f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} f \left(c -d \right) \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}"," ",0,"-2/a^3/f*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))+4/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*c-6/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^2*d-16/3/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*c+20/3/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^3*d-2/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*c^2+6/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*c*d-6/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)*d^2-8/5/a^3/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)^5+4/a^3/f/(c-d)/(tan(1/2*f*x+1/2*e)+1)^4","A"
478,1,511,285,0.352000," ","int(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x)","-\frac{2 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{3} f \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{2 d^{4}}{a^{3} f \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{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) c}{a^{3} f \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\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^{3} f \left(c -d \right)^{4} \left(c +d \right) \sqrt{c^{2}-d^{2}}}-\frac{16 c}{3 a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{8 d}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{8 d}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{4 c}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{2 c^{2}}{a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{8 c d}{a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{12 d^{2}}{a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{8}{5 a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} f \left(c -d \right)^{2} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}"," ",0,"-2/a^3/f*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)-2/a^3/f*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)-8/a^3/f*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))*c-6/a^3/f*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))-16/3/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*c+8/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^3*d-8/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*d+4/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^2*c-2/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*c^2+8/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*c*d-12/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)*d^2-8/5/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^5+4/a^3/f/(c-d)^2/(tan(1/2*f*x+1/2*e)+1)^4","A"
479,1,1462,363,0.370000," ","int(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x)","-\frac{6 d^{5} c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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 d^{7} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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{20 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) c^{2}}{a^{3} f \left(c -d \right)^{5} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{30 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) c}{a^{3} f \left(c -d \right)^{5} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{11 d^{5} c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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{10 d^{4} c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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 d^{7} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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{2 d^{7} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{3} f \left(c -d \right)^{5} \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 d^{8} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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^{2} \left(c^{2}+2 c d +d^{2}\right)}-\frac{29 d^{5} c \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{3} f \left(c -d \right)^{5} \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}{5 a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{4}{a^{3} f \left(c -d \right)^{3} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{2 c^{2}}{a^{3} f \left(c -d \right)^{5} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{20 d^{2}}{a^{3} f \left(c -d \right)^{5} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{10 c d}{a^{3} f \left(c -d \right)^{5} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}+\frac{d^{6}}{a^{3} f \left(c -d \right)^{5} \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{18 d^{6} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{a^{3} f \left(c -d \right)^{5} \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{10 d^{4} c^{2}}{a^{3} f \left(c -d \right)^{5} \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{6 d^{5} c}{a^{3} f \left(c -d \right)^{5} \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{6 d^{6} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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{19 d^{6} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{a^{3} f \left(c -d \right)^{5} \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 c}{a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{10 d}{a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}-\frac{16 c}{3 a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{28 d}{3 a^{3} f \left(c -d \right)^{4} \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{13 d^{5} \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^{3} f \left(c -d \right)^{5} \left(c^{2}+2 c d +d^{2}\right) \sqrt{c^{2}-d^{2}}}"," ",0,"-6/a^3/f*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)^2-12/a^3/f*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)^2+2/a^3/f*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/(c^2+2*c*d+d^2)*tan(1/2*f*x+1/2*e)^2-29/a^3/f*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^3/f*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)-20/a^3/f*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))*c^2-30/a^3/f*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))*c+2/a^3/f*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)^3-11/a^3/f*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)^3-10/a^3/f*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)^2-8/5/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^5+4/a^3/f/(c-d)^3/(tan(1/2*f*x+1/2*e)+1)^4-2/a^3/f/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*c^2-20/a^3/f/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*d^2+1/a^3/f*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)+10/a^3/f/(c-d)^5/(tan(1/2*f*x+1/2*e)+1)*c*d+4/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*c-10/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^2*d-16/3/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*c+28/3/a^3/f/(c-d)^4/(tan(1/2*f*x+1/2*e)+1)^3*d-18/a^3/f*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)-10/a^3/f*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^2-6/a^3/f*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-13/a^3/f*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))-6/a^3/f*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)^3-19/a^3/f*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"
480,1,115,67,0.096000," ","int((A+B*sin(x))/(1+sin(x))^4,x)","-\frac{2 \left(8 A -8 B \right)}{7 \left(\tan \left(\frac{x}{2}\right)+1\right)^{7}}-\frac{2 \left(36 A -32 B \right)}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)^{5}}-\frac{-6 A +2 B}{\left(\tan \left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 \left(18 A -10 B \right)}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{3}}-\frac{-32 A +24 B}{2 \left(\tan \left(\frac{x}{2}\right)+1\right)^{4}}-\frac{2 A}{\tan \left(\frac{x}{2}\right)+1}-\frac{-24 A +24 B}{3 \left(\tan \left(\frac{x}{2}\right)+1\right)^{6}}"," ",0,"-2/7*(8*A-8*B)/(tan(1/2*x)+1)^7-2/5*(36*A-32*B)/(tan(1/2*x)+1)^5-(-6*A+2*B)/(tan(1/2*x)+1)^2-2/3*(18*A-10*B)/(tan(1/2*x)+1)^3-1/2*(-32*A+24*B)/(tan(1/2*x)+1)^4-2*A/(tan(1/2*x)+1)-1/3*(-24*A+24*B)/(tan(1/2*x)+1)^6","A"
481,1,115,73,0.098000," ","int((A+B*sin(x))/(1-sin(x))^4,x)","-\frac{2 \left(18 A +10 B \right)}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)^{3}}-\frac{24 A +24 B}{3 \left(\tan \left(\frac{x}{2}\right)-1\right)^{6}}-\frac{2 \left(8 A +8 B \right)}{7 \left(\tan \left(\frac{x}{2}\right)-1\right)^{7}}-\frac{2 A}{\tan \left(\frac{x}{2}\right)-1}-\frac{2 \left(36 A +32 B \right)}{5 \left(\tan \left(\frac{x}{2}\right)-1\right)^{5}}-\frac{6 A +2 B}{\left(\tan \left(\frac{x}{2}\right)-1\right)^{2}}-\frac{32 A +24 B}{2 \left(\tan \left(\frac{x}{2}\right)-1\right)^{4}}"," ",0,"-2/3*(18*A+10*B)/(tan(1/2*x)-1)^3-1/3*(24*A+24*B)/(tan(1/2*x)-1)^6-2/7*(8*A+8*B)/(tan(1/2*x)-1)^7-2*A/(tan(1/2*x)-1)-2/5*(36*A+32*B)/(tan(1/2*x)-1)^5-(6*A+2*B)/(tan(1/2*x)-1)^2-1/2*(32*A+24*B)/(tan(1/2*x)-1)^4","A"
482,1,1315,332,1.720000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x)","\frac{2 a \left(77 c^{2} d^{3} \left(\sin^{2}\left(f x +e \right)\right)+90 c^{2} d^{3} \left(\sin^{3}\left(f x +e \right)\right)+98 c \,d^{4} \left(\sin^{3}\left(f x +e \right)\right)+60 c \,d^{4} \left(\sin^{4}\left(f x +e \right)\right)+45 c^{3} d^{2} \left(\sin^{2}\left(f x +e \right)\right)-35 c \,d^{4} \left(\sin^{2}\left(f x +e \right)\right)+15 d^{5} \left(\sin^{5}\left(f x +e \right)\right)-25 c \,d^{4}-77 c^{2} d^{3}-45 c^{3} d^{2}-15 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5}+63 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}-88 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}-21 d^{5} \left(\sin^{2}\left(f x +e \right)\right)-25 d^{5} \sin \left(f x +e \right)-90 c^{2} d^{3} \sin \left(f x +e \right)-98 c \,d^{4} \sin \left(f x +e \right)+10 d^{5} \left(\sin^{3}\left(f x +e \right)\right)+21 d^{5} \left(\sin^{4}\left(f x +e \right)\right)-161 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d -130 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}+120 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d +176 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}-32 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}-176 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}+98 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}+145 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}\right)}{105 d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/105*a*(-161*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d-25*c*d^4-77*c^2*d^3-45*c^3*d^2-15*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5+63*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5-88*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5+15*d^5*sin(f*x+e)^5+21*d^5*sin(f*x+e)^4+10*d^5*sin(f*x+e)^3-21*d^5*sin(f*x+e)^2-25*d^5*sin(f*x+e)+45*c^3*d^2*sin(f*x+e)^2+77*c^2*d^3*sin(f*x+e)^2-35*c*d^4*sin(f*x+e)^2-90*c^2*d^3*sin(f*x+e)-98*c*d^4*sin(f*x+e)+60*c*d^4*sin(f*x+e)^4+90*c^2*d^3*sin(f*x+e)^3+98*c*d^4*sin(f*x+e)^3-130*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2+120*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d+176*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2-32*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3-176*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4+98*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3+145*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
483,1,1034,277,1.459000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x)","\frac{2 a \left(18 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d +14 c^{2} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}-18 c \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-14 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-3 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}-20 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}+20 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}+9 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}+3 d^{4} \left(\sin^{4}\left(f x +e \right)\right)+9 c \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)+5 d^{4} \left(\sin^{3}\left(f x +e \right)\right)+6 c^{2} d^{2} \left(\sin^{2}\left(f x +e \right)\right)+5 c \,d^{3} \left(\sin^{2}\left(f x +e \right)\right)-3 d^{4} \left(\sin^{2}\left(f x +e \right)\right)-9 c \,d^{3} \sin \left(f x +e \right)-5 d^{4} \sin \left(f x +e \right)-6 c^{2} d^{2}-5 c \,d^{3}\right)}{15 d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/15*a*(18*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d+14*c^2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2-18*c*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3-14*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4-20*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-6*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2+20*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^3+9*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4+3*d^4*sin(f*x+e)^4+9*c*d^3*sin(f*x+e)^3+5*d^4*sin(f*x+e)^3+6*c^2*d^2*sin(f*x+e)^2+5*c*d^3*sin(f*x+e)^2-3*d^4*sin(f*x+e)^2-9*c*d^3*sin(f*x+e)-5*d^4*sin(f*x+e)-6*c^2*d^2-5*c*d^3)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
484,1,657,229,1.266000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x)","\frac{2 a \left(4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}-3 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d +\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}+3 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}+d^{3} \left(\sin^{3}\left(f x +e \right)\right)+c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)-d^{3} \sin \left(f x +e \right)-c \,d^{2}\right)}{3 d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/3*a*(4*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-4*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3-((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d+((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^2+3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3+d^3*sin(f*x+e)^3+c*d^2*sin(f*x+e)^2-d^3*sin(f*x+e)-c*d^2)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
485,1,203,196,1.307000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","-\frac{2 a \left(c -d \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \left(\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c +\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d -2 \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d \right)}{d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2*a*(c-d)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c+EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d-2*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
486,1,246,225,1.089000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","\frac{2 \left(\sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, c^{2}-\sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, d^{2}+d^{2} \left(\sin^{2}\left(f x +e \right)\right)-d^{2}\right) a}{d^{2} \left(c +d \right) \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2*((-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*c^2-(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*d^2+d^2*sin(f*x+e)^2-d^2)/d^2*a/(c+d)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
487,1,884,283,4.678000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(\frac{\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{d}+\frac{\left(-c +d \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a*(1/d*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(-c+d)/d*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
488,1,1046,360,6.395000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(\frac{\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{d}+\frac{\left(-c +d \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a*(1/d*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(-c+d)/d*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
489,1,1614,416,1.593000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x)","-\frac{2 a^{2} \left(-360 c \,d^{5} \left(\sin^{4}\left(f x +e \right)\right)-170 c^{2} d^{4} \left(\sin^{4}\left(f x +e \right)\right)-270 c^{3} d^{3} \left(\sin^{2}\left(f x +e \right)\right)+210 c \,d^{5} \left(\sin^{2}\left(f x +e \right)\right)-5 c^{4} d^{2} \left(\sin^{2}\left(f x +e \right)\right)-224 c^{2} d^{4} \left(\sin^{2}\left(f x +e \right)\right)-35 d^{6} \left(\sin^{6}\left(f x +e \right)\right)-80 c^{3} d^{3} \left(\sin^{3}\left(f x +e \right)\right)-376 c \,d^{5} \left(\sin^{3}\left(f x +e \right)\right)-77 d^{6} \left(\sin^{4}\left(f x +e \right)\right)-60 d^{6} \left(\sin^{3}\left(f x +e \right)\right)+112 d^{6} \left(\sin^{2}\left(f x +e \right)\right)+5 c^{4} d^{2}-540 c^{2} d^{4} \left(\sin^{3}\left(f x +e \right)\right)-426 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{4}+90 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d -130 c \,d^{5} \left(\sin^{5}\left(f x +e \right)\right)+270 c^{3} d^{3}+150 c \,d^{5}-10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{6}-336 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{6}+486 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{6}+80 c^{3} d^{3} \sin \left(f x +e \right)+540 c^{2} d^{4} \sin \left(f x +e \right)+506 c \,d^{5} \sin \left(f x +e \right)-90 d^{6} \left(\sin^{5}\left(f x +e \right)\right)+150 d^{6} \sin \left(f x +e \right)-870 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{5}+10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d -570 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{2}-1012 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{3}+84 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{4}+1002 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{5}+772 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{2}+780 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{3}+394 c^{2} d^{4}\right)}{315 d^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/315*a^2*(-426*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^4+5*c^4*d^2+90*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d-870*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^5+10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d-570*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^2-1012*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^3+84*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^4+1002*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^5+772*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^2+780*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^3+270*c^3*d^3+150*c*d^5-10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^6-336*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^6+486*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^6-130*c*d^5*sin(f*x+e)^5-170*c^2*d^4*sin(f*x+e)^4-360*c*d^5*sin(f*x+e)^4-80*c^3*d^3*sin(f*x+e)^3-540*c^2*d^4*sin(f*x+e)^3-376*c*d^5*sin(f*x+e)^3-5*c^4*d^2*sin(f*x+e)^2-270*c^3*d^3*sin(f*x+e)^2-224*c^2*d^4*sin(f*x+e)^2+210*c*d^5*sin(f*x+e)^2+80*c^3*d^3*sin(f*x+e)+540*c^2*d^4*sin(f*x+e)+506*c*d^5*sin(f*x+e)-90*d^6*sin(f*x+e)^5-77*d^6*sin(f*x+e)^4-60*d^6*sin(f*x+e)^3+112*d^6*sin(f*x+e)^2+150*d^6*sin(f*x+e)-35*d^6*sin(f*x+e)^6+394*c^2*d^4)/d^3/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
490,1,1316,340,1.626000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x)","-\frac{2 a^{2} \left(-28 c^{2} d^{3} \left(\sin^{2}\left(f x +e \right)\right)-9 c^{2} d^{3} \left(\sin^{3}\left(f x +e \right)\right)-42 c \,d^{4} \left(\sin^{3}\left(f x +e \right)\right)-13 c \,d^{4} \left(\sin^{4}\left(f x +e \right)\right)-c^{3} d^{2} \left(\sin^{2}\left(f x +e \right)\right)-7 c \,d^{4} \left(\sin^{2}\left(f x +e \right)\right)-5 d^{5} \left(\sin^{5}\left(f x +e \right)\right)+20 c \,d^{4}+28 c^{2} d^{3}+c^{3} d^{2}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5}-42 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}+62 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}+14 d^{5} \left(\sin^{2}\left(f x +e \right)\right)+20 d^{5} \sin \left(f x +e \right)+9 c^{2} d^{3} \sin \left(f x +e \right)+42 c \,d^{4} \sin \left(f x +e \right)-15 d^{5} \left(\sin^{3}\left(f x +e \right)\right)-14 d^{5} \left(\sin^{4}\left(f x +e \right)\right)+14 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d +76 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}+2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d -68 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}-64 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}+68 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}+28 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}-74 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}\right)}{35 d^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/35*a^2*(14*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d+20*c*d^4+28*c^2*d^3+c^3*d^2-2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5-42*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5+62*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5-5*d^5*sin(f*x+e)^5-14*d^5*sin(f*x+e)^4-15*d^5*sin(f*x+e)^3+14*d^5*sin(f*x+e)^2+20*d^5*sin(f*x+e)-c^3*d^2*sin(f*x+e)^2-28*c^2*d^3*sin(f*x+e)^2-7*c*d^4*sin(f*x+e)^2+9*c^2*d^3*sin(f*x+e)+42*c*d^4*sin(f*x+e)-13*c*d^4*sin(f*x+e)^4-9*c^2*d^3*sin(f*x+e)^3-42*c*d^4*sin(f*x+e)^3+76*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2+2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d-68*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2-64*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3+68*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4+28*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3-74*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4)/d^3/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
491,1,1035,285,1.447000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x)","-\frac{2 a^{2} \left(2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -34 c^{2} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}-2 c \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}+34 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}+10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d +26 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}-10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}-24 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-3 d^{4} \left(\sin^{4}\left(f x +e \right)\right)-4 c \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)-10 d^{4} \left(\sin^{3}\left(f x +e \right)\right)-c^{2} d^{2} \left(\sin^{2}\left(f x +e \right)\right)-10 c \,d^{3} \left(\sin^{2}\left(f x +e \right)\right)+3 d^{4} \left(\sin^{2}\left(f x +e \right)\right)+4 c \,d^{3} \sin \left(f x +e \right)+10 d^{4} \sin \left(f x +e \right)+c^{2} d^{2}+10 c \,d^{3}\right)}{15 d^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*a^2*(2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-34*c^2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2-2*c*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3+34*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4+10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d+26*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2-10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^3-24*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-3*d^4*sin(f*x+e)^4-4*c*d^3*sin(f*x+e)^3-10*d^4*sin(f*x+e)^3-c^2*d^2*sin(f*x+e)^2-10*c*d^3*sin(f*x+e)^2+3*d^4*sin(f*x+e)^2+4*c*d^3*sin(f*x+e)+10*d^4*sin(f*x+e)+c^2*d^2+10*c*d^3)/d^3/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
492,1,758,239,1.465000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x)","-\frac{2 a^{2} \left(2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -12 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2} c +10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}+6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d +2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}-6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-d^{3} \left(\sin^{3}\left(f x +e \right)\right)-c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)+d^{3} \sin \left(f x +e \right)+c \,d^{2}\right)}{3 d^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*a^2*(2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-12*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2*c+10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3-2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3+6*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d+2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^2-6*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3-d^3*sin(f*x+e)^3-c*d^2*sin(f*x+e)^2+d^3*sin(f*x+e)+c*d^2)/d^3/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
493,1,463,245,1.398000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x)","-\frac{2 \left(2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d +2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}+c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)-d^{3} \left(\sin^{2}\left(f x +e \right)\right)-c \,d^{2}+d^{3}\right) a^{2}}{d^{3} \left(c +d \right) \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2*(2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3-2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^2-2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d+2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3+c*d^2*sin(f*x+e)^2-d^3*sin(f*x+e)^2-c*d^2+d^3)/d^3*a^2/(c+d)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
494,1,1221,293,1.519000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x)","-\frac{2 a^{2} \left(\left(2 c \,d^{3}+6 d^{4}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, d \left(\EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}+3 \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -\EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}-3 \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-\EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d +\EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}\right) \sin \left(f x +e \right)+\left(c^{2} d^{2}+6 c \,d^{3}+d^{4}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}-2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}-6 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d +2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}+6 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}\right)}{3 \left(c +d \right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}} d^{3} \cos \left(f x +e \right) f}"," ",0,"-2/3*a^2*((2*c*d^3+6*d^4)*sin(f*x+e)*cos(f*x+e)^2-2*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*d*(EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3+3*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^2-3*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3-EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d+EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3)*sin(f*x+e)+(c^2*d^2+6*c*d^3+d^4)*cos(f*x+e)^2+2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^3-2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^4-6*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3*d+2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2+6*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^3)/(c+d)^2/(c+d*sin(f*x+e))^(3/2)/d^3/cos(f*x+e)/f","B"
495,1,1436,362,6.392000," ","int((a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2} \left(\frac{\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{d^{2}}+\frac{2 \left(-c +d \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}+\frac{\left(c^{2}-2 c d +d^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a^2*(1/d^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(-c+d)/d^2*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(c^2-2*c*d+d^2)/d^2*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
496,1,1926,501,1.705000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x)","\frac{2 a^{3} \left(c^{4} d^{3} \sin \left(f x +e \right)-528 c^{3} d^{4} \sin \left(f x +e \right)-2216 c^{2} d^{5} \sin \left(f x +e \right)-2046 c \,d^{6} \sin \left(f x +e \right)+4 c^{5} d^{2}-1096 c^{3} d^{4}-33 c^{4} d^{3}+528 c^{3} d^{4} \left(\sin^{3}\left(f x +e \right)\right)+1188 c \,d^{6} \left(\sin^{3}\left(f x +e \right)\right)-c^{4} d^{3} \left(\sin^{3}\left(f x +e \right)\right)+1942 c^{2} d^{5} \left(\sin^{3}\left(f x +e \right)\right)+858 c \,d^{6} \left(\sin^{5}\left(f x +e \right)\right)-630 c \,d^{6}-1584 c^{2} d^{5}+33 c^{4} d^{3} \left(\sin^{2}\left(f x +e \right)\right)-868 c \,d^{6} \left(\sin^{2}\left(f x +e \right)\right)+462 c^{2} d^{5} \left(\sin^{2}\left(f x +e \right)\right)-4 c^{5} d^{2} \left(\sin^{2}\left(f x +e \right)\right)+980 c^{3} d^{4} \left(\sin^{2}\left(f x +e \right)\right)-630 d^{7} \sin \left(f x +e \right)+1122 c^{2} d^{5} \left(\sin^{4}\left(f x +e \right)\right)+116 c^{3} d^{4} \left(\sin^{4}\left(f x +e \right)\right)+1274 c \,d^{6} \left(\sin^{4}\left(f x +e \right)\right)+274 c^{2} d^{5} \left(\sin^{5}\left(f x +e \right)\right)+1386 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{7}-2016 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{7}-8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{7}+224 c \,d^{6} \left(\sin^{6}\left(f x +e \right)\right)+63 d^{7} \left(\sin^{7}\left(f x +e \right)\right)+231 d^{7} \left(\sin^{6}\left(f x +e \right)\right)+315 d^{7} \left(\sin^{5}\left(f x +e \right)\right)+231 d^{7} \left(\sin^{4}\left(f x +e \right)\right)+252 d^{7} \left(\sin^{3}\left(f x +e \right)\right)-462 d^{7} \left(\sin^{2}\left(f x +e \right)\right)-72 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d^{2}-340 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d^{2}-2970 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{3}-3264 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{4}+1518 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{5}+3612 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{6}+2128 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{3}+4176 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{4}-120 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{5}-4104 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{6}+66 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{6} d +8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{6} d \right)}{693 d^{4} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/693*a^3*(2128*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^3+116*c^3*d^4*sin(f*x+e)^4+1122*c^2*d^5*sin(f*x+e)^4+1274*c*d^6*sin(f*x+e)^4-c^4*d^3*sin(f*x+e)^3+528*c^3*d^4*sin(f*x+e)^3+1942*c^2*d^5*sin(f*x+e)^3+1188*c*d^6*sin(f*x+e)^3-4*c^5*d^2*sin(f*x+e)^2+33*c^4*d^3*sin(f*x+e)^2+980*c^3*d^4*sin(f*x+e)^2+462*c^2*d^5*sin(f*x+e)^2-868*c*d^6*sin(f*x+e)^2+c^4*d^3*sin(f*x+e)-528*c^3*d^4*sin(f*x+e)-2216*c^2*d^5*sin(f*x+e)-2046*c*d^6*sin(f*x+e)+224*c*d^6*sin(f*x+e)^6+274*c^2*d^5*sin(f*x+e)^5+858*c*d^6*sin(f*x+e)^5+4*c^5*d^2-1096*c^3*d^4-33*c^4*d^3-630*c*d^6-1584*c^2*d^5+63*d^7*sin(f*x+e)^7+231*d^7*sin(f*x+e)^6+315*d^7*sin(f*x+e)^5+231*d^7*sin(f*x+e)^4+252*d^7*sin(f*x+e)^3-462*d^7*sin(f*x+e)^2-630*d^7*sin(f*x+e)+1386*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^7-2016*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^7-8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^7+4176*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^4-120*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^5-4104*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^6+66*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^6*d+8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^6*d-72*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d^2-340*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d^2-2970*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^3-3264*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^4+1518*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^5+3612*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^6)/d^4/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
497,1,1613,428,1.483000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x)","-\frac{2 a^{3} \left(-351 c \,d^{5} \left(\sin^{4}\left(f x +e \right)\right)-53 c^{2} d^{4} \left(\sin^{4}\left(f x +e \right)\right)-619 c \,d^{5} \left(\sin^{3}\left(f x +e \right)\right)-27 c^{3} d^{3} \left(\sin^{2}\left(f x +e \right)\right)+21 c \,d^{5} \left(\sin^{2}\left(f x +e \right)\right)+4 c^{4} d^{2} \left(\sin^{2}\left(f x +e \right)\right)-35 d^{6} \left(\sin^{6}\left(f x +e \right)\right)+c^{3} d^{3} \left(\sin^{3}\left(f x +e \right)\right)-413 c^{2} d^{4} \left(\sin^{2}\left(f x +e \right)\right)-203 d^{6} \left(\sin^{4}\left(f x +e \right)\right)-195 d^{6} \left(\sin^{3}\left(f x +e \right)\right)-4 c^{4} d^{2}-243 c^{2} d^{4} \left(\sin^{3}\left(f x +e \right)\right)-54 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d +27 c^{3} d^{3}+330 c \,d^{5}+8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{6}-714 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{6}-85 c \,d^{5} \left(\sin^{5}\left(f x +e \right)\right)-c^{3} d^{3} \sin \left(f x +e \right)+243 c^{2} d^{4} \sin \left(f x +e \right)+704 c \,d^{5} \sin \left(f x +e \right)-135 d^{6} \left(\sin^{5}\left(f x +e \right)\right)+330 d^{6} \sin \left(f x +e \right)+238 d^{6} \left(\sin^{2}\left(f x +e \right)\right)+60 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{2}-1048 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{3}+1044 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{6}+466 c^{2} d^{4}+492 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{4}-1158 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{5}-8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5} d -1104 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{4}+1056 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{5}+214 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d^{2}+1212 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{3}\right)}{315 d^{4} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/315*a^3*(492*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^4-4*c^4*d^2-54*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d-1158*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^5-8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5*d+60*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^2-1048*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^3-1104*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^4+1056*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^5+214*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d^2+1212*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^3+27*c^3*d^3+330*c*d^5+8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^6-714*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^6+1044*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^6-85*c*d^5*sin(f*x+e)^5-53*c^2*d^4*sin(f*x+e)^4-351*c*d^5*sin(f*x+e)^4+c^3*d^3*sin(f*x+e)^3-243*c^2*d^4*sin(f*x+e)^3-619*c*d^5*sin(f*x+e)^3+4*c^4*d^2*sin(f*x+e)^2-27*c^3*d^3*sin(f*x+e)^2-413*c^2*d^4*sin(f*x+e)^2+21*c*d^5*sin(f*x+e)^2-c^3*d^3*sin(f*x+e)+243*c^2*d^4*sin(f*x+e)+704*c*d^5*sin(f*x+e)-135*d^6*sin(f*x+e)^5-203*d^6*sin(f*x+e)^4-195*d^6*sin(f*x+e)^3+238*d^6*sin(f*x+e)^2+330*d^6*sin(f*x+e)-35*d^6*sin(f*x+e)^6+466*c^2*d^4)/d^4/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
498,1,1316,360,1.378000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x)","\frac{2 a^{3} \left(21 c^{2} d^{3} \left(\sin^{2}\left(f x +e \right)\right)-c^{2} d^{3} \left(\sin^{3}\left(f x +e \right)\right)+84 c \,d^{4} \left(\sin^{3}\left(f x +e \right)\right)+18 c \,d^{4} \left(\sin^{4}\left(f x +e \right)\right)-4 c^{3} d^{2} \left(\sin^{2}\left(f x +e \right)\right)+112 c \,d^{4} \left(\sin^{2}\left(f x +e \right)\right)+15 d^{5} \left(\sin^{5}\left(f x +e \right)\right)-130 c \,d^{4}-21 c^{2} d^{3}+4 c^{3} d^{2}-8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{5}+294 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}-424 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{5}-63 d^{5} \left(\sin^{2}\left(f x +e \right)\right)-130 d^{5} \sin \left(f x +e \right)+c^{2} d^{3} \sin \left(f x +e \right)-84 c \,d^{4} \sin \left(f x +e \right)+115 d^{5} \left(\sin^{3}\left(f x +e \right)\right)+63 d^{5} \left(\sin^{4}\left(f x +e \right)\right)+42 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d -116 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}+8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4} d -48 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d^{2}+416 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}+48 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}-336 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{3}+124 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{4}\right)}{105 d^{4} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/105*a^3*(42*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d-130*c*d^4-21*c^2*d^3+4*c^3*d^2-8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^5+294*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5-424*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^5+15*d^5*sin(f*x+e)^5+63*d^5*sin(f*x+e)^4+115*d^5*sin(f*x+e)^3-63*d^5*sin(f*x+e)^2-130*d^5*sin(f*x+e)-4*c^3*d^2*sin(f*x+e)^2+21*c^2*d^3*sin(f*x+e)^2+112*c*d^4*sin(f*x+e)^2+c^2*d^3*sin(f*x+e)-84*c*d^4*sin(f*x+e)+18*c*d^4*sin(f*x+e)^4-c^2*d^3*sin(f*x+e)^3+84*c*d^4*sin(f*x+e)^3-116*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2+8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4*d-48*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d^2+416*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3+48*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4-336*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^3+124*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^4)/d^4/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
499,1,1035,304,1.569000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x)","\frac{2 a^{3} \left(8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -36 c^{2} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}+112 c \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-84 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}+30 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -46 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}-30 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}+54 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}+3 d^{4} \left(\sin^{4}\left(f x +e \right)\right)-c \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)+15 d^{4} \left(\sin^{3}\left(f x +e \right)\right)-4 c^{2} d^{2} \left(\sin^{2}\left(f x +e \right)\right)+15 c \,d^{3} \left(\sin^{2}\left(f x +e \right)\right)-3 d^{4} \left(\sin^{2}\left(f x +e \right)\right)+c \,d^{3} \sin \left(f x +e \right)-15 d^{4} \sin \left(f x +e \right)+4 c^{2} d^{2}-15 c \,d^{3}\right)}{15 d^{4} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/15*a^3*(8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-36*c^2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2+112*c*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3-84*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4+30*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-46*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2-30*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^3+54*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4+3*d^4*sin(f*x+e)^4-c*d^3*sin(f*x+e)^3+15*d^4*sin(f*x+e)^3-4*c^2*d^2*sin(f*x+e)^2+15*c*d^3*sin(f*x+e)^2-3*d^4*sin(f*x+e)^2+c*d^3*sin(f*x+e)-15*d^4*sin(f*x+e)+4*c^2*d^2-15*c*d^3)/d^4/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
500,1,1031,318,1.406000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x)","-\frac{2 \left(8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -16 c^{2} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}-8 c \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}+16 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}+10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d +14 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}-10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}-6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-c \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)-d^{4} \left(\sin^{3}\left(f x +e \right)\right)-4 c^{2} d^{2} \left(\sin^{2}\left(f x +e \right)\right)+5 c \,d^{3} \left(\sin^{2}\left(f x +e \right)\right)-3 d^{4} \left(\sin^{2}\left(f x +e \right)\right)+c \,d^{3} \sin \left(f x +e \right)+d^{4} \sin \left(f x +e \right)+4 c^{2} d^{2}-5 c \,d^{3}+3 d^{4}\right) a^{3}}{3 d^{4} \left(c +d \right) \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*(8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-16*c^2*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2-8*c*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^3+16*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-8*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^4+10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^3*d+14*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2-10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*c*d^3-6*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^4-c*d^3*sin(f*x+e)^3-d^4*sin(f*x+e)^3-4*c^2*d^2*sin(f*x+e)^2+5*c*d^3*sin(f*x+e)^2-3*d^4*sin(f*x+e)^2+c*d^3*sin(f*x+e)+d^4*sin(f*x+e)+4*c^2*d^2-5*c*d^3+3*d^4)*a^3/d^4/(c+d)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
501,1,1257,326,5.408000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{3} \left(-\frac{2 \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \left(\EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2}-\EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}+2 \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2}-6 \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c d +4 \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}\right)}{d^{4} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +c \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{3 \left(c^{2}-2 c d +d^{2}\right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\left(-c^{3}+3 c^{2} d -3 c \,d^{2}+d^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a^3*(-2/d^4/(cos(f*x+e)^2*sin(f*x+e)*d+c*cos(f*x+e)^2)^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2-EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^2+2*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2-6*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d+4*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^2)+3/d^3*(c^2-2*c*d+d^2)*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/d^3*(-c^3+3*c^2*d-3*c*d^2+d^3)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
502,1,1589,378,6.597000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{3} \left(\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{3 \left(-c +d \right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 \left(c^{2}-2 c d +d^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\left(-c^{3}+3 c^{2} d -3 c \,d^{2}+d^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a^3*(2/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+3*(-c+d)/d^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3/d^3*(c^2-2*c*d+d^2)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/d^3*(-c^3+3*c^2*d-3*c*d^2+d^3)*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
503,1,2079,457,9.864000," ","int((a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{3} \left(\frac{\left(-c^{3}+3 c^{2} d -3 c \,d^{2}+d^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 \left(c^{2}-d^{2}\right) d^{3} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{4}}+\frac{24 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 \left(c^{2}-d^{2}\right)^{2} d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{2 \left(71 c^{2}+25 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{105 d \left(c^{2}-d^{2}\right)^{3} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{32 d \left(\cos^{2}\left(f x +e \right)\right) c \left(11 c^{2}+13 d^{2}\right)}{105 \left(c^{2}-d^{2}\right)^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(105 c^{4}+254 c^{2} d^{2}+25 d^{4}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(105 c^{8}-420 d^{2} c^{6}+630 d^{4} c^{4}-420 c^{2} d^{6}+105 d^{8}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{32 c d \left(11 c^{2}+13 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 \left(c^{2}-d^{2}\right)^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{d^{3}}+\frac{3 \left(-c +d \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 \left(c^{2}-2 c d +d^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*a^3*((-c^3+3*c^2*d-3*c*d^2+d^3)/d^3*(2/7/(c^2-d^2)/d^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^4+24/35/(c^2-d^2)^2/d^2*c*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+2/105*(71*c^2+25*d^2)/d/(c^2-d^2)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+32/105*d*cos(f*x+e)^2/(c^2-d^2)^4*c*(11*c^2+13*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(105*c^4+254*c^2*d^2+25*d^4)/(105*c^8-420*c^6*d^2+630*c^4*d^4-420*c^2*d^6+105*d^8)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+32/105*c*d*(11*c^2+13*d^2)/(c^2-d^2)^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/d^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*(-c+d)/d^3*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*(c^2-2*c*d+d^2)/d^3*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
504,1,1372,294,1.649000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +c \left(\cos^{2}\left(f x +e \right)\right)}\, \left(12 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d -4 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}-12 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}+4 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}+3 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{4}-20 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3} d +6 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d^{2}+20 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{3}-9 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{4}-2 d^{4} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3 c^{2} \left(\cos^{2}\left(f x +e \right)\right) d^{2}+4 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{3}-3 \left(\cos^{2}\left(f x +e \right)\right) d^{4}+3 c^{3} d \sin \left(f x +e \right)-9 c^{2} d^{2} \sin \left(f x +e \right)+9 c \,d^{3} \sin \left(f x +e \right)-3 d^{4} \sin \left(f x +e \right)-3 c^{3} d +9 c^{2} d^{2}-9 c \,d^{3}+3 d^{4}\right)}{3 d \sqrt{-\left(c +d \sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"1/3*(cos(f*x+e)^2*sin(f*x+e)*d+c*cos(f*x+e)^2)^(1/2)*(12*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3*d-4*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2-12*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^3+4*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^4+3*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^4-20*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3*d+6*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d^2+20*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^3-9*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^4-2*d^4*sin(f*x+e)*cos(f*x+e)^2-3*c^2*cos(f*x+e)^2*d^2+4*cos(f*x+e)^2*c*d^3-3*cos(f*x+e)^2*d^4+3*c^3*d*sin(f*x+e)-9*c^2*d^2*sin(f*x+e)+9*c*d^3*sin(f*x+e)-3*d^4*sin(f*x+e)-3*c^3*d+9*c^2*d^2-9*c*d^3+3*d^4)/d/(-(c+d*sin(f*x+e))*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/a/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
505,1,925,242,1.605000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +c \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -2 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}+\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}-3 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}+3 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-c \left(\cos^{2}\left(f x +e \right)\right) d^{2}+\left(\cos^{2}\left(f x +e \right)\right) d^{3}+c^{2} d \sin \left(f x +e \right)-2 c \,d^{2} \sin \left(f x +e \right)+d^{3} \sin \left(f x +e \right)-c^{2} d +2 c \,d^{2}-d^{3}\right)}{d \sqrt{-\left(c +d \sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(cos(f*x+e)^2*sin(f*x+e)*d+c*cos(f*x+e)^2)^(1/2)*(2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-2*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3+(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3-3*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^2+3*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3-c*cos(f*x+e)^2*d^2+cos(f*x+e)^2*d^3+c^2*d*sin(f*x+e)-2*c*d^2*sin(f*x+e)+d^3*sin(f*x+e)-c^2*d+2*c*d^2-d^3)/d/(-(c+d*sin(f*x+e))*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/a/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
506,1,382,226,1.586000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +c \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2}-\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}-\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c d \sin \left(f x +e \right)-d^{2} \sin \left(f x +e \right)-c d +d^{2}\right)}{d \sqrt{-\left(c +d \sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(cos(f*x+e)^2*sin(f*x+e)*d+c*cos(f*x+e)^2)^(1/2)*((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2-(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^2-cos(f*x+e)^2*d^2+c*d*sin(f*x+e)-d^2*sin(f*x+e)-c*d+d^2)/d/(-(c+d*sin(f*x+e))*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/a/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
507,1,443,237,3.467000," ","int(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
508,1,925,298,1.968000," ","int(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +c \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{3}+3 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d -\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c \,d^{2}-3 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticE \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-4 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) c^{2} d +4 \sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c +d}+\frac{d}{c +d}}\, \sqrt{-\frac{d \sin \left(f x +e \right)}{c -d}-\frac{d}{c -d}}\, \EllipticF \left(\sqrt{\frac{d \sin \left(f x +e \right)}{c -d}+\frac{c}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{3}-c \left(\cos^{2}\left(f x +e \right)\right) d^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+c^{2} d \sin \left(f x +e \right)-d^{3} \sin \left(f x +e \right)-c^{2} d +d^{3}\right)}{d \sqrt{-\left(c +d \sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(c^{2}-d^{2}\right) \left(c -d \right) a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(cos(f*x+e)^2*sin(f*x+e)*d+c*cos(f*x+e)^2)^(1/2)*((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^3+3*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d-(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c*d^2-3*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticE((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3-4*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*c^2*d+4*(d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2)*(-d/(c+d)*sin(f*x+e)+d/(c+d))^(1/2)*(-d/(c-d)*sin(f*x+e)-d/(c-d))^(1/2)*EllipticF((d/(c-d)*sin(f*x+e)+1/(c-d)*c)^(1/2),((c-d)/(c+d))^(1/2))*d^3-c*cos(f*x+e)^2*d^2-3*cos(f*x+e)^2*d^3+c^2*d*sin(f*x+e)-d^3*sin(f*x+e)-c^2*d+d^3)/d/(-(c+d*sin(f*x+e))*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(c^2-d^2)/(c-d)/a/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
509,1,1291,377,6.546000," ","int(1/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{d \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{2}}+\frac{-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{\left(c -d \right)^{2}}-\frac{d \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{c -d}\right)}{a \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a*(-d/(c-d)^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/(c-d)^2*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d/(c-d)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
510,1,1372,302,5.559000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 c \,d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 d^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+3 d \left(c^{2}-2 c d +d^{2}\right) \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}\right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(2*d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+6*c*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4*d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+3*d*(c^2-2*c*d+d^2)*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(c^3-3*c^2*d+3*c*d^2-d^3)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
511,1,1049,283,5.278000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+2 d \left(c -d \right) \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(c^{2}-2 c d +d^{2}\right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(2*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*d*(c-d)*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(c^2-2*c*d+d^2)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
512,1,906,279,5.179000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(d \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(c -d \right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(d*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(c-d)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
513,1,507,303,3.720000," ","int(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
514,1,1299,368,5.979000," ","int(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{d^{2} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{2}}-\frac{d \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{2}}+\frac{-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{c -d}\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(d^2/(c-d)^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d/(c-d)^2*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/(c-d)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
515,1,1758,443,8.658000," ","int(1/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{2} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{3}}-\frac{2 d \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{3}}+\frac{-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{\left(c -d \right)^{2}}+\frac{d^{2} \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{2}}\right)}{a^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^2*(2*d^2/(c-d)^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-2/(c-d)^3*d*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/(c-d)^2*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+d^2/(c-d)^2*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
516,1,1615,364,7.626000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\left(c^{3}-3 c^{2} d +3 c \,d^{2}-d^{3}\right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{3}}-\frac{2 \left(c -3 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c -d \right)^{2} \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(4 c^{2}-15 c d +27 d^{2}\right)}{30 \left(c -d \right)^{3} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 \left(-c \,d^{2}-15 d^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(60 c^{3}-180 c^{2} d +180 c \,d^{2}-60 d^{3}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(4 c^{2}-15 c d +27 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{30 \left(c -d \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+3 d^{2} \left(c -d \right) \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+3 d \left(c^{2}-2 c d +d^{2}\right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*(2*d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+(c^3-3*c^2*d+3*c*d^2-d^3)*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*d^2*(c-d)*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*d*(c^2-2*c*d+d^2)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
517,1,1462,365,7.637000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\left(c^{2}-2 c d +d^{2}\right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{3}}-\frac{2 \left(c -3 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c -d \right)^{2} \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(4 c^{2}-15 c d +27 d^{2}\right)}{30 \left(c -d \right)^{3} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 \left(-c \,d^{2}-15 d^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(60 c^{3}-180 c^{2} d +180 c \,d^{2}-60 d^{3}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(4 c^{2}-15 c d +27 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{30 \left(c -d \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+d^{2} \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+2 d \left(c -d \right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*((c^2-2*c*d+d^2)*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+d^2*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*d*(c-d)*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
518,1,1056,376,6.802000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\left(c -d \right) \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{3}}-\frac{2 \left(c -3 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c -d \right)^{2} \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(4 c^{2}-15 c d +27 d^{2}\right)}{30 \left(c -d \right)^{3} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 \left(-c \,d^{2}-15 d^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(60 c^{3}-180 c^{2} d +180 c \,d^{2}-60 d^{3}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(4 c^{2}-15 c d +27 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{30 \left(c -d \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+d \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{a^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*((c-d)*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+d*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
519,1,593,386,4.631000," ","int(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{3}}-\frac{2 \left(c -3 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c -d \right)^{2} \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(4 c^{2}-15 c d +27 d^{2}\right)}{30 \left(c -d \right)^{3} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 \left(-c \,d^{2}-15 d^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(60 c^{3}-180 c^{2} d +180 c \,d^{2}-60 d^{3}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(4 c^{2}-15 c d +27 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{30 \left(c -d \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{a^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
520,1,1851,461,8.769000," ","int(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{3}}-\frac{2 \left(c -3 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c -d \right)^{2} \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(4 c^{2}-15 c d +27 d^{2}\right)}{30 \left(c -d \right)^{3} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 \left(-c \,d^{2}-15 d^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(60 c^{3}-180 c^{2} d +180 c \,d^{2}-60 d^{3}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(4 c^{2}-15 c d +27 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{30 \left(c -d \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}}{c -d}-\frac{d^{3} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{3}}+\frac{d^{2} \left(-\frac{-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c}{\left(c -d \right) \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(2 c -2 d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c -d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{3}}-\frac{d \left(-\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c -d \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{\left(-\left(\sin^{2}\left(f x +e \right)\right) d -c \sin \left(f x +e \right)+d \sin \left(f x +e \right)+c \right) \left(c -3 d \right)}{3 \left(c -d \right)^{2} \sqrt{\left(-d \sin \left(f x +e \right)-c \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}}+\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{2}-6 c d +3 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{d \left(c -3 d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c -d \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(c -d \right)^{2}}\right)}{a^{3} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*(1/(c-d)*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d^3/(c-d)^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+d^2/(c-d)^3*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d/(c-d)^2*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
521,1,2311,552,11.455000," ","int(1/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/a^3*(1/(c-d)^2*(-1/5/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^3-2/15*(c-3*d)/(c-d)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/30*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^3*(4*c^2-15*c*d+27*d^2)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*(-c*d^2-15*d^3)/(60*c^3-180*c^2*d+180*c*d^2-60*d^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/30*d*(4*c^2-15*c*d+27*d^2)/(c-d)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d^3/(c-d)^3*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-3*d^3/(c-d)^4*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3/(c-d)^4*d^2*(-(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)-2*d/(2*c-2*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-d/(c-d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-2/(c-d)^3*d*(-1/3/(c-d)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(1+sin(f*x+e))^2-1/3*(-sin(f*x+e)^2*d-c*sin(f*x+e)+d*sin(f*x+e)+c)/(c-d)^2*(c-3*d)/((-d*sin(f*x+e)-c)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)+2*d^2/(3*c^2-6*c*d+3*d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-1/3*d*(c-3*d)/(c-d)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
522,1,141,145,0.920000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^3,x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a \left(\sin \left(f x +e \right)-1\right) \left(5 d^{3} \left(\sin^{3}\left(f x +e \right)\right)+21 c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)+6 d^{3} \left(\sin^{2}\left(f x +e \right)\right)+35 c^{2} d \sin \left(f x +e \right)+28 c \,d^{2} \sin \left(f x +e \right)+8 d^{3} \sin \left(f x +e \right)+35 c^{3}+70 c^{2} d +56 c \,d^{2}+16 d^{3}\right)}{35 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/35*(1+sin(f*x+e))*a*(sin(f*x+e)-1)*(5*d^3*sin(f*x+e)^3+21*c*d^2*sin(f*x+e)^2+6*d^3*sin(f*x+e)^2+35*c^2*d*sin(f*x+e)+28*c*d^2*sin(f*x+e)+8*d^3*sin(f*x+e)+35*c^3+70*c^2*d+56*c*d^2+16*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
523,1,92,100,0.806000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^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 d^{2} \left(\sin^{2}\left(f x +e \right)\right)+10 c d \sin \left(f x +e \right)+4 d^{2} \sin \left(f x +e \right)+15 c^{2}+20 c d +8 d^{2}\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*d^2*sin(f*x+e)^2+10*c*d*sin(f*x+e)+4*d^2*sin(f*x+e)+15*c^2+20*c*d+8*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
524,1,58,54,0.640000," ","int((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) a \left(\sin \left(f x +e \right)-1\right) \left(d \sin \left(f x +e \right)+3 c +2 d \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)*(d*sin(f*x+e)+3*c+2*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
525,1,43,24,0.507000," ","int((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)}{\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)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
526,1,80,47,0.793000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x)","-\frac{2 a \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \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 \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2*a*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)/(a*(c+d)*d)^(1/2)*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
527,1,155,89,1.273000," ","int((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(\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 d +\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 +\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\right)}{\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)*(arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a*d+arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a*c+(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2))/(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","A"
528,1,254,130,1.450000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(3 \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 \,d^{2}+6 \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 c d +3 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sin \left(f x +e \right) d +3 \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^{2}+5 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, c +2 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, d \right)}{4 \left(c +d \right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{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,"-1/4*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(3*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a*d^2+6*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a*c*d+3*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*sin(f*x+e)*d+3*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a*c^2+5*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*c+2*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*d)/(c+d)^2/(c+d*sin(f*x+e))^2/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
529,1,195,211,0.923000," ","int((a+a*sin(f*x+e))^(3/2)*(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(35 d^{3} \left(\sin^{4}\left(f x +e \right)\right)+135 c \,d^{2} \left(\sin^{3}\left(f x +e \right)\right)+85 d^{3} \left(\sin^{3}\left(f x +e \right)\right)+189 c^{2} d \left(\sin^{2}\left(f x +e \right)\right)+351 c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)+102 d^{3} \left(\sin^{2}\left(f x +e \right)\right)+105 c^{3} \sin \left(f x +e \right)+567 c^{2} d \sin \left(f x +e \right)+468 c \,d^{2} \sin \left(f x +e \right)+136 d^{3} \sin \left(f x +e \right)+525 c^{3}+1134 c^{2} d +936 c \,d^{2}+272 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^2*(sin(f*x+e)-1)*(35*d^3*sin(f*x+e)^4+135*c*d^2*sin(f*x+e)^3+85*d^3*sin(f*x+e)^3+189*c^2*d*sin(f*x+e)^2+351*c*d^2*sin(f*x+e)^2+102*d^3*sin(f*x+e)^2+105*c^3*sin(f*x+e)+567*c^2*d*sin(f*x+e)+468*c*d^2*sin(f*x+e)+136*d^3*sin(f*x+e)+525*c^3+1134*c^2*d+936*c*d^2+272*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
530,1,130,141,0.886000," ","int((a+a*sin(f*x+e))^(3/2)*(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(15 d^{2} \left(\sin^{3}\left(f x +e \right)\right)+42 c d \left(\sin^{2}\left(f x +e \right)\right)+39 d^{2} \left(\sin^{2}\left(f x +e \right)\right)+35 c^{2} \sin \left(f x +e \right)+126 c d \sin \left(f x +e \right)+52 d^{2} \sin \left(f x +e \right)+175 c^{2}+252 c d +104 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^2*(sin(f*x+e)-1)*(15*d^2*sin(f*x+e)^3+42*c*d*sin(f*x+e)^2+39*d^2*sin(f*x+e)^2+35*c^2*sin(f*x+e)+126*c*d*sin(f*x+e)+52*d^2*sin(f*x+e)+175*c^2+252*c*d+104*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
531,1,77,89,0.709000," ","int((a+a*sin(f*x+e))^(3/2)*(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(\sin \left(f x +e \right) \left(5 c +9 d \right)-3 \left(\cos^{2}\left(f x +e \right)\right) d +25 c +21 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^2*(sin(f*x+e)-1)*(sin(f*x+e)*(5*c+9*d)-3*cos(f*x+e)^2*d+25*c+21*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
532,1,53,51,0.664000," ","int((a+a*sin(f*x+e))^(3/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{2} \left(\sin \left(f x +e \right)-1\right) \left(\sin \left(f x +e \right)+5\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^2*(sin(f*x+e)-1)*(sin(f*x+e)+5)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
533,1,137,82,1.122000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x)","-\frac{2 a \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-\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 +a \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) d +\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*a*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a*c+a*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*d+(-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"
534,1,233,103,1.419000," ","int((a+a*sin(f*x+e))^(3/2)/(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) \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a d \left(c +3 d \right)-\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 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d +\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c -\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, d \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,"a*(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*(c+3*d)-arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2-3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d+(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c-(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*d)/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"
535,1,429,155,1.497000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x)","\frac{\left(-\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^{2}-7 \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^{3}-2 \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 -14 \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^{2}+\left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c d +7 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{2}-\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}-7 \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 +\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2}-8 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a c d -9 \sqrt{-a \left(\sin \left(f x +e \right)-1\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 \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*(-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^2-7*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)^2*a^2*d^3-2*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-14*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*sin(f*x+e)*a^2*c*d^2+(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*c*d+7*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*d^2-arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^3-7*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^2*d+(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2-8*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d-9*(-a*(sin(f*x+e)-1))^(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"
536,1,249,304,0.888000," ","int((a+a*sin(f*x+e))^(5/2)*(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(315 d^{3} \left(\sin^{5}\left(f x +e \right)\right)+1155 c \,d^{2} \left(\sin^{4}\left(f x +e \right)\right)+1120 d^{3} \left(\sin^{4}\left(f x +e \right)\right)+1485 c^{2} d \left(\sin^{3}\left(f x +e \right)\right)+4290 c \,d^{2} \left(\sin^{3}\left(f x +e \right)\right)+1775 d^{3} \left(\sin^{3}\left(f x +e \right)\right)+693 c^{3} \left(\sin^{2}\left(f x +e \right)\right)+5940 c^{2} d \left(\sin^{2}\left(f x +e \right)\right)+7227 c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)+2130 d^{3} \left(\sin^{2}\left(f x +e \right)\right)+3234 c^{3} \sin \left(f x +e \right)+11385 c^{2} d \sin \left(f x +e \right)+9636 c \,d^{2} \sin \left(f x +e \right)+2840 d^{3} \sin \left(f x +e \right)+9933 c^{3}+22770 c^{2} d +19272 c \,d^{2}+5680 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^3*(sin(f*x+e)-1)*(315*d^3*sin(f*x+e)^5+1155*c*d^2*sin(f*x+e)^4+1120*d^3*sin(f*x+e)^4+1485*c^2*d*sin(f*x+e)^3+4290*c*d^2*sin(f*x+e)^3+1775*d^3*sin(f*x+e)^3+693*c^3*sin(f*x+e)^2+5940*c^2*d*sin(f*x+e)^2+7227*c*d^2*sin(f*x+e)^2+2130*d^3*sin(f*x+e)^2+3234*c^3*sin(f*x+e)+11385*c^2*d*sin(f*x+e)+9636*c*d^2*sin(f*x+e)+2840*d^3*sin(f*x+e)+9933*c^3+22770*c^2*d+19272*c*d^2+5680*d^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
537,1,168,182,0.943000," ","int((a+a*sin(f*x+e))^(5/2)*(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(35 d^{2} \left(\sin^{4}\left(f x +e \right)\right)+90 c d \left(\sin^{3}\left(f x +e \right)\right)+130 d^{2} \left(\sin^{3}\left(f x +e \right)\right)+63 c^{2} \left(\sin^{2}\left(f x +e \right)\right)+360 c d \left(\sin^{2}\left(f x +e \right)\right)+219 d^{2} \left(\sin^{2}\left(f x +e \right)\right)+294 c^{2} \sin \left(f x +e \right)+690 c d \sin \left(f x +e \right)+292 d^{2} \sin \left(f x +e \right)+903 c^{2}+1380 c d +584 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^3*(sin(f*x+e)-1)*(35*d^2*sin(f*x+e)^4+90*c*d*sin(f*x+e)^3+130*d^2*sin(f*x+e)^3+63*c^2*sin(f*x+e)^2+360*c*d*sin(f*x+e)^2+219*d^2*sin(f*x+e)^2+294*c^2*sin(f*x+e)+690*c*d*sin(f*x+e)+292*d^2*sin(f*x+e)+903*c^2+1380*c*d+584*d^2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
538,1,99,122,0.782000," ","int((a+a*sin(f*x+e))^(5/2)*(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(-15 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) d +\left(98 c +130 d \right) \sin \left(f x +e \right)+\left(-21 c -60 d \right) \left(\cos^{2}\left(f x +e \right)\right)+322 c +290 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^3*(sin(f*x+e)-1)*(-15*cos(f*x+e)^2*sin(f*x+e)*d+(98*c+130*d)*sin(f*x+e)+(-21*c-60*d)*cos(f*x+e)^2+322*c+290*d)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
539,1,65,77,0.772000," ","int((a+a*sin(f*x+e))^(5/2),x)","\frac{2 \left(1+\sin \left(f x +e \right)\right) a^{3} \left(\sin \left(f x +e \right)-1\right) \left(3 \left(\sin^{2}\left(f x +e \right)\right)+14 \sin \left(f x +e \right)+43\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^3*(sin(f*x+e)-1)*(3*sin(f*x+e)^2+14*sin(f*x+e)+43)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
540,1,229,120,1.431000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x)","-\frac{2 a \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(3 \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}-6 \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 \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}-\left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d -3 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a c +9 \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*a*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(3*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c^2-6*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*c*d+3*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^2*d^2-(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*d-3*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a*c+9*(-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","A"
541,1,393,148,1.482000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x)","-\frac{a^{2} \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 \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 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a c d -5 \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 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c -2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, d \right)-3 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a \,c^{3}-2 \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 +5 \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 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, c^{2}+\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, d^{2}\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^2*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-sin(f*x+e)*d*(3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2+2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d-5*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*d^2-2*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c-2*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*d)-3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^3-2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c^2*d+5*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a*c*d^2+3*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*c^2+(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*d^2)/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"
542,1,567,170,1.807000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x)","-\frac{a \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 c^{2}+10 c d +19 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(3 c^{2}+10 c d +19 d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+3 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{2} c^{4}+10 \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 +22 \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}+10 \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}+19 \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 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c^{2} d +6 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, c \,d^{2}-11 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, d^{3}-3 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{3}-13 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a \,c^{2} d +3 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a c \,d^{2}+13 \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*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*c^2+10*c*d+19*d^2)-arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^2*(3*c^2+10*c*d+19*d^2)*cos(f*x+e)^2+3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^4+10*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^3*d+22*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c^2*d^2+10*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*c*d^3+19*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^2*d^4+5*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c^2*d+6*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*c*d^2-11*(a-a*sin(f*x+e))^(3/2)*(a*(c+d)*d)^(1/2)*d^3-3*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^3-13*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c^2*d+3*(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a*c*d^2+13*(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"
543,1,285,157,1.234000," ","int((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(15 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^{3}-45 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} d +45 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^{2}-15 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^{3}+6 d^{3} \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}}-30 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a c \,d^{2}-10 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a \,d^{3}+90 c^{2} d \,a^{2} \sqrt{a -a \sin \left(f x +e \right)}+30 a^{2} d^{3} \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^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^3-45*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*d+45*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^2-15*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^3+6*d^3*(a-a*sin(f*x+e))^(5/2)-30*(a-a*sin(f*x+e))^(3/2)*a*c*d^2-10*(a-a*sin(f*x+e))^(3/2)*a*d^3+90*c^2*d*a^2*(a-a*sin(f*x+e))^(1/2)+30*a^2*d^3*(a-a*sin(f*x+e))^(1/2))/a^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
544,1,185,106,1.250000," ","int((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(3 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^{2}-6 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 d +3 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}-2 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} d^{2}+12 a c d \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^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c^2-6*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*c*d+3*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d^2-2*(a-a*sin(f*x+e))^(3/2)*d^2+12*a*c*d*(a-a*sin(f*x+e))^(1/2))/a^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
545,1,128,68,0.997000," ","int((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{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) c -\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) d +2 \sqrt{a -a \sin \left(f x +e \right)}\, d \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))*c-a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*d+2*(a-a*sin(f*x+e))^(1/2)*d)/a/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
546,1,75,38,0.520000," ","int(1/(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)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{\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)/a^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
547,1,131,100,1.237000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-2 d \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sqrt{a \left(c +d \right) d}\right)}{\left(c -d \right) \sqrt{a \left(c +d \right) d}\, a^{\frac{3}{2}} \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*d*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)+2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*(a*(c+d)*d)^(1/2))/(c-d)/(a*(c+d)*d)^(1/2)/a^(3/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
548,1,449,150,1.865000," ","int(1/(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) d \left(3 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{7}{2}} c d +\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{7}{2}} d^{2}-\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, a^{3} c -\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, a^{3} d \right)+3 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{7}{2}} c^{2} d +\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, d}{\sqrt{a c d +a \,d^{2}}}\right) a^{\frac{7}{2}} c \,d^{2}+\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{5}{2}} c d -\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{5}{2}} d^{2}-\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^{3} c^{2}-\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^{3} c d \right)}{a^{\frac{7}{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^(7/2)*(sin(f*x+e)*d*(3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(7/2)*c*d+arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(7/2)*d^2-arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a*(c+d)*d)^(1/2)*2^(1/2)*a^3*c-arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a*(c+d)*d)^(1/2)*2^(1/2)*a^3*d)+3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(7/2)*c^2*d+arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(7/2)*c*d^2+(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*c*d-(a-a*sin(f*x+e))^(1/2)*(a*(c+d)*d)^(1/2)*a^(5/2)*d^2-(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^3*c^2-(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^3*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"
549,1,1065,214,2.196000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x)","\frac{\left(10 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \left(\sin^{2}\left(f x +e \right)\right) c \,d^{4}-4 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{5} d^{4}-4 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} c^{2} d^{2}-8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} c^{3} d +\left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a^{\frac{7}{2}} d^{4}+\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{9}{2}} d^{4}+15 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} c^{4} d +10 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} c^{3} d^{2}+7 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} c^{2} d^{3}+7 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \left(\sin^{2}\left(f x +e \right)\right) d^{5}+15 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \left(\sin^{2}\left(f x +e \right)\right) c^{2} d^{3}-8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a^{5} c^{3} d -16 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a^{5} c^{2} d^{2}-8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a^{5} c \,d^{3}-4 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{5} c^{2} d^{2}-8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{5} c \,d^{3}+9 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{9}{2}} c^{3} d -\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{9}{2}} c^{2} d^{2}-7 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a^{\frac{7}{2}} c^{2} d^{2}+6 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a \left(c +d \right) d}\, a^{\frac{7}{2}} c \,d^{3}-9 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, a^{\frac{9}{2}} c \,d^{3}+30 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \sin \left(f x +e \right) c^{3} d^{2}+20 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \sin \left(f x +e \right) c^{2} d^{3}+14 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{11}{2}} \sin \left(f x +e \right) c \,d^{4}-4 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} c^{4}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(1+\sin \left(f x +e \right)\right)}{4 a^{\frac{11}{2}} \sqrt{a \left(c +d \right) d}\, \left(c +d \sin \left(f x +e \right)\right)^{2} \left(c +d \right)^{2} \left(c -d \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/4*(-4*(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^5*c^2*d^2-4*(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^5*d^4-4*(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^5*c^2*d^2-8*(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^5*c^3*d+(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*d^4+7*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)^2*d^5+15*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*c^4*d+10*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*c^3*d^2+7*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*c^2*d^3+(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(9/2)*d^4-8*(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^5*c*d^3-8*(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^5*c^3*d-16*(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^5*c^2*d^2-8*(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^5*c*d^3+30*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)*c^3*d^2+20*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)*c^2*d^3+14*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)*c*d^4+9*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(9/2)*c^3*d-(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(9/2)*c^2*d^2-7*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c^2*d^2+6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(7/2)*c*d^3-4*(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^5*c^4-9*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(9/2)*c*d^3+15*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)^2*c^2*d^3+10*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(11/2)*sin(f*x+e)^2*c*d^4)*(-a*(sin(f*x+e)-1))^(1/2)*(1+sin(f*x+e))/a^(11/2)/(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"
550,1,490,169,1.092000," ","int((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(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+27 \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 -63 \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}+33 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}-8 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} d^{3} \sqrt{a}+72 c \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}-24 d^{3} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\right)+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+27 \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 -63 \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}+33 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}-8 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} d^{3} \sqrt{a}+6 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{3}-18 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2} d +90 c \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}-30 d^{3} 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*(sin(f*x+e)*(3*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+27*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-63*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+33*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-8*(a-a*sin(f*x+e))^(3/2)*d^3*a^(1/2)+72*c*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)-24*d^3*a^(3/2)*(a-a*sin(f*x+e))^(1/2))+3*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+27*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-63*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+33*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-8*(a-a*sin(f*x+e))^(3/2)*d^3*a^(1/2)+6*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^3-18*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2*d+90*c*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)-30*d^3*a^(3/2)*(a-a*sin(f*x+e))^(1/2))*(-a*(sin(f*x+e)-1))^(1/2)/a^(7/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
551,1,316,119,1.010000," ","int((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(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,c^{2}+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c d -7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,d^{2}+8 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d^{2}\right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,c^{2}+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c d -7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,d^{2}+2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c^{2}-4 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c d +10 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, d^{2}\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*c^2+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c*d-7*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d^2+8*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d^2)+2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c^2+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c*d-7*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*d^2+2*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c^2-4*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c*d+10*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*d^2)*(-a*(sin(f*x+e)-1))^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
552,1,176,72,0.861000," ","int((c+d*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(c +3 d \right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c +3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a d +2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c -2 \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)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*(c+3*d)+2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a*c+3*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*sin(f*x+e))^(1/2)*a^(1/2)*c-2*(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"
553,1,125,62,0.809000," ","int(1/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \sin \left(f x +e \right)+2 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}+\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{4 a^{\frac{7}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4/a^(7/2)*(2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*sin(f*x+e)+2*(a-a*sin(f*x+e))^(1/2)*a^(3/2)+2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2)*(-a*(sin(f*x+e)-1))^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
554,1,338,135,1.322000," ","int(1/(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 d^{2} \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}}+\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 \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 d^{2} \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}}+\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 \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 \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\, c -2 \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*d^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)+(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*(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*d^2*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(3/2)+(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*(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*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(1/2)*c-2*(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"
555,1,978,210,1.809000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x)","-\frac{\left(\sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a \,c^{2} d -8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a c \,d^{2}-9 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a \,d^{3}+20 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right) c \,d^{3}+12 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right) d^{4}+\sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a \,c^{3}-7 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a \,c^{2} d -17 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a c \,d^{2}-9 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sin \left(f x +e \right) a \,d^{3}+20 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} \sin \left(f x +e \right) c^{2} d^{2}+32 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} \sin \left(f x +e \right) c \,d^{3}+12 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} \sin \left(f x +e \right) d^{4}+2 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, \sin \left(f x +e \right) c^{2} d +4 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, \sin \left(f x +e \right) c \,d^{2}-6 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, \sin \left(f x +e \right) d^{3}+\sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,c^{3}-8 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \,c^{2} d -9 \sqrt{a \left(c +d \right) d}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a c \,d^{2}+20 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} c^{2} d^{2}+12 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) a^{\frac{3}{2}} c \,d^{3}+2 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, c^{3}+2 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, c \,d^{2}-4 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a \left(c +d \right) d}\, \sqrt{a}\, d^{3}\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 \sin \left(f x +e \right)\right) \left(c +d \right) \left(c -d \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/4/a^(5/2)*((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*(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^2-9*(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+20*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+12*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+(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^3-7*(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-17*(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^2-9*(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+20*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+32*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*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+2*(-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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^2-6*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^3+(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^3-8*(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*(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+20*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c^2*d^2+12*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(3/2)*c*d^3+2*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3+2*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^2-4*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^3)*(-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"
556,1,2219,279,2.432000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-1/4*(-a*(sin(f*x+e)-1))^(1/2)*(-13*(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+42*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^3*d^3+19*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^4+2*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^5-3*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^5+19*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+(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*(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*(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*(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+4*(-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*(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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^3-17*(-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*(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*(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+19*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*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^4*d^2+5*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^5-2*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^4-13*(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^5-11*(-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*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^4-51*(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^4-9*(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*(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*(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^3-26*(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*(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^2-11*(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^3-25*(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+2*(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-21*(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^2-61*(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+5*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^5-11*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^3+6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^4+(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+35*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*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+70*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*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+80*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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^5+35*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+112*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+103*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*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^5-3*(-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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4*d+11*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d^2+(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^3-13*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^4)/a^(7/2)/(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"
557,1,688,171,1.317000," ","int((c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(2 \sin \left(f x +e \right) \left(64 d^{3} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+15 \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 +57 \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}-75 \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)+\left(-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}-15 \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 -57 \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}+75 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}-64 d^{3} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}\right) \left(\cos^{2}\left(f x +e \right)\right)+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} c^{3}+30 \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 +114 \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}-150 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} d^{3}-6 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{3}-30 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2} d +78 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c \,d^{2}-42 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} d^{3} \sqrt{a}+20 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{3}+36 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2} d -132 c \,d^{2} a^{\frac{3}{2}} \sqrt{a -a \sin \left(f x +e \right)}+204 d^{3} 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)}}{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)*(64*d^3*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+3*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+15*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+57*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-75*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3)+(-3*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3-15*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-57*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+75*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-64*d^3*a^(3/2)*(a-a*sin(f*x+e))^(1/2))*cos(f*x+e)^2+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c^3+30*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+114*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*c*d^2-150*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*d^3-6*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^3-30*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2*d+78*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d^2-42*(a-a*sin(f*x+e))^(3/2)*d^3*a^(1/2)+20*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^3+36*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2*d-132*c*d^2*a^(3/2)*(a-a*sin(f*x+e))^(1/2)+204*d^3*a^(3/2)*(a-a*sin(f*x+e))^(1/2))*(-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"
558,1,378,128,1.433000," ","int((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) \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a^{2} \left(3 c^{2}+10 c d +19 d^{2}\right)+\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, a^{2} \left(3 c^{2}+10 c d +19 d^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)-6 \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 \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 \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 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c^{2}+20 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, c d -26 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a}\, d^{2}-20 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}-24 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c d +44 \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) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/32/a^(9/2)*(-2*sin(f*x+e)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a^2*(3*c^2+10*c*d+19*d^2)+arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a^2*(3*c^2+10*c*d+19*d^2)*cos(f*x+e)^2-6*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*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*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*sin(f*x+e))^(3/2)*a^(1/2)*c^2+20*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d-26*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^2-20*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2-24*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d+44*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*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"
559,1,279,107,1.177000," ","int((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^{3} \left(3 c +5 d \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 c +5 d \right) \left(\cos^{2}\left(f x +e \right)\right)+20 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}} c +12 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}} d -6 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} c -10 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} d +6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} c +10 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} d \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*c+5*d)-2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*(3*c+5*d)*cos(f*x+e)^2+20*(a-a*sin(f*x+e))^(1/2)*a^(5/2)*c+12*(a-a*sin(f*x+e))^(1/2)*a^(5/2)*d-6*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*c-10*(a-a*sin(f*x+e))^(3/2)*a^(3/2)*d+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*c+10*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3*d)*(-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"
560,1,195,88,0.911000," ","int(1/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(\sin \left(f x +e \right) \left(6 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}\right)-3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(\cos^{2}\left(f x +e \right)\right)+14 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{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/a^(9/2)*(sin(f*x+e)*(6*(a-a*sin(f*x+e))^(1/2)*a^(3/2)+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2)-3*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2*cos(f*x+e)^2+14*(a-a*sin(f*x+e))^(1/2)*a^(3/2)+6*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^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"
561,1,732,185,1.666000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x)","\frac{\left(\sin \left(f x +e \right) \left(128 d^{3} \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}}-6 \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 \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 \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 d^{3} \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}}+3 \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 \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 \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 d^{3} \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}}-6 \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 \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 \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 \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 \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 \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 \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c^{2}+72 \sqrt{a \left(c +d \right) d}\, \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}} c d -52 \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/a^(9/2)*(sin(f*x+e)*(128*d^3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)-6*(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*(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*(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*d^3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)+3*(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*(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*(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*d^3*arctanh((a-a*sin(f*x+e))^(1/2)*d/(a*c*d+a*d^2)^(1/2))*a^(5/2)-6*(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*(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*(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*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c^2-28*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*c*d+22*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(3/2)*a^(1/2)*d^2-20*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c^2+72*(a*(c+d)*d)^(1/2)*(a-a*sin(f*x+e))^(1/2)*a^(3/2)*c*d-52*(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)/(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"
562,1,1972,276,2.394000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x)","\text{Expression too large to display}"," ",0,"-1/32*(323*(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*(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*(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^2-84*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^3-6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^4+32*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^4-160*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^5-320*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*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)*d^5-224*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^3-160*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c*d^4+20*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4+3*(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^4-84*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d-20*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^2+52*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^3+32*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^4-448*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^3-38*(-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*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3*d+6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^2-224*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^4-224*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*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^4-544*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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^4-38*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^3+3*(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-19*(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+93*(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+301*(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+55*(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^2-13*(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-6*(-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*(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*(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*(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+115*(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+115*(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+3*(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*(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+20*(-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*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^2-19*(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-32*(-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+93*(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+115*(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)*(-a*(sin(f*x+e)-1))^(1/2)/a^(9/2)/(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"
563,1,3535,357,3.264000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"1/32/a^(9/2)*(-a*(sin(f*x+e)-1))^(1/2)*(-219*(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^4+504*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^4*d^3+720*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^3*d^4+312*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*c^2*d^5+72*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*d^6+6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^6-20*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^6-56*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*d^6+312*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^4*d^7+624*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^7+312*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^7+42*(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^4*d^2-276*(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^3-1140*(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^4-1254*(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^5+12*(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^5*d-69*(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^2+12*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^5*d-96*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^4*d^2-120*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^3*d^3-144*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c^2*d^4+204*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*c*d^5-6*(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^6-219*(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)^4*a^2*d^6-438*(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^6+6*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)^2*c^4*d^2-219*(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^6-20*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c^4*d^2-48*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)^2*c^3*d^3-180*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)^2*c^2*d^4+96*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)^2*c*d^5-3*(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^6-1032*(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^3-2013*(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^4-1284*(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^5+42*(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*d-276*(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^2-1140*(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^3-1254*(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^4-438*(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^5-3*(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)^4*a^2*c^4*d^2+24*(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)^4*a^2*c^3*d^3-162*(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)^4*a^2*c^2*d^4-408*(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)^4*a^2*c*d^5-6*(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^5*d+624*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^6-112*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*d^6+96*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^5*d+136*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^4*d^2+40*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^3*d^3-60*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c^2*d^4-136*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*c*d^5+2736*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^4+2448*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^5+2064*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^6+504*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^3+3696*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^5+1968*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^6-172*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*d^6+1008*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^3+2448*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^4+2064*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^5+126*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)^2*d^6+144*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*sin(f*x+e)*d^6-48*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^5*d-60*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^4*d^2+48*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^3*d^3-66*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c^2*d^4+48*(-a*(sin(f*x+e)-1))^(3/2)*(a*(c+d)*d)^(1/2)*a^(1/2)*c*d^5-3*(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^6+504*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^4*c^2*d^5+720*arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(5/2)*sin(f*x+e)^4*c*d^6+1008*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^4+192*(-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^4-232*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)^2*c*d^5-40*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^5*d+192*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^4*d^2+544*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^3*d^3-80*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c^2*d^4-504*(-a*(sin(f*x+e)-1))^(1/2)*(a*(c+d)*d)^(1/2)*a^(3/2)*sin(f*x+e)*c*d^5+24*(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*d-162*(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^2-408*(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^3+232*(-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^3)/(1+sin(f*x+e))/(a*(c+d)*d)^(1/2)/(c+d*sin(f*x+e))^2/(c+d)^2/(c-d)^5/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","B"
564,-2,0,171,180.000000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x)","\int \sqrt{a +a \sin \left(f x +e \right)}\, \left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x)","F"
565,-2,0,130,180.000000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x)","\int \sqrt{a +a \sin \left(f x +e \right)}\, \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x)","F"
566,-2,0,89,180.000000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x)","\int \sqrt{a +a \sin \left(f x +e \right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x)","F"
567,1,2707,49,0.539000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/f*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*(c+d*sin(f*x+e))^(1/2)*(a*(1+sin(f*x+e)))^(1/2)*((d^2/c^2)^(1/2)*sin(f*x+e)*cos(f*x+e)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c*d+cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^5+sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^5-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^3*d^2+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3+arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4-(d^2/c^2)^(1/2)*cos(f*x+e)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c^2+sin(f*x+e)*cos(f*x+e)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d^2-arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^5-(d^2/c^2)^(1/2)*cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^3*d^2+2*(d^2/c^2)^(1/2)*cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3-(d^2/c^2)^(1/2)*cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4-(d^2/c^2)^(1/2)*sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^4*d+(d^2/c^2)^(1/2)*sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^3*d^2+(d^2/c^2)^(1/2)*sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3-(d^2/c^2)^(1/2)*sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4-sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3-sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4+cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3-2*cos(f*x+e)^2*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4+(d^2/c^2)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^4*d-(d^2/c^2)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^3*d^2-(d^2/c^2)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^2*d^3+(d^2/c^2)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c*d^4+sin(f*x+e)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*c^3*d^2-cos(f*x+e)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*c*d)/d^2/cos(f*x+e)/(cos(f*x+e)^2*d^2+c^2-d^2)/(-(d^2/c^2)^(1/2)*c)^(1/2)/(c^2-2*c*d+d^2)","B"
568,1,99,41,0.312000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x)","\frac{2 \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \left(\left(\cos^{2}\left(f x +e \right)\right) d +c \sin \left(f x +e \right)+d \sin \left(f x +e \right)-c -d \right)}{f \cos \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right) \left(c +d \right)}"," ",0,"2/f*(a*(1+sin(f*x+e)))^(1/2)*(c+d*sin(f*x+e))^(1/2)*(cos(f*x+e)^2*d+c*sin(f*x+e)+d*sin(f*x+e)-c-d)/cos(f*x+e)/(cos(f*x+e)^2*d^2+c^2-d^2)/(c+d)","B"
569,1,222,83,0.341000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x)","\frac{2 \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \left(2 \left(\cos^{4}\left(f x +e \right)\right) d^{3}+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{3}+4 c^{2} \left(\cos^{2}\left(f x +e \right)\right) d +c \left(\cos^{2}\left(f x +e \right)\right) d^{2}-3 \left(\cos^{2}\left(f x +e \right)\right) d^{3}+3 c^{3} \sin \left(f x +e \right)+5 c^{2} d \sin \left(f x +e \right)+c \,d^{2} \sin \left(f x +e \right)-d^{3} \sin \left(f x +e \right)-3 c^{3}-5 c^{2} d -c \,d^{2}+d^{3}\right)}{3 f \cos \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{2} \left(c +d \right)^{2}}"," ",0,"2/3/f*(a*(1+sin(f*x+e)))^(1/2)*(c+d*sin(f*x+e))^(1/2)*(2*cos(f*x+e)^4*d^3+sin(f*x+e)*cos(f*x+e)^2*c*d^2+sin(f*x+e)*cos(f*x+e)^2*d^3+4*c^2*cos(f*x+e)^2*d+c*cos(f*x+e)^2*d^2-3*cos(f*x+e)^2*d^3+3*c^3*sin(f*x+e)+5*c^2*d*sin(f*x+e)+c*d^2*sin(f*x+e)-d^3*sin(f*x+e)-3*c^3-5*c^2*d-c*d^2+d^3)/cos(f*x+e)/(cos(f*x+e)^2*d^2+c^2-d^2)^2/(c+d)^2","B"
570,1,430,124,0.362000," ","int((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(7/2),x)","\frac{2 \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \left(19 c^{3} \left(\cos^{2}\left(f x +e \right)\right) d^{2}-11 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{5}+25 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d +21 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{3}-2 c \left(\cos^{4}\left(f x +e \right)\right) d^{4}+13 c \left(\cos^{2}\left(f x +e \right)\right) d^{4}-11 c \,d^{4}-6 c^{2} d^{3}-22 c^{3} d^{2}-35 c^{4} d +4 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{4}+7 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{2}+3 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}-15 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{4}+7 d^{5} \sin \left(f x +e \right)+6 c^{2} d^{3} \sin \left(f x +e \right)+11 c \,d^{4} \sin \left(f x +e \right)+35 \sin \left(f x +e \right) c^{4} d +22 \sin \left(f x +e \right) c^{3} d^{2}-7 d^{5}+4 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{5}-15 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}+8 \left(\cos^{6}\left(f x +e \right)\right) d^{5}+22 \left(\cos^{2}\left(f x +e \right)\right) d^{5}-23 \left(\cos^{4}\left(f x +e \right)\right) d^{5}-15 c^{5}+15 c^{5} \sin \left(f x +e \right)\right)}{15 f \cos \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{3} \left(c +d \right)^{3}}"," ",0,"2/15/f*(a*(1+sin(f*x+e)))^(1/2)*(c+d*sin(f*x+e))^(1/2)*(4*sin(f*x+e)*cos(f*x+e)^4*d^5+4*sin(f*x+e)*cos(f*x+e)^4*c*d^4+7*sin(f*x+e)*cos(f*x+e)^2*c^3*d^2+3*sin(f*x+e)*cos(f*x+e)^2*c^2*d^3-15*sin(f*x+e)*cos(f*x+e)^2*c*d^4-11*c*d^4-6*c^2*d^3-22*c^3*d^2-35*c^4*d-15*cos(f*x+e)^2*c^2*d^3-23*cos(f*x+e)^4*d^5+22*cos(f*x+e)^2*d^5+8*cos(f*x+e)^6*d^5+7*d^5*sin(f*x+e)-2*c*cos(f*x+e)^4*d^4+19*c^3*cos(f*x+e)^2*d^2+13*c*cos(f*x+e)^2*d^4+6*c^2*d^3*sin(f*x+e)+11*c*d^4*sin(f*x+e)+21*cos(f*x+e)^4*c^2*d^3-11*sin(f*x+e)*cos(f*x+e)^2*d^5+25*cos(f*x+e)^2*c^4*d+35*sin(f*x+e)*c^4*d+22*sin(f*x+e)*c^3*d^2-7*d^5-15*c^5+15*c^5*sin(f*x+e))/cos(f*x+e)/(cos(f*x+e)^2*d^2+c^2-d^2)^3/(c+d)^3","B"
571,-2,0,247,180.000000," ","int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(5/2),x)","F"
572,-2,0,196,180.000000," ","int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(3/2),x)","F"
573,-2,0,145,180.000000," ","int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^(1/2),x)","F"
574,0,0,95,0.490000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{\sqrt{c +d \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x)","F"
575,1,6630,101,0.559000," ","int((a+a*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"
576,1,345,103,0.313000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{2}+5 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{3}-2 c^{2} \left(\cos^{4}\left(f x +e \right)\right) d -7 c \left(\cos^{4}\left(f x +e \right)\right) d^{2}-9 \left(\cos^{4}\left(f x +e \right)\right) d^{3}-\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3}+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d -11 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{2}-13 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{3}-3 c^{3} \left(\cos^{2}\left(f x +e \right)\right)-5 c^{2} \left(\cos^{2}\left(f x +e \right)\right) d +15 c \left(\cos^{2}\left(f x +e \right)\right) d^{2}+17 \left(\cos^{2}\left(f x +e \right)\right) d^{3}-8 c^{3} \sin \left(f x +e \right)-8 c^{2} d \sin \left(f x +e \right)+8 c \,d^{2} \sin \left(f x +e \right)+8 d^{3} \sin \left(f x +e \right)+8 c^{3}+8 c^{2} d -8 c \,d^{2}-8 d^{3}\right)}{3 f \cos \left(f x +e \right)^{3} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{2} \left(c +d \right)^{2}}"," ",0,"-2/3/f*(a*(1+sin(f*x+e)))^(3/2)*(c+d*sin(f*x+e))^(1/2)*(sin(f*x+e)*cos(f*x+e)^4*c*d^2+5*sin(f*x+e)*cos(f*x+e)^4*d^3-2*c^2*cos(f*x+e)^4*d-7*c*cos(f*x+e)^4*d^2-9*cos(f*x+e)^4*d^3-sin(f*x+e)*cos(f*x+e)^2*c^3+sin(f*x+e)*cos(f*x+e)^2*c^2*d-11*sin(f*x+e)*cos(f*x+e)^2*c*d^2-13*sin(f*x+e)*cos(f*x+e)^2*d^3-3*c^3*cos(f*x+e)^2-5*c^2*cos(f*x+e)^2*d+15*c*cos(f*x+e)^2*d^2+17*cos(f*x+e)^2*d^3-8*c^3*sin(f*x+e)-8*c^2*d*sin(f*x+e)+8*c*d^2*sin(f*x+e)+8*d^3*sin(f*x+e)+8*c^3+8*c^2*d-8*c*d^2-8*d^3)/cos(f*x+e)^3/(cos(f*x+e)^2*d^2+c^2-d^2)^2/(c+d)^2","B"
577,1,625,154,0.364000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(7/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(114 c^{3} \left(\cos^{2}\left(f x +e \right)\right) d^{2}+63 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{5}-31 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d -105 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{3}+23 c \left(\cos^{4}\left(f x +e \right)\right) d^{4}-19 c \left(\cos^{2}\left(f x +e \right)\right) d^{4}-\left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{3}-63 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{2}-5 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{5}-13 \left(\cos^{4}\left(f x +e \right)\right) c^{4} d +18 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) d^{5}-12 \left(\cos^{6}\left(f x +e \right)\right) c \,d^{4}+8 c \,d^{4}-80 c^{2} d^{3}-48 c^{3} d^{2}+56 c^{4} d -9 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{4}-90 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{2}-146 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}+15 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{4}-24 d^{5} \sin \left(f x +e \right)+57 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{3}+3 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{4} d +2 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c \,d^{4}+9 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{2}+80 c^{2} d^{3} \sin \left(f x +e \right)-8 c \,d^{4} \sin \left(f x +e \right)-56 \sin \left(f x +e \right) c^{4} d +48 \sin \left(f x +e \right) c^{3} d^{2}+24 d^{5}-57 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{5}+186 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}-15 \left(\cos^{2}\left(f x +e \right)\right) c^{5}-27 \left(\cos^{6}\left(f x +e \right)\right) d^{5}-75 \left(\cos^{2}\left(f x +e \right)\right) d^{5}+78 \left(\cos^{4}\left(f x +e \right)\right) d^{5}+40 c^{5}-40 c^{5} \sin \left(f x +e \right)\right)}{15 f \cos \left(f x +e \right)^{3} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{3} \left(c +d \right)^{3}}"," ",0,"-2/15/f*(a*(1+sin(f*x+e)))^(3/2)*(c+d*sin(f*x+e))^(1/2)*(-57*sin(f*x+e)*cos(f*x+e)^4*d^5-9*sin(f*x+e)*cos(f*x+e)^4*c*d^4-90*sin(f*x+e)*cos(f*x+e)^2*c^3*d^2-146*sin(f*x+e)*cos(f*x+e)^2*c^2*d^3+15*sin(f*x+e)*cos(f*x+e)^2*c*d^4+8*c*d^4-80*c^2*d^3-48*c^3*d^2+56*c^4*d+186*cos(f*x+e)^2*c^2*d^3+18*sin(f*x+e)*cos(f*x+e)^6*d^5-cos(f*x+e)^6*c^2*d^3-12*cos(f*x+e)^6*c*d^4-13*cos(f*x+e)^4*c^4*d-63*cos(f*x+e)^4*c^3*d^2-5*sin(f*x+e)*cos(f*x+e)^2*c^5+78*cos(f*x+e)^4*d^5-75*cos(f*x+e)^2*d^5-27*cos(f*x+e)^6*d^5-24*d^5*sin(f*x+e)+57*sin(f*x+e)*cos(f*x+e)^4*c^2*d^3+3*sin(f*x+e)*cos(f*x+e)^2*c^4*d+2*sin(f*x+e)*cos(f*x+e)^6*c*d^4+9*sin(f*x+e)*cos(f*x+e)^4*c^3*d^2+23*c*cos(f*x+e)^4*d^4+114*c^3*cos(f*x+e)^2*d^2-19*c*cos(f*x+e)^2*d^4+80*c^2*d^3*sin(f*x+e)-8*c*d^4*sin(f*x+e)-105*cos(f*x+e)^4*c^2*d^3+63*sin(f*x+e)*cos(f*x+e)^2*d^5-31*cos(f*x+e)^2*c^4*d-56*sin(f*x+e)*c^4*d+48*sin(f*x+e)*c^3*d^2+24*d^5-15*cos(f*x+e)^2*c^5+40*c^5-40*c^5*sin(f*x+e))/cos(f*x+e)^3/(cos(f*x+e)^2*d^2+c^2-d^2)^3/(c+d)^3","B"
578,1,979,205,0.478000," ","int((a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(9/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(8 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c \,d^{6}+29 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{4}+371 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{5}-113 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c \,d^{6}+106 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{2}+754 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{3}+72 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{4}-944 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{5}+382 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{6}+7 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{6} d -887 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{2}-1797 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{3}-25 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{4}+997 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{5}-397 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{6}+776 c^{4} d^{3} \sin \left(f x +e \right)-136 c^{3} d^{4} \sin \left(f x +e \right)-424 c^{2} d^{5} \sin \left(f x +e \right)+120 c \,d^{6} \sin \left(f x +e \right)-280 \sin \left(f x +e \right) c^{7}-156 \left(\cos^{8}\left(f x +e \right)\right) d^{7}-296 c^{5} d^{2}+136 c^{3} d^{4}+280 c^{7}-776 c^{4} d^{3}+2185 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{3}-4 \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{5}+457 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{6}+104 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) d^{7}-1209 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{5}-259 \left(\cos^{2}\left(f x +e \right)\right) c^{6} d -43 \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{4}-64 \left(\cos^{8}\left(f x +e \right)\right) c \,d^{6}-455 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) d^{7}+4 \left(\cos^{6}\left(f x +e \right)\right) c^{4} d^{3}-149 \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{4}-443 \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{5}+345 \left(\cos^{6}\left(f x +e \right)\right) c \,d^{6}+750 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{7}-112 \left(\cos^{4}\left(f x +e \right)\right) c^{6} d -670 \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{2}-1398 \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{3}+56 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{4}+1232 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{5}-618 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{6}-35 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{7}-551 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{7}+1035 \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{2}-120 c \,d^{6}+424 c^{2} d^{5}+504 c^{6} d -152 d^{7}+152 d^{7} \sin \left(f x +e \right)-504 \sin \left(f x +e \right) c^{6} d +296 \sin \left(f x +e \right) c^{5} d^{2}+635 \left(\cos^{6}\left(f x +e \right)\right) d^{7}-954 \left(\cos^{4}\left(f x +e \right)\right) d^{7}-105 \left(\cos^{2}\left(f x +e \right)\right) c^{7}+627 \left(\cos^{2}\left(f x +e \right)\right) d^{7}\right)}{105 f \cos \left(f x +e \right)^{3} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{4} \left(c +d \right)^{4}}"," ",0,"-2/105/f*(a*(1+sin(f*x+e)))^(3/2)*(c+d*sin(f*x+e))^(1/2)*(776*c^4*d^3*sin(f*x+e)-136*c^3*d^4*sin(f*x+e)-424*c^2*d^5*sin(f*x+e)+120*c*d^6*sin(f*x+e)+8*sin(f*x+e)*cos(f*x+e)^8*c*d^6+29*sin(f*x+e)*cos(f*x+e)^6*c^3*d^4+371*sin(f*x+e)*cos(f*x+e)^6*c^2*d^5-113*sin(f*x+e)*cos(f*x+e)^6*c*d^6+106*sin(f*x+e)*cos(f*x+e)^4*c^5*d^2+754*sin(f*x+e)*cos(f*x+e)^4*c^4*d^3+72*sin(f*x+e)*cos(f*x+e)^4*c^3*d^4-944*sin(f*x+e)*cos(f*x+e)^4*c^2*d^5+382*sin(f*x+e)*cos(f*x+e)^4*c*d^6+7*sin(f*x+e)*cos(f*x+e)^2*c^6*d-887*sin(f*x+e)*cos(f*x+e)^2*c^5*d^2-1797*sin(f*x+e)*cos(f*x+e)^2*c^4*d^3-25*sin(f*x+e)*cos(f*x+e)^2*c^3*d^4+997*sin(f*x+e)*cos(f*x+e)^2*c^2*d^5-397*sin(f*x+e)*cos(f*x+e)^2*c*d^6-280*sin(f*x+e)*c^7-156*cos(f*x+e)^8*d^7+635*cos(f*x+e)^6*d^7-954*cos(f*x+e)^4*d^7-105*cos(f*x+e)^2*c^7+627*cos(f*x+e)^2*d^7-296*c^5*d^2+136*c^3*d^4+280*c^7-776*c^4*d^3-120*c*d^6+424*c^2*d^5+504*c^6*d-152*d^7+152*d^7*sin(f*x+e)-259*cos(f*x+e)^2*c^6*d+2185*cos(f*x+e)^2*c^4*d^3-43*cos(f*x+e)^2*c^3*d^4-1209*cos(f*x+e)^2*c^2*d^5+457*cos(f*x+e)^2*c*d^6-504*sin(f*x+e)*c^6*d+296*sin(f*x+e)*c^5*d^2+104*sin(f*x+e)*cos(f*x+e)^8*d^7-4*cos(f*x+e)^8*c^2*d^5-64*cos(f*x+e)^8*c*d^6-455*sin(f*x+e)*cos(f*x+e)^6*d^7+4*cos(f*x+e)^6*c^4*d^3-149*cos(f*x+e)^6*c^3*d^4-443*cos(f*x+e)^6*c^2*d^5+345*cos(f*x+e)^6*c*d^6+750*sin(f*x+e)*cos(f*x+e)^4*d^7-112*cos(f*x+e)^4*c^6*d-670*cos(f*x+e)^4*c^5*d^2-1398*cos(f*x+e)^4*c^4*d^3+56*cos(f*x+e)^4*c^3*d^4+1232*cos(f*x+e)^4*c^2*d^5-618*cos(f*x+e)^4*c*d^6-35*sin(f*x+e)*cos(f*x+e)^2*c^7-551*sin(f*x+e)*cos(f*x+e)^2*d^7+1035*cos(f*x+e)^2*c^5*d^2)/cos(f*x+e)^3/(cos(f*x+e)^2*d^2+c^2-d^2)^4/(c+d)^4","B"
579,-2,0,333,180.000000," ","int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x)","F"
580,-2,0,274,180.000000," ","int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x)","F"
581,-2,0,209,180.000000," ","int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x)","F"
582,-2,0,152,180.000000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\sqrt{c +d \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x)","F"
583,0,0,160,0.374000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x)","F"
584,1,16223,159,0.615000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
585,1,793,171,0.397000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(7/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(480 c^{3} \left(\cos^{2}\left(f x +e \right)\right) d^{2}+368 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{5}-112 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d -290 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{3}+439 c \left(\cos^{4}\left(f x +e \right)\right) d^{4}-400 c \left(\cos^{2}\left(f x +e \right)\right) d^{4}-\left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{3}-194 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{2}+16 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{5}+7 \left(\cos^{4}\left(f x +e \right)\right) c^{4} d +115 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) d^{5}-181 \left(\cos^{6}\left(f x +e \right)\right) c \,d^{4}+128 c \,d^{4}-256 c^{2} d^{3}-256 c^{3} d^{2}+128 c^{4} d -287 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{4}-352 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{2}-416 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}+336 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{4}-27 \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{2}-9 \left(\cos^{6}\left(f x +e \right)\right) c^{4} d -3 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{5}-128 d^{5} \sin \left(f x +e \right)+114 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{3}+48 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{4} d +79 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c \,d^{4}+50 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{2}+256 c^{2} d^{3} \sin \left(f x +e \right)-128 c \,d^{4} \sin \left(f x +e \right)-128 \sin \left(f x +e \right) c^{4} d +256 \sin \left(f x +e \right) c^{3} d^{2}+14 \left(\cos^{8}\left(f x +e \right)\right) c \,d^{4}+3 \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{3}+128 d^{5}-355 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{5}+544 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{3}-80 \left(\cos^{2}\left(f x +e \right)\right) c^{5}-262 \left(\cos^{6}\left(f x +e \right)\right) d^{5}-432 \left(\cos^{2}\left(f x +e \right)\right) d^{5}+523 \left(\cos^{4}\left(f x +e \right)\right) d^{5}+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{4} d +9 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{2}+37 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{3}+43 \left(\cos^{8}\left(f x +e \right)\right) d^{5}-5 \left(\cos^{4}\left(f x +e \right)\right) c^{5}+128 c^{5}-128 c^{5} \sin \left(f x +e \right)\right)}{15 f \cos \left(f x +e \right)^{5} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{3} \left(c +d \right)^{3}}"," ",0,"-2/15/f*(a*(1+sin(f*x+e)))^(5/2)*(c+d*sin(f*x+e))^(1/2)*(-355*sin(f*x+e)*cos(f*x+e)^4*d^5-287*sin(f*x+e)*cos(f*x+e)^4*c*d^4-352*sin(f*x+e)*cos(f*x+e)^2*c^3*d^2-416*sin(f*x+e)*cos(f*x+e)^2*c^2*d^3+336*sin(f*x+e)*cos(f*x+e)^2*c*d^4+128*c*d^4-256*c^2*d^3-256*c^3*d^2+128*c^4*d+544*cos(f*x+e)^2*c^2*d^3+3*cos(f*x+e)^8*c^2*d^3+14*cos(f*x+e)^8*c*d^4-9*cos(f*x+e)^6*c^4*d-27*cos(f*x+e)^6*c^3*d^2-3*sin(f*x+e)*cos(f*x+e)^4*c^5+115*sin(f*x+e)*cos(f*x+e)^6*d^5-cos(f*x+e)^6*c^2*d^3-181*cos(f*x+e)^6*c*d^4+7*cos(f*x+e)^4*c^4*d-194*cos(f*x+e)^4*c^3*d^2+16*sin(f*x+e)*cos(f*x+e)^2*c^5+523*cos(f*x+e)^4*d^5-432*cos(f*x+e)^2*d^5-262*cos(f*x+e)^6*d^5-128*d^5*sin(f*x+e)+114*sin(f*x+e)*cos(f*x+e)^4*c^2*d^3+48*sin(f*x+e)*cos(f*x+e)^2*c^4*d+79*sin(f*x+e)*cos(f*x+e)^6*c*d^4+50*sin(f*x+e)*cos(f*x+e)^4*c^3*d^2+439*c*cos(f*x+e)^4*d^4+480*c^3*cos(f*x+e)^2*d^2-400*c*cos(f*x+e)^2*d^4+256*c^2*d^3*sin(f*x+e)-128*c*d^4*sin(f*x+e)-290*cos(f*x+e)^4*c^2*d^3+368*sin(f*x+e)*cos(f*x+e)^2*d^5-112*cos(f*x+e)^2*c^4*d-128*sin(f*x+e)*c^4*d+256*sin(f*x+e)*c^3*d^2+128*d^5+43*cos(f*x+e)^8*d^5-5*cos(f*x+e)^4*c^5-80*cos(f*x+e)^2*c^5+sin(f*x+e)*cos(f*x+e)^4*c^4*d+9*sin(f*x+e)*cos(f*x+e)^6*c^3*d^2+37*sin(f*x+e)*cos(f*x+e)^6*c^2*d^3+128*c^5-128*c^5*sin(f*x+e))/cos(f*x+e)^5/(cos(f*x+e)^2*d^2+c^2-d^2)^3/(c+d)^3","B"
586,1,1223,230,0.513000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(9/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(-35 \left(\cos^{4}\left(f x +e \right)\right) c^{7}+225 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c \,d^{6}+1408 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{4}+2392 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{5}-950 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c \,d^{6}+479 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{2}+1261 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{3}-4367 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{4}-7117 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{5}+1669 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{6}+368 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{6} d -3344 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{2}-5008 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{3}+4560 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{4}+7120 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{5}-1328 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{6}+2944 c^{4} d^{3} \sin \left(f x +e \right)-1664 c^{3} d^{4} \sin \left(f x +e \right)-2432 c^{2} d^{5} \sin \left(f x +e \right)+384 c \,d^{6} \sin \left(f x +e \right)-896 \sin \left(f x +e \right) c^{7}+44 \left(\cos^{10}\left(f x +e \right)\right) c \,d^{6}-21 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{7}-78 \left(\cos^{6}\left(f x +e \right)\right) c^{6} d -302 \left(\cos^{6}\left(f x +e \right)\right) c^{5} d^{2}-1555 \left(\cos^{8}\left(f x +e \right)\right) d^{7}-2176 c^{5} d^{2}+1664 c^{3} d^{4}+896 c^{7}-2944 c^{4} d^{3}+6480 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{3}+1520 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{6}+575 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) d^{7}-8336 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{5}-944 \left(\cos^{2}\left(f x +e \right)\right) c^{6} d -485 \left(\cos^{8}\left(f x +e \right)\right) c \,d^{6}-2350 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) d^{7}-172 \left(\cos^{6}\left(f x +e \right)\right) c^{4} d^{3}-2968 \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{4}-5370 \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{5}+1590 \left(\cos^{6}\left(f x +e \right)\right) c \,d^{6}+3615 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{7}+39 \left(\cos^{4}\left(f x +e \right)\right) c^{6} d -1879 \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{2}-3397 \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{3}+10373 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{5}-2285 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{6}+112 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{7}-2480 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{7}+4432 \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{2}-384 c \,d^{6}+2432 c^{2} d^{5}+230 \left(\cos^{10}\left(f x +e \right)\right) d^{7}+1152 c^{6} d -640 d^{7}+640 d^{7} \sin \left(f x +e \right)+3 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{3} d^{4}+37 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{5}+102 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{5} d^{2}+518 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{4} d^{3}+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{6} d +257 \left(\cos^{8}\left(f x +e \right)\right) c^{3} d^{4}+6 \left(\cos^{10}\left(f x +e \right)\right) c^{2} d^{5}+48 \left(\cos^{8}\left(f x +e \right)\right) c^{4} d^{3}-1152 \sin \left(f x +e \right) c^{6} d +2176 \sin \left(f x +e \right) c^{5} d^{2}+3940 \left(\cos^{6}\left(f x +e \right)\right) d^{7}+895 \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{5}-5392 \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{4}+6439 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{4}-4775 \left(\cos^{4}\left(f x +e \right)\right) d^{7}-560 \left(\cos^{2}\left(f x +e \right)\right) c^{7}+2800 \left(\cos^{2}\left(f x +e \right)\right) d^{7}\right)}{105 f \cos \left(f x +e \right)^{5} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{4} \left(c +d \right)^{4}}"," ",0,"-2/105/f*(a*(1+sin(f*x+e)))^(5/2)*(c+d*sin(f*x+e))^(1/2)*(2944*c^4*d^3*sin(f*x+e)-1664*c^3*d^4*sin(f*x+e)-2432*c^2*d^5*sin(f*x+e)+384*c*d^6*sin(f*x+e)+225*sin(f*x+e)*cos(f*x+e)^8*c*d^6+1408*sin(f*x+e)*cos(f*x+e)^6*c^3*d^4+2392*sin(f*x+e)*cos(f*x+e)^6*c^2*d^5-950*sin(f*x+e)*cos(f*x+e)^6*c*d^6+479*sin(f*x+e)*cos(f*x+e)^4*c^5*d^2+1261*sin(f*x+e)*cos(f*x+e)^4*c^4*d^3-4367*sin(f*x+e)*cos(f*x+e)^4*c^3*d^4-7117*sin(f*x+e)*cos(f*x+e)^4*c^2*d^5+1669*sin(f*x+e)*cos(f*x+e)^4*c*d^6+368*sin(f*x+e)*cos(f*x+e)^2*c^6*d-3344*sin(f*x+e)*cos(f*x+e)^2*c^5*d^2-5008*sin(f*x+e)*cos(f*x+e)^2*c^4*d^3+4560*sin(f*x+e)*cos(f*x+e)^2*c^3*d^4+7120*sin(f*x+e)*cos(f*x+e)^2*c^2*d^5-1328*sin(f*x+e)*cos(f*x+e)^2*c*d^6-896*sin(f*x+e)*c^7-1555*cos(f*x+e)^8*d^7+3940*cos(f*x+e)^6*d^7-4775*cos(f*x+e)^4*d^7-560*cos(f*x+e)^2*c^7+2800*cos(f*x+e)^2*d^7-2176*c^5*d^2+1664*c^3*d^4+896*c^7-2944*c^4*d^3-384*c*d^6+2432*c^2*d^5+1152*c^6*d-640*d^7+640*d^7*sin(f*x+e)-944*cos(f*x+e)^2*c^6*d+6480*cos(f*x+e)^2*c^4*d^3-5392*cos(f*x+e)^2*c^3*d^4-8336*cos(f*x+e)^2*c^2*d^5+1520*cos(f*x+e)^2*c*d^6-1152*sin(f*x+e)*c^6*d+2176*sin(f*x+e)*c^5*d^2+575*sin(f*x+e)*cos(f*x+e)^8*d^7+895*cos(f*x+e)^8*c^2*d^5-485*cos(f*x+e)^8*c*d^6-2350*sin(f*x+e)*cos(f*x+e)^6*d^7-172*cos(f*x+e)^6*c^4*d^3-2968*cos(f*x+e)^6*c^3*d^4-5370*cos(f*x+e)^6*c^2*d^5+1590*cos(f*x+e)^6*c*d^6+3615*sin(f*x+e)*cos(f*x+e)^4*d^7+39*cos(f*x+e)^4*c^6*d-1879*cos(f*x+e)^4*c^5*d^2-3397*cos(f*x+e)^4*c^4*d^3+6439*cos(f*x+e)^4*c^3*d^4+10373*cos(f*x+e)^4*c^2*d^5-2285*cos(f*x+e)^4*c*d^6+112*sin(f*x+e)*cos(f*x+e)^2*c^7-2480*sin(f*x+e)*cos(f*x+e)^2*d^7+4432*cos(f*x+e)^2*c^5*d^2+3*sin(f*x+e)*cos(f*x+e)^8*c^3*d^4+37*sin(f*x+e)*cos(f*x+e)^8*c^2*d^5+102*sin(f*x+e)*cos(f*x+e)^6*c^5*d^2+518*sin(f*x+e)*cos(f*x+e)^6*c^4*d^3+sin(f*x+e)*cos(f*x+e)^4*c^6*d+6*cos(f*x+e)^10*c^2*d^5+44*cos(f*x+e)^10*c*d^6+48*cos(f*x+e)^8*c^4*d^3+257*cos(f*x+e)^8*c^3*d^4-78*cos(f*x+e)^6*c^6*d-302*cos(f*x+e)^6*c^5*d^2-21*sin(f*x+e)*cos(f*x+e)^4*c^7-35*cos(f*x+e)^4*c^7+230*cos(f*x+e)^10*d^7)/cos(f*x+e)^5/(cos(f*x+e)^2*d^2+c^2-d^2)^4/(c+d)^4","B"
587,1,1730,287,0.563000," ","int((a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(11/2),x)","-\frac{2 \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(-279 \left(\cos^{6}\left(f x +e \right)\right) c^{8} d +11406 \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{6}-17010 \left(\cos^{6}\left(f x +e \right)\right) c^{5} d^{4}-35980 \left(\cos^{6}\left(f x +e \right)\right) c^{4} d^{5}-1482 \left(\cos^{6}\left(f x +e \right)\right) c^{6} d^{3}+13568 c^{4} d^{5}-4599 \left(\cos^{10}\left(f x +e \right)\right) d^{9}+14245 \left(\cos^{8}\left(f x +e \right)\right) d^{9}-22645 \left(\cos^{6}\left(f x +e \right)\right) d^{9}-105 \left(\cos^{4}\left(f x +e \right)\right) c^{9}+19695 \left(\cos^{4}\left(f x +e \right)\right) d^{9}-1680 \left(\cos^{2}\left(f x +e \right)\right) c^{9}-8944 \left(\cos^{2}\left(f x +e \right)\right) d^{9}+8010 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c \,d^{8}-15 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{8} d +1812 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{7} d^{2}+5380 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{6} d^{3}-22482 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{4}-44418 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{5}+13860 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{6}+38772 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{7}-9255 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c \,d^{8}+4224 c^{8} d -7168 c^{7} d^{2}+7424 c^{5} d^{4}-12288 c^{6} d^{3}-4224 \sin \left(f x +e \right) c^{8} d +7168 \sin \left(f x +e \right) c^{7} d^{2}+12288 \sin \left(f x +e \right) c^{6} d^{3}-7424 \sin \left(f x +e \right) c^{5} d^{4}-13568 \sin \left(f x +e \right) c^{4} d^{5}+4096 \sin \left(f x +e \right) c^{3} d^{6}+7168 \sin \left(f x +e \right) c^{2} d^{7}-1152 \sin \left(f x +e \right) c \,d^{8}+1664 d^{9}+8 \left(\cos^{12}\left(f x +e \right)\right) c^{2} d^{7}-4096 d^{6} c^{3}-7168 d^{7} c^{2}+1152 d^{8} c +2688 c^{9}-15847 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) d^{9}+63090 \left(\cos^{4}\left(f x +e \right)\right) c^{4} d^{5}-15204 \left(\cos^{4}\left(f x +e \right)\right) c^{6} d^{3}+31650 \left(\cos^{4}\left(f x +e \right)\right) c^{5} d^{4}-7220 \left(\cos^{4}\left(f x +e \right)\right) c^{7} d^{2}-63 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right) c^{9}+87 \left(\cos^{4}\left(f x +e \right)\right) c^{8} d -19908 \left(\cos^{4}\left(f x +e \right)\right) c^{3} d^{6}-51540 \left(\cos^{4}\left(f x +e \right)\right) c^{2} d^{7}+11711 \left(\cos^{4}\left(f x +e \right)\right) c \,d^{8}+15474 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) d^{9}-1310 \left(\cos^{6}\left(f x +e \right)\right) c^{7} d^{2}+41570 \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{7}-11902 \left(\cos^{6}\left(f x +e \right)\right) c \,d^{8}+8112 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) d^{9}+336 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{9}+80 \left(\cos^{12}\left(f x +e \right)\right) c \,d^{8}-3312 \left(\cos^{2}\left(f x +e \right)\right) c^{8} d +15168 \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{6}-23904 \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{4}-47520 \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{5}+28864 \left(\cos^{2}\left(f x +e \right)\right) c^{6} d^{3}-7535 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) d^{9}+16192 \left(\cos^{2}\left(f x +e \right)\right) c^{7} d^{2}+30912 \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{7}-5776 \left(\cos^{2}\left(f x +e \right)\right) c \,d^{8}+310 \left(\cos^{8}\left(f x +e \right)\right) c^{6} d^{3}+1875 \left(\cos^{8}\left(f x +e \right)\right) c^{5} d^{4}+6805 \left(\cos^{8}\left(f x +e \right)\right) c^{4} d^{5}-2930 \left(\cos^{8}\left(f x +e \right)\right) c^{3} d^{6}-16320 \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{7}+6095 \left(\cos^{8}\left(f x +e \right)\right) c \,d^{8}+37 \left(\cos^{10}\left(f x +e \right)\right) c^{4} d^{5}-1360 \left(\cos^{10}\left(f x +e \right)\right) c \,d^{8}+2538 \left(\cos^{10}\left(f x +e \right)\right) c^{2} d^{7}+1460 \sin \left(f x +e \right) \left(\cos^{10}\left(f x +e \right)\right) d^{9}+360 \left(\cos^{10}\left(f x +e \right)\right) c^{3} d^{6}+584 \left(\cos^{12}\left(f x +e \right)\right) d^{9}+4 \sin \left(f x +e \right) \left(\cos^{10}\left(f x +e \right)\right) c^{3} d^{6}+60 \sin \left(f x +e \right) \left(\cos^{10}\left(f x +e \right)\right) c^{2} d^{7}+492 \sin \left(f x +e \right) \left(\cos^{10}\left(f x +e \right)\right) c \,d^{8}-35 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{5} d^{4}+5 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{4} d^{5}+1650 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{3} d^{6}+5850 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c^{2} d^{7}-3295 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) c \,d^{8}+1200 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{8} d -12608 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{7} d^{2}-22720 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{6} d^{3}+20192 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{5} d^{4}+40736 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{4} d^{5}-13120 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{3} d^{6}-27328 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c^{2} d^{7}+5200 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) c \,d^{8}+458 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{7} d^{2}+2730 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{6} d^{3}+8774 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{5} d^{4}+17070 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{4} d^{5}-6490 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{3} d^{6}-24522 \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) c^{2} d^{7}-2688 \sin \left(f x +e \right) c^{9}-1664 \sin \left(f x +e \right) d^{9}\right)}{315 f \cos \left(f x +e \right)^{5} \left(\left(\cos^{2}\left(f x +e \right)\right) d^{2}+c^{2}-d^{2}\right)^{5} \left(c +d \right)^{5}}"," ",0,"-2/315/f*(a*(1+sin(f*x+e)))^(5/2)*(c+d*sin(f*x+e))^(1/2)*(8*cos(f*x+e)^12*c^2*d^7+13568*c^4*d^5+4224*c^8*d-7168*c^7*d^2+7424*c^5*d^4+15474*sin(f*x+e)*cos(f*x+e)^6*d^9-12288*c^6*d^3-279*cos(f*x+e)^6*c^8*d-1310*cos(f*x+e)^6*c^7*d^2-1482*cos(f*x+e)^6*c^6*d^3-17010*cos(f*x+e)^6*c^5*d^4-35980*cos(f*x+e)^6*c^4*d^5+11406*cos(f*x+e)^6*c^3*d^6+41570*cos(f*x+e)^6*c^2*d^7-11902*cos(f*x+e)^6*c*d^8-63*sin(f*x+e)*cos(f*x+e)^4*c^9-15847*sin(f*x+e)*cos(f*x+e)^4*d^9+87*cos(f*x+e)^4*c^8*d-7220*cos(f*x+e)^4*c^7*d^2-15204*cos(f*x+e)^4*c^6*d^3+31650*cos(f*x+e)^4*c^5*d^4+63090*cos(f*x+e)^4*c^4*d^5-19908*cos(f*x+e)^4*c^3*d^6-51540*cos(f*x+e)^4*c^2*d^7+11711*cos(f*x+e)^4*c*d^8+336*sin(f*x+e)*cos(f*x+e)^2*c^9+8112*sin(f*x+e)*cos(f*x+e)^2*d^9+80*cos(f*x+e)^12*c*d^8+1460*sin(f*x+e)*cos(f*x+e)^10*d^9+37*cos(f*x+e)^10*c^4*d^5+360*cos(f*x+e)^10*c^3*d^6+2538*cos(f*x+e)^10*c^2*d^7-1360*cos(f*x+e)^10*c*d^8-7535*sin(f*x+e)*cos(f*x+e)^8*d^9-3312*cos(f*x+e)^2*c^8*d+16192*cos(f*x+e)^2*c^7*d^2+28864*cos(f*x+e)^2*c^6*d^3-23904*cos(f*x+e)^2*c^5*d^4-47520*cos(f*x+e)^2*c^4*d^5+15168*cos(f*x+e)^2*c^3*d^6+30912*cos(f*x+e)^2*c^2*d^7-5776*cos(f*x+e)^2*c*d^8-4224*sin(f*x+e)*c^8*d+7168*sin(f*x+e)*c^7*d^2+12288*sin(f*x+e)*c^6*d^3-7424*sin(f*x+e)*c^5*d^4-13568*sin(f*x+e)*c^4*d^5+4096*sin(f*x+e)*c^3*d^6+7168*sin(f*x+e)*c^2*d^7-1152*sin(f*x+e)*c*d^8+310*cos(f*x+e)^8*c^6*d^3+1875*cos(f*x+e)^8*c^5*d^4+6805*cos(f*x+e)^8*c^4*d^5+4*sin(f*x+e)*cos(f*x+e)^10*c^3*d^6+60*sin(f*x+e)*cos(f*x+e)^10*c^2*d^7+492*sin(f*x+e)*cos(f*x+e)^10*c*d^8-35*sin(f*x+e)*cos(f*x+e)^8*c^5*d^4+5*sin(f*x+e)*cos(f*x+e)^8*c^4*d^5+1650*sin(f*x+e)*cos(f*x+e)^8*c^3*d^6+1664*d^9-4096*d^6*c^3-7168*d^7*c^2+1152*d^8*c+5850*sin(f*x+e)*cos(f*x+e)^8*c^2*d^7-3295*sin(f*x+e)*cos(f*x+e)^8*c*d^8+1200*sin(f*x+e)*cos(f*x+e)^2*c^8*d-12608*sin(f*x+e)*cos(f*x+e)^2*c^7*d^2-22720*sin(f*x+e)*cos(f*x+e)^2*c^6*d^3+20192*sin(f*x+e)*cos(f*x+e)^2*c^5*d^4+40736*sin(f*x+e)*cos(f*x+e)^2*c^4*d^5-13120*sin(f*x+e)*cos(f*x+e)^2*c^3*d^6-27328*sin(f*x+e)*cos(f*x+e)^2*c^2*d^7+5200*sin(f*x+e)*cos(f*x+e)^2*c*d^8+458*sin(f*x+e)*cos(f*x+e)^6*c^7*d^2+2730*sin(f*x+e)*cos(f*x+e)^6*c^6*d^3+8774*sin(f*x+e)*cos(f*x+e)^6*c^5*d^4+17070*sin(f*x+e)*cos(f*x+e)^6*c^4*d^5-6490*sin(f*x+e)*cos(f*x+e)^6*c^3*d^6-24522*sin(f*x+e)*cos(f*x+e)^6*c^2*d^7+8010*sin(f*x+e)*cos(f*x+e)^6*c*d^8-15*sin(f*x+e)*cos(f*x+e)^4*c^8*d+1812*sin(f*x+e)*cos(f*x+e)^4*c^7*d^2+5380*sin(f*x+e)*cos(f*x+e)^4*c^6*d^3-22482*sin(f*x+e)*cos(f*x+e)^4*c^5*d^4-44418*sin(f*x+e)*cos(f*x+e)^4*c^4*d^5+13860*sin(f*x+e)*cos(f*x+e)^4*c^3*d^6+38772*sin(f*x+e)*cos(f*x+e)^4*c^2*d^7-9255*sin(f*x+e)*cos(f*x+e)^4*c*d^8+2688*c^9-2930*cos(f*x+e)^8*c^3*d^6-16320*cos(f*x+e)^8*c^2*d^7+6095*cos(f*x+e)^8*c*d^8+584*cos(f*x+e)^12*d^9-4599*cos(f*x+e)^10*d^9+14245*cos(f*x+e)^8*d^9-22645*cos(f*x+e)^6*d^9-105*cos(f*x+e)^4*c^9+19695*cos(f*x+e)^4*d^9-1680*cos(f*x+e)^2*c^9-8944*cos(f*x+e)^2*d^9-2688*sin(f*x+e)*c^9-1664*sin(f*x+e)*d^9)/cos(f*x+e)^5/(cos(f*x+e)^2*d^2+c^2-d^2)^5/(c+d)^5","B"
588,-2,0,208,180.000000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","F"
589,0,0,157,0.481000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","F"
590,1,3359,114,0.444000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/2/f*(-2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d*sin(f*x+e)+2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^2*sin(f*x+e)-2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3*sin(f*x+e)-cos(f*x+e)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d+2*cos(f*x+e)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2-cos(f*x+e)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3-2*(d^2/c^2)^(1/2)*c^3*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d*cos(f*x+e)+4*(d^2/c^2)^(1/2)*c^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^2*cos(f*x+e)-2*(d^2/c^2)^(1/2)*c*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^3*cos(f*x+e)-2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d+2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2-2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3+2*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(d^2/c^2)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*sin(f*x+e)+2*c^2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^2*cos(f*x+e)-4*c*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^3*cos(f*x+e)+2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*d^4*cos(f*x+e)+2*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d*sin(f*x+e)+2*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(d^2/c^2)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))+2*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*d)/(a*(1+sin(f*x+e)))^(1/2)/(c+d*sin(f*x+e))^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2)/d/(c^2-2*c*d+d^2)","B"
591,1,191,64,0.233000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","-\frac{\left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{c +d \sin \left(f x +e \right)}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{2 c -2 d}}"," ",0,"-1/f*(1-cos(f*x+e)+sin(f*x+e))*(c+d*sin(f*x+e))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)*2^(1/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/(2*c-2*d)^(1/2)","B"
592,1,874,112,0.343000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x)","-\frac{\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c \sin \left(f x +e \right)+\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d \sin \left(f x +e \right)+\cos \left(f x +e \right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c +\cos \left(f x +e \right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d -2 d \sqrt{2 c -2 d}\, \cos \left(f x +e \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \left(c +d \right) \sqrt{2 c -2 d}\, \left(c -d \right)}"," ",0,"-1/f*(ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*sin(f*x+e)+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d*sin(f*x+e)+cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c+cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d-2*d*(2*c-2*d)^(1/2)*cos(f*x+e))/(a*(1+sin(f*x+e)))^(1/2)/(c+d*sin(f*x+e))^(1/2)/(c+d)/(2*c-2*d)^(1/2)/(c-d)","B"
593,1,2572,164,0.366000," ","int(1/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/3/f*(-3*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2*d-6*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d^2-3*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3+3*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2*d+6*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d^2+3*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3-3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-9*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-9*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-3*sin(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3-3*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^3-6*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)-3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)+10*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d^2+2*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*d^3-3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^3-9*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)-9*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)-3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)+12*cos(f*x+e)*(2*c-2*d)^(1/2)*c^2*d+2*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d^2-2*cos(f*x+e)*(2*c-2*d)^(1/2)*d^3)*(c+d*sin(f*x+e))^(1/2)/(-cos(f*x+e)^2*d^2+2*c*d*sin(f*x+e)+c^2+d^2)/(a*(1+sin(f*x+e)))^(1/2)/(c+d)^2/(2*c-2*d)^(1/2)/(c-d)^2","B"
594,0,0,210,0.553000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","F"
595,1,6681,159,0.474000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
596,1,1373,103,0.332000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2 c -2 d}\, c +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2 c -2 d}\, d +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2 c -2 d}\, c +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2 c -2 d}\, d -2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) \sqrt{2 c -2 d}\, c -2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sin \left(f x +e \right) \sqrt{2 c -2 d}\, d +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \cos \left(f x +e \right) \sqrt{2 c -2 d}\, c +\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \cos \left(f x +e \right) \sqrt{2 c -2 d}\, d -2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{2 c -2 d}\, c -2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{2 c -2 d}\, d -4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \cos \left(f x +e \right) c +4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \cos \left(f x +e \right) d \right) \sqrt{c +d \sin \left(f x +e \right)}}{8 f \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(c -d \right)}"," ",0,"1/8/f*(ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*d+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*c+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*d-2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*sin(f*x+e)*(2*c-2*d)^(1/2)*c-2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*sin(f*x+e)*(2*c-2*d)^(1/2)*d+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*cos(f*x+e)*(2*c-2*d)^(1/2)*c+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*cos(f*x+e)*(2*c-2*d)^(1/2)*d-2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*(2*c-2*d)^(1/2)*c-2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*(2*c-2*d)^(1/2)*d-4*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*c+4*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*d)*(c+d*sin(f*x+e))^(1/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/(c-d)","B"
597,1,1268,112,0.331000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x)","-\frac{\left(-\sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c +3 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d -\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c +3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d +2 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2 c -2 d}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+2 \sin \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c -6 \sin \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d -\cos \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c +3 \cos \left(f x +e \right) \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d +2 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c -6 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d \right) \sqrt{c +d \sin \left(f x +e \right)}}{4 f \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{2 c -2 d}\, \left(c -d \right)}"," ",0,"-1/4/f*(-sin(f*x+e)*cos(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c+3*sin(f*x+e)*cos(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d-cos(f*x+e)^2*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c+3*cos(f*x+e)^2*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d+2*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)+2*sin(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c-6*sin(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d-cos(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c+3*cos(f*x+e)*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d+2*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c-6*2^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/(2*c-2*d)^(1/2)/(c-d)","B"
598,1,2246,168,0.373000," ","int(1/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x)","-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c^{2}-6 \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c d -7 \sin \left(f x +e \right) \cos \left(f x +e \right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d^{2}-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c^{2}+6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c d +7 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d^{2}+2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c^{2} \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-12 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c d \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-14 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d^{2} \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+\ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c^{2} \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right)-6 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c d \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right)-7 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) d^{2} \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2 c -2 d}\, c d +10 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{2 c -2 d}\, d^{2}+2 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, c^{2}-12 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) c d \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-14 \ln \left(\frac{2 \sqrt{2 c -2 d}\, \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+2 c \sin \left(f x +e \right)-2 d \sin \left(f x +e \right)+2 c \cos \left(f x +e \right)-2 d \cos \left(f x +e \right)-2 c +2 d}{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}\right) \sqrt{2}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, d^{2}+2 \cos \left(f x +e \right) \sqrt{2 c -2 d}\, c^{2}+2 \cos \left(f x +e \right) \sqrt{2 c -2 d}\, c d +8 \cos \left(f x +e \right) \sqrt{2 c -2 d}\, d^{2}}{4 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{c +d \sin \left(f x +e \right)}\, \left(c +d \right) \sqrt{2 c -2 d}\, \left(c -d \right)^{2}}"," ",0,"-1/4/f*(sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-6*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d-7*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2-cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2+6*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d+7*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2+2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-12*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-14*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)-6*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)-7*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)+2*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d+10*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*d^2+2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-12*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)-14*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2+2*cos(f*x+e)*(2*c-2*d)^(1/2)*c^2+2*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d+8*cos(f*x+e)*(2*c-2*d)^(1/2)*d^2)/(a*(1+sin(f*x+e)))^(3/2)/(c+d*sin(f*x+e))^(1/2)/(c+d)/(2*c-2*d)^(1/2)/(c-d)^2","B"
599,1,5040,236,0.411000," ","int(1/(a+a*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"
600,1,10738,219,0.616000," ","int((c+d*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
601,1,3050,155,0.361000," ","int((c+d*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"1/64/f*(12*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-12*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-28*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2+12*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2-12*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-12*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-28*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2+3*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+3*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+28*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2+9*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+9*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-12*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-12*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+6*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+6*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+16*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d+16*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d-16*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d-6*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+6*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+6*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+18*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-24*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+12*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+6*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+12*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-24*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-3*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-3*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/(c-d)","B"
602,1,3050,162,0.364000," ","int((c+d*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"1/64/f*(12*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-12*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-28*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2-20*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2-12*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+20*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+4*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2-5*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+3*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-4*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^2+9*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-15*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-12*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+20*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+6*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-10*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+48*sin(f*x+e)*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d-16*cos(f*x+e)^3*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d+16*cos(f*x+e)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d+2*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+6*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-10*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-6*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+8*sin(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-4*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-2*sin(f*x+e)*cos(f*x+e)^2*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-4*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+8*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-3*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+5*cos(f*x+e)^3*(2*c-2*d)^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/(c-d)^2","B"
603,1,2805,172,0.357000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/32/f*(-12*sin(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-76*sin(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+6*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+38*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+40*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+6*cos(f*x+e)^3*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c-18*cos(f*x+e)^3*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d-10*sin(f*x+e)*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-20*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-6*cos(f*x+e)*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c+18*cos(f*x+e)*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d-3*cos(f*x+e)^3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-19*cos(f*x+e)^3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+9*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+57*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-12*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2-76*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-20*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+3*sin(f*x+e)*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+19*sin(f*x+e)*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2+10*cos(f*x+e)^3*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d+6*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c^2+38*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*d^2-30*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d-14*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c+26*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d+40*sin(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*c*d)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)/(2*c-2*d)^(1/2)/(c-d)^2","B"
604,1,4262,235,0.373000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/32/f*(-15*cos(f*x+e)^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d-98*cos(f*x+e)^3*(2*c-2*d)^(1/2)*d^3+162*cos(f*x+e)*(2*c-2*d)^(1/2)*d^3+22*cos(f*x+e)*(2*c-2*d)^(1/2)*c^2*d+70*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d^2-150*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3-14*cos(f*x+e)*(2*c-2*d)^(1/2)*c^3-45*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2*d+171*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d^2+60*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-228*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+30*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)-114*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)+170*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*d^3-12*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^3-300*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)+6*cos(f*x+e)^3*(2*c-2*d)^(1/2)*c^2*d-28*cos(f*x+e)^3*(2*c-2*d)^(1/2)*c*d^2-6*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c^3+57*cos(f*x+e)^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2-6*sin(f*x+e)*cos(f*x+e)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3+3*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3+75*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3+3*cos(f*x+e)^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3+75*cos(f*x+e)^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3+9*cos(f*x+e)^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3+14*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c^2*d-150*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*d^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)+225*cos(f*x+e)^2*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3-12*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^3*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-300*sin(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*d^3-6*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^3+62*sin(f*x+e)*cos(f*x+e)*(2*c-2*d)^(1/2)*c*d^2+60*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)-228*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)-15*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c^2*d+57*sin(f*x+e)*cos(f*x+e)^2*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*c*d^2+30*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c^2*d-114*sin(f*x+e)*cos(f*x+e)*ln(2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(1-cos(f*x+e)+sin(f*x+e)))*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*c*d^2)/(a*(1+sin(f*x+e)))^(5/2)/(c+d*sin(f*x+e))^(1/2)/(c+d)/(2*c-2*d)^(1/2)/(c-d)^3","B"
605,1,8035,314,0.404000," ","int(1/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
606,0,0,117,2.018000," ","int((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)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
607,0,0,308,6.748000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x)","F"
608,0,0,181,6.609000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","F"
609,0,0,105,2.117000," ","int((a+a*sin(f*x+e))^m*(c+d*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)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x)","F"
610,0,0,62,0.009000," ","int((a+a*sin(f*x+e))^m,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m,x)","F"
611,0,0,88,1.412000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","F"
612,0,0,88,1.845000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","F"
613,0,0,88,2.003000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","F"
614,0,0,120,0.295000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x)","F"
615,0,0,118,0.294000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x)","F"
616,0,0,113,0.285000," ","int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x)","F"
617,0,0,113,0.286000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c +d \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x)","F"
618,0,0,120,0.237000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x)","F"
619,0,0,120,0.250000," ","int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x)","\int \frac{\left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x)","F"
620,0,0,58,0.622000," ","int((1+sin(f*x+e))^m*(3+5*sin(f*x+e))^(-1-m),x)","\int \left(1+\sin \left(f x +e \right)\right)^{m} \left(3+5 \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((1+sin(f*x+e))^m*(3+5*sin(f*x+e))^(-1-m),x)","F"
621,0,0,58,0.668000," ","int((1+sin(f*x+e))^m*(3+4*sin(f*x+e))^(-1-m),x)","\int \left(1+\sin \left(f x +e \right)\right)^{m} \left(3+4 \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((1+sin(f*x+e))^m*(3+4*sin(f*x+e))^(-1-m),x)","F"
622,0,0,28,0.513000," ","int((1+sin(f*x+e))^m*(3+3*sin(f*x+e))^(-1-m),x)","\int \left(1+\sin \left(f x +e \right)\right)^{m} \left(3+3 \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((1+sin(f*x+e))^m*(3+3*sin(f*x+e))^(-1-m),x)","F"
623,0,0,110,0.675000," ","int((1+sin(f*x+e))^m*(3+2*sin(f*x+e))^(-1-m),x)","\int \left(1+\sin \left(f x +e \right)\right)^{m} \left(3+2 \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((1+sin(f*x+e))^m*(3+2*sin(f*x+e))^(-1-m),x)","F"
624,0,0,98,0.654000," ","int((1+sin(f*x+e))^m*(3+sin(f*x+e))^(-1-m),x)","\int \left(1+\sin \left(f x +e \right)\right)^{m} \left(3+\sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((1+sin(f*x+e))^m*(3+sin(f*x+e))^(-1-m),x)","F"
625,0,0,53,0.533000," ","int(3^(-1-m)*(1+sin(f*x+e))^m,x)","\int 3^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(3^(-1-m)*(1+sin(f*x+e))^m,x)","F"
626,0,0,92,0.869000," ","int((3-sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","\int \left(3-\sin \left(f x +e \right)\right)^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","F"
627,0,0,108,0.745000," ","int((3-2*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","\int \left(3-2 \sin \left(f x +e \right)\right)^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-2*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","F"
628,0,0,43,0.779000," ","int((3-3*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","\int \left(3-3 \sin \left(f x +e \right)\right)^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-3*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","F"
629,0,0,81,0.780000," ","int((3-4*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","\int \left(3-4 \sin \left(f x +e \right)\right)^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-4*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","F"
630,0,0,76,0.685000," ","int((3-5*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","\int \left(3-5 \sin \left(f x +e \right)\right)^{-1-m} \left(1+\sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-5*sin(f*x+e))^(-1-m)*(1+sin(f*x+e))^m,x)","F"
631,0,0,77,0.575000," ","int((3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3+5 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
632,0,0,77,0.617000," ","int((3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3+4 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
633,0,0,39,0.530000," ","int((3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3+3 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
634,0,0,78,0.557000," ","int((3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3+2 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
635,0,0,78,0.598000," ","int((3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3+\sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
636,0,0,69,0.597000," ","int(3^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int 3^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(3^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
637,0,0,70,0.645000," ","int((3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3-\sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
638,0,0,75,0.623000," ","int((3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3-2 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
639,0,0,45,0.636000," ","int((3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3-3 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
640,0,0,112,0.639000," ","int((3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3-4 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
641,0,0,108,0.634000," ","int((3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(3-5 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
642,0,0,70,0.567000," ","int((-3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3+5 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3+5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
643,0,0,75,0.596000," ","int((-3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3+4 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3+4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
644,0,0,45,0.633000," ","int((-3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3+3 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3+3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
645,0,0,110,0.585000," ","int((-3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3+2 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3+2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
646,0,0,107,0.597000," ","int((-3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3+\sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3+sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
647,0,0,69,0.666000," ","int((-3)^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3)^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
648,0,0,108,0.733000," ","int((-3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3-\sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3-sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
649,0,0,110,0.714000," ","int((-3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3-2 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3-2*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
650,0,0,39,0.641000," ","int((-3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3-3 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3-3*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
651,0,0,112,0.740000," ","int((-3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3-4 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3-4*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
652,0,0,109,0.682000," ","int((-3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(-3-5 \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((-3-5*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
653,0,0,114,0.563000," ","int((d*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","\int \left(d \sin \left(f x +e \right)\right)^{-1-m} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*sin(f*x+e))^(-1-m)*(a+a*sin(f*x+e))^m,x)","F"
654,0,0,119,0.635000," ","int((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)^{m} \left(c +d \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x)","F"
655,0,0,93,1.286000," ","int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{3} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","F"
656,0,0,93,1.382000," ","int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
657,0,0,91,0.523000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \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))*(c+d*sin(f*x+e))^n,x)","F"
658,0,0,90,0.727000," ","int((c+d*sin(f*x+e))^n,x)","\int \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((c+d*sin(f*x+e))^n,x)","F"
659,0,0,93,0.734000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
660,0,0,93,1.471000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\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((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
661,0,0,93,1.470000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","F"
662,0,0,249,0.354000," ","int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^n,x)","F"
663,0,0,154,0.267000," ","int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^n,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^(3/2)*(c+d*sin(f*x+e))^n,x)","F"
664,0,0,81,0.314000," ","int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^n,x)","\int \sqrt{a +a \sin \left(f x +e \right)}\, \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^n,x)","F"
665,0,0,89,0.257000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{n}}{\sqrt{a +a \sin \left(f x +e \right)}}\, dx"," ",0,"int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x)","F"
666,0,0,92,0.254000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","\int \frac{\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((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x)","F"
667,0,0,92,0.249000," ","int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(5/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(5/2),x)","F"
668,0,0,87,0.419000," ","int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/3),x)","\int \left(a +a \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((a+a*sin(f*x+e))*(c+d*sin(f*x+e))^(1/3),x)","F"
669,0,0,87,0.810000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/3),x)","\int \frac{a +a \sin \left(f x +e \right)}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(1/3),x)","F"
670,0,0,92,0.359000," ","int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(4/3),x)","\int \frac{a +a \sin \left(f x +e \right)}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+a*sin(f*x+e))/(c+d*sin(f*x+e))^(4/3),x)","F"
671,1,182,161,0.262000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^3,x)","\frac{a \,c^{3} \left(f x +e \right)-3 a \,c^{2} d \cos \left(f x +e \right)+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)-\frac{a \,d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-b \,c^{3} \cos \left(f x +e \right)+3 b \,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)-c \,d^{2} b \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+b \,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*c^3*(f*x+e)-3*a*c^2*d*cos(f*x+e)+3*a*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)-b*c^3*cos(f*x+e)+3*b*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-c*d^2*b*(2+sin(f*x+e)^2)*cos(f*x+e)+b*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"
672,1,115,98,0.190000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^2,x)","\frac{c^{2} a \left(f x +e \right)-2 a c d \cos \left(f x +e \right)+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 \,c^{2} \cos \left(f x +e \right)+2 b 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{d^{2} b \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(c^2*a*(f*x+e)-2*a*c*d*cos(f*x+e)+a*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-b*c^2*cos(f*x+e)+2*b*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*d^2*b*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
673,1,59,49,0.089000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{b d \left(-\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)-d a \cos \left(f x +e \right)-c b \cos \left(f x +e \right)+a c \left(f x +e \right)}{f}"," ",0,"1/f*(b*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-d*a*cos(f*x+e)-c*b*cos(f*x+e)+a*c*(f*x+e))","A"
674,1,17,16,0.012000," ","int(a+b*sin(f*x+e),x)","a x -\frac{b \cos \left(f x +e \right)}{f}"," ",0,"a*x-b*cos(f*x+e)/f","A"
675,1,119,60,0.131000," ","int((a+b*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}{f \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) c b}{f d \sqrt{c^{2}-d^{2}}}+\frac{2 b \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d}"," ",0,"2/f/(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/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*b+2/f*b/d*arctan(tan(1/2*f*x+1/2*e))","A"
676,1,309,93,0.231000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{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) \left(c^{2}-d^{2}\right) c}-\frac{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) \left(c^{2}-d^{2}\right)}+\frac{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) \left(c^{2}-d^{2}\right)}-\frac{2 c 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 \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 a}{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) b d}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}"," ",0,"2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d^2/(c^2-d^2)/c*tan(1/2*f*x+1/2*e)*a-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)*d/(c^2-d^2)*tan(1/2*f*x+1/2*e)*b+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)*d*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^2-d^2)*c*b+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))*c*a-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))*b*d","B"
677,1,1291,155,0.276000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\frac{5 d^{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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 d^{4} \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} c \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{3 d \,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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{4 c^{2} \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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{7 \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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a \,d^{5}}{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^{4}-2 c^{2} d^{2}+d^{4}\right) c^{2}}-\frac{2 c^{3} \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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{5 c \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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b \,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^{4}-2 c^{2} d^{2}+d^{4}\right) c}+\frac{11 d^{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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 d^{4} \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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{5 d \,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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{4 d^{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)^{2} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{4 c^{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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{d^{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)^{2} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 b \,c^{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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{c \,d^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\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) c^{2} a}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}+\frac{\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}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}-\frac{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 d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}"," ",0,"5/f/(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/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^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*d^4/c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^3*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*d*c^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^3*b+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a*d+7/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a*d^3-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2*a*d^5-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*b-5/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*b*d^2-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^2*b*d^4+11/f/(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/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*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*d^4/c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a-5/f/(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/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b-4/f/(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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*d*a-1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*d^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^4-2*c^2*d^2+d^4)*b*c^3-1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*d^2*b+2/f/(c^4-2*c^2*d^2+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))*c^2*a+1/f/(c^4-2*c^2*d^2+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))*a*d^2-3/f/(c^4-2*c^2*d^2+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*d","B"
678,1,325,302,0.312000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^3,x)","\frac{a^{2} c^{3} \left(f x +e \right)-3 a^{2} c^{2} d \cos \left(f x +e \right)+3 a^{2} 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} d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-2 a b \,c^{3} \cos \left(f x +e \right)+6 a b \,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 b c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+2 a b \,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^{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)-b^{2} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 b^{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{b^{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}}{f}"," ",0,"1/f*(a^2*c^3*(f*x+e)-3*a^2*c^2*d*cos(f*x+e)+3*a^2*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^2*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)-2*a*b*c^3*cos(f*x+e)+6*a*b*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*b*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*a*b*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^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-b^2*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*b^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)-1/5*b^2*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e))","A"
679,1,216,207,0.263000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^2,x)","\frac{a^{2} c^{2} \left(f x +e \right)-2 a^{2} c d \cos \left(f x +e \right)+a^{2} 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)-2 a b \,c^{2} \cos \left(f x +e \right)+4 a b 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 b \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+b^{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{2 b^{2} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+b^{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)}{f}"," ",0,"1/f*(a^2*c^2*(f*x+e)-2*a^2*c*d*cos(f*x+e)+a^2*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*b*c^2*cos(f*x+e)+4*a*b*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*a*b*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+b^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2/3*b^2*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+b^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"
680,1,115,99,0.197000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e)),x)","\frac{a^{2} c \left(f x +e \right)-a^{2} d \cos \left(f x +e \right)-2 a b c \cos \left(f x +e \right)+2 a b 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^{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{b^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}}{f}"," ",0,"1/f*(a^2*c*(f*x+e)-a^2*d*cos(f*x+e)-2*a*b*c*cos(f*x+e)+2*a*b*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+b^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*b^2*d*(2+sin(f*x+e)^2)*cos(f*x+e))","A"
681,1,51,46,0.097000," ","int((a+b*sin(f*x+e))^2,x)","\frac{b^{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 b \cos \left(f x +e \right)+a^{2} \left(f x +e \right)}{f}"," ",0,"1/f*(b^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*b*cos(f*x+e)+a^2*(f*x+e))","A"
682,1,226,88,0.199000," ","int((a+b*sin(f*x+e))^2/(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)}{f \sqrt{c^{2}-d^{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) a b c}{f d \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^{2} c^{2}}{f \,d^{2} \sqrt{c^{2}-d^{2}}}-\frac{2 b^{2}}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{4 b \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f d}-\frac{2 b^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{2}}"," ",0,"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))-4/f/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*b*c+2/f/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*c^2-2/f*b^2/d/(1+tan(1/2*f*x+1/2*e)^2)+4/f*b/d*arctan(tan(1/2*f*x+1/2*e))*a-2/f*b^2/d^2*arctan(tan(1/2*f*x+1/2*e))*c","B"
683,1,556,124,0.257000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x)","\frac{2 d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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) c}-\frac{4 d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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{2 d \,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{4 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 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 \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^{2} c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{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) 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) 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^{2} c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,d^{2}}"," ",0,"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^2-4/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*b+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)*b^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^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*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)*b^2*c^2+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^2*c-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*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))*b^2*c^3+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))*b^2*c+2/f*b^2/d^2*arctan(tan(1/2*f*x+1/2*e))","B"
684,1,1923,187,0.276000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x)","-\frac{c^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) 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)^{2} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{4 a^{2} c^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{4 a b \,c^{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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{3 b^{2} c^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{c^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{2} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{7 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{6 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{10 c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{4 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a b \,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^{4}-2 c^{2} d^{2}+d^{4}\right) c}-\frac{10 c \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{6 c^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\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) a b c d}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}+\frac{5 c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right) c}+\frac{2 c \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{4 c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} d^{5}}{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^{4}-2 c^{2} d^{2}+d^{4}\right) c^{2}}-\frac{4 c^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) 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)^{2} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{3 c^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{11 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\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^{2} c^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}+\frac{\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^{2} d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}+\frac{\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^{2} c^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\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^{2} d^{2}}{f \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{c^{2}-d^{2}}}-\frac{a^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a^{2} 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} c \left(c^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{8 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a 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^{4}-2 c^{2} d^{2}+d^{4}\right)}+\frac{10 c \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{2} 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^{4}-2 c^{2} d^{2}+d^{4}\right)}-\frac{2 a b c \,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^{4}-2 c^{2} d^{2}+d^{4}\right)}"," ",0,"-8/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b*d^3+10/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^2*d^2-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c*d^2-6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^3*a*b*d-10/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b*d-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^2*a*b*d^4-6/f/(c^4-2*c^2*d^2+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))*a*b*c*d-10/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*a*b*d^2-1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2*d^3-1/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*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)^2/(c^4-2*c^2*d^2+d^4)*a^2*c^2*d-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c^3+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^4-2*c^2*d^2+d^4)*b^2*c^2*d+2/f/(c^4-2*c^2*d^2+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))*a^2*c^2+1/f/(c^4-2*c^2*d^2+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))*a^2*d^2+1/f/(c^4-2*c^2*d^2+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^2*c^2+2/f/(c^4-2*c^2*d^2+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^2*d^2+1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^3*b^2+7/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a^2*d^3+6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*b^2*d^3+5/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*a^2*d^2-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^3*a^2*d^4+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^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*b^2*d^2+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a^2*d-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^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2*a^2*d^5-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*a*b+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^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*b^2*d+11/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2*d^2-2/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2*d^4","B"
685,1,4818,294,0.330000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^4,x)","\text{output too large to display}"," ",0,"2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a^2*d^6+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/c^2*tan(1/2*f*x+1/2*e)^4*a^2*d^7-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^5*tan(1/2*f*x+1/2*e)^4*a*b+5/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^4*tan(1/2*f*x+1/2*e)^4*b^2*d+20/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^2*tan(1/2*f*x+1/2*e)^4*b^2*d^3-6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*a^2*d^4+2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*a^2*d^6-16/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a*b*d-38/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a*b*d^3-2/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*a*b*d^3-28/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^3*tan(1/2*f*x+1/2*e)^4*a*b*d^2-22/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c*tan(1/2*f*x+1/2*e)^4*a*b*d^4+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/c*tan(1/2*f*x+1/2*e)^4*a*b*d^6-24/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^4*d/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a*b-40/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a*b*d^2-8/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*a*b*d+8/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2*d^7/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a*b-56/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2*d^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a*b-8/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*c^2*d-56/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a*b*d^4+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a*b*d^6+2/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*b^2*c^2*d^3-12/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^4*a^2*d^5+2/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*c^3+1/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*c^3-6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a^2*d^5+8/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*b^2*d^5+1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^5/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*b^2-1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^5/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*b^2+6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a^2*c^4*d-5/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a^2*c^2*d^3+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*b^2*d^2+6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^4*tan(1/2*f*x+1/2*e)^4*a^2*d+27/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*c^2*tan(1/2*f*x+1/2*e)^4*a^2*d^3-8/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c*d^6/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a^2+8/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^3*d^8/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a^2+26/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3*d^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*b^2+36/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3*d^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a^2+14/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c*d^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a^2+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a*b*d^5-68/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*d^5/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*a*b-20/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a*b*c^3*d^2+2/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a*b*c*d^4+22/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*b^2*d^2+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*b^2*d^4+3/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*c*d^2-2/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*d^3+64/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c*d^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*b^2+4/f/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)/(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*c*d^2+9/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^5*a^2*d^2+8/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c*d^6/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^3*b^2+12/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a^2*d+40/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a^2*d^3+4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a^2*d^7-8/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^5/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*a*b+8/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^4/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*b^2*d+34/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^2/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)^2*b^2*d^3+27/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a^2*d^2-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3*c/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*tan(1/2*f*x+1/2*e)*a^2*d^4+2/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a^2*d^5-4/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*a*b*c^5+13/3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^3/(c^6-3*c^4*d^2+3*c^2*d^4-d^6)*b^2*c^4*d","B"
686,1,489,386,0.328000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^3,x)","\frac{c^{3} a^{3} \left(f x +e \right)-3 a^{3} c^{2} d \cos \left(f x +e \right)+3 a^{3} 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^{3} d^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}-3 a^{2} b \,c^{3} \cos \left(f x +e \right)+9 a^{2} b \,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^{2} b c \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a^{2} b \,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 a \,b^{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)-3 a \,b^{2} c^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+9 a \,b^{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{3 a \,b^{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}-\frac{b^{3} c^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 b^{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{3 b^{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}+b^{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)}{f}"," ",0,"1/f*(c^3*a^3*(f*x+e)-3*a^3*c^2*d*cos(f*x+e)+3*a^3*c*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-1/3*a^3*d^3*(2+sin(f*x+e)^2)*cos(f*x+e)-3*a^2*b*c^3*cos(f*x+e)+9*a^2*b*c^2*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^2*b*c*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a^2*b*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)+3*a*b^2*c^3*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a*b^2*c^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)+9*a*b^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)-3/5*a*b^2*d^3*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)-1/3*b^3*c^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*b^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)-3/5*b^3*c*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e)+b^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))","A"
687,1,325,303,0.324000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^2,x)","\frac{a^{3} c^{2} \left(f x +e \right)-2 a^{3} c d \cos \left(f x +e \right)+a^{3} 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^{2} b \,c^{2} \cos \left(f x +e \right)+6 a^{2} b 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^{2} b \,d^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a \,b^{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)-2 a \,b^{2} c d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)+3 a \,b^{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)-\frac{b^{3} c^{2} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+2 b^{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{b^{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}}{f}"," ",0,"1/f*(a^3*c^2*(f*x+e)-2*a^3*c*d*cos(f*x+e)+a^3*d^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^2*b*c^2*cos(f*x+e)+6*a^2*b*c*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a^2*b*d^2*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a*b^2*c^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-2*a*b^2*c*d*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a*b^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)-1/3*b^3*c^2*(2+sin(f*x+e)^2)*cos(f*x+e)+2*b^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)-1/5*b^3*d^2*(8/3+sin(f*x+e)^4+4/3*sin(f*x+e)^2)*cos(f*x+e))","A"
688,1,182,161,0.267000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e)),x)","\frac{a^{3} c \left(f x +e \right)-a^{3} d \cos \left(f x +e \right)-3 a^{2} b c \cos \left(f x +e \right)+3 a^{2} b 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 \,b^{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 \,b^{2} d \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)-\frac{b^{3} c \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+b^{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)}{f}"," ",0,"1/f*(a^3*c*(f*x+e)-a^3*d*cos(f*x+e)-3*a^2*b*c*cos(f*x+e)+3*a^2*b*d*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+3*a*b^2*c*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-a*b^2*d*(2+sin(f*x+e)^2)*cos(f*x+e)-1/3*b^3*c*(2+sin(f*x+e)^2)*cos(f*x+e)+b^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))","A"
689,1,76,82,0.184000," ","int((a+b*sin(f*x+e))^3,x)","\frac{-\frac{b^{3} \left(2+\sin^{2}\left(f x +e \right)\right) \cos \left(f x +e \right)}{3}+3 a \,b^{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^{2} b \cos \left(f x +e \right)+\left(f x +e \right) a^{3}}{f}"," ",0,"1/f*(-1/3*b^3*(2+sin(f*x+e)^2)*cos(f*x+e)+3*a*b^2*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)-3*a^2*b*cos(f*x+e)+(f*x+e)*a^3)","A"
690,1,506,145,0.240000," ","int((a+b*sin(f*x+e))^3/(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^{3}}{f \sqrt{c^{2}-d^{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) a^{2} b c}{f d \sqrt{c^{2}-d^{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) a \,b^{2} c^{2}}{f \,d^{2} \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^{3} c^{3}}{f \,d^{3} \sqrt{c^{2}-d^{2}}}+\frac{b^{3} \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{6 b^{2} \left(\tan^{2}\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)^{2}}+\frac{2 b^{3} \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{b^{3} \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{6 b^{2} a}{f d \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 b^{3} c}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{6 b \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}}{f d}-\frac{6 b^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a c}{f \,d^{2}}+\frac{2 b^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f \,d^{3}}+\frac{b^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f d}"," ",0,"2/f/(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^3-6/f/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*b*c+6/f/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*b^2*c^2-2/f/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^3*c^3+1/f/d*b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-6/f/d*b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*a+2/f/d^2*b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c-1/f/d*b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)-6/f/d*b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*a+2/f/d^2*b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*c+6/f/d*b*arctan(tan(1/2*f*x+1/2*e))*a^2-6/f/d^2*b^2*arctan(tan(1/2*f*x+1/2*e))*a*c+2/f/d^3*b^3*arctan(tan(1/2*f*x+1/2*e))*c^2+1/f/d*b^3*arctan(tan(1/2*f*x+1/2*e))","B"
691,1,842,203,0.286000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x)","\frac{2 d^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a^{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) \left(c^{2}-d^{2}\right) c}-\frac{6 d \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a^{2} 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{6 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{2 c^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{3}}{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 d \,a^{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) \left(c^{2}-d^{2}\right)}-\frac{6 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) \left(c^{2}-d^{2}\right)}+\frac{6 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^{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) \left(c^{2}-d^{2}\right)}+\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^{3} c}{f \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{6 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^{2} b}{f \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) a \,b^{2} c^{3}}{f \,d^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{12 \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{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^{3} 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^{3} c^{2}}{f d \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}-\frac{2 b^{3}}{f \,d^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{6 b^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,d^{2}}-\frac{4 b^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,d^{3}}"," ",0,"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^3-6/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^2*b+6/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^2-2/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^3+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^3-6/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^2*b*c+6/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^3+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^3*c-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))*a^2*b-6/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+12/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+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^3*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^3*c^2-2/f*b^3/d^2/(1+tan(1/2*f*x+1/2*e)^2)+6/f*b^2/d^2*arctan(tan(1/2*f*x+1/2*e))*a-4/f*b^3/d^3*arctan(tan(1/2*f*x+1/2*e))*c","B"
692,1,2785,246,0.299000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"2/f*b^3/d^3*arctan(tan(1/2*f*x+1/2*e))+9/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^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a*b^2-15/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2*b+30/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b^2-9/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^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^3*a^2*b-9/f*d/(c^4-2*c^2*d^2+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))*a^2*b*c+6/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^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*a*b^2-6/f*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^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^2*a^2*b-15/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^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*a^2*b+7/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^4/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^3-16/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^3+18/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a*b^2+6/f*d^2/(c^4-2*c^2*d^2+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))*a*b^2+1/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^4-2*c^2*d^2+d^4)*c^4*tan(1/2*f*x+1/2*e)^3*b^3-3/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c^3/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b^2+3/f/(c^4-2*c^2*d^2+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))*a*b^2*c^2+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^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^3*a*b^2-6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*a^2*b+5/f/d/(c^4-2*c^2*d^2+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^3*c^3-6/f*d/(c^4-2*c^2*d^2+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^3*c+4/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^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a^3-2/f/d^3/(c^4-2*c^2*d^2+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^3*c^5-4/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^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^3*b^3+9/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^4-2*c^2*d^2+d^4)*a*b^2*c^2-12/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2*b+5/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^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*a^3-1/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^4-2*c^2*d^2+d^4)*a^3-5/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*b^3*c^3-3/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^4-2*c^2*d^2+d^4)*a^2*b*c-2/f*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^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2*a^3+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^4-2*c^2*d^2+d^4)*c^5*tan(1/2*f*x+1/2*e)^2*b^3-10/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^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*b^3+11/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^3-2/f*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^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^3*a^3-2/f*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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^3+2/f/(c^4-2*c^2*d^2+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))*a^3*c^2+7/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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a^3+4/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^4-2*c^2*d^2+d^4)*a^3*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)^2/(c^4-2*c^2*d^2+d^4)*b^3*c^5+1/f*d^2/(c^4-2*c^2*d^2+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))*a^3-6/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2*b*c^3-1/f/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*b^3","B"
693,1,6128,314,0.333000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
694,1,99,48,0.085000," ","int((b*B/a+B*sin(x))/(a+b*sin(x)),x)","\frac{2 B \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{b}-\frac{2 B a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{b \sqrt{a^{2}-b^{2}}}+\frac{2 B b \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{a \sqrt{a^{2}-b^{2}}}"," ",0,"2*B/b*arctan(tan(1/2*x))-2*B*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))+2*B/a*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*x)+2*b)/(a^2-b^2)^(1/2))","B"
695,1,7,6,0.007000," ","int((a*B/b+B*sin(x))/(a+b*sin(x)),x)","\frac{B x}{b}"," ",0,"B*x/b","A"
696,1,34,12,0.109000," ","int((a+b*sin(x))/(b+a*sin(x))^2,x)","\frac{-\frac{2 a \tan \left(\frac{x}{2}\right)}{b}-2}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +2 a \tan \left(\frac{x}{2}\right)+b}"," ",0,"2*(-a/b*tan(1/2*x)-1)/(tan(1/2*x)^2*b+2*a*tan(1/2*x)+b)","B"
697,1,24,28,0.096000," ","int((2-sin(x))/(2+sin(x)),x)","\frac{8 \sqrt{3}\, \arctan \left(\frac{\left(1+2 \tan \left(\frac{x}{2}\right)\right) \sqrt{3}}{3}\right)}{3}-x"," ",0,"8/3*3^(1/2)*arctan(1/3*(1+2*tan(1/2*x))*3^(1/2))-x","A"
698,1,948,222,0.237000," ","int((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e)),x)","\frac{8 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2} c}{f \,b^{3}}-\frac{12 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a \,c^{2}}{f \,b^{2}}+\frac{8 d^{3} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a c}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 d^{4} a^{2}}{f \,b^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 d^{2} c^{2}}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{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) a^{4} d^{4}}{f \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{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) c^{4}}{f \sqrt{a^{2}-b^{2}}}-\frac{4 d^{4}}{3 f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{2}}+\frac{4 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f b}-\frac{2 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{3}}{f \,b^{4}}+\frac{8 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{3}}{f b}-\frac{8 \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 \,c^{3} d}{f b \sqrt{a^{2}-b^{2}}}-\frac{8 \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^{3} c \,d^{3}}{f \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{12 \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^{2} c^{2} d^{2}}{f \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{d^{4} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{4 d^{3} \left(\tan^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{16 d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a c}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{8 d^{3} a c}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{2 d^{4} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}}{f \,b^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{12 d^{2} \left(\tan^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{4 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}}{f \,b^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}-\frac{24 d^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}+\frac{d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{3}}"," ",0,"8/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*a^2*c-12/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))*a*c^2+2/f/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^4*d^4-1/f*d^4/b^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*a-4/3/f*d^4/b/(1+tan(1/2*f*x+1/2*e)^2)^3+2/f/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^4-1/f*d^4/b^2*arctan(tan(1/2*f*x+1/2*e))*a+4/f*d^3/b*arctan(tan(1/2*f*x+1/2*e))*c-4/f*d^4/b/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2-2/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^3*a^2-12/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)^3*c^2-2/f*d^4/b^4*arctan(tan(1/2*f*x+1/2*e))*a^3+8/f*d/b*arctan(tan(1/2*f*x+1/2*e))*c^3+8/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*a*c-8/f/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^3*d+16/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*a*c-8/f/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*c*d^3+12/f/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^2*d^2+4/f*d^3/b/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^5*c-4/f*d^3/b/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*c+8/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^3*a*c-2/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*a^2-12/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^4*c^2-4/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*a^2-24/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)^2*c^2+1/f*d^4/b^2/(1+tan(1/2*f*x+1/2*e)^2)^3*tan(1/2*f*x+1/2*e)*a","B"
699,1,506,145,0.215000," ","int((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e)),x)","\frac{d^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 d^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 d^{3} a}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{6 d^{2} c}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{2 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}}{f \,b^{3}}-\frac{6 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a c}{f \,b^{2}}+\frac{6 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f b}+\frac{d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f b}-\frac{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) a^{3} d^{3}}{f \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{6 \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^{2} c \,d^{2}}{f \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 \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 \,c^{2} d}{f b \sqrt{a^{2}-b^{2}}}+\frac{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) c^{3}}{f \sqrt{a^{2}-b^{2}}}"," ",0,"1/f*d^3/b/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3+2/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*a-6/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c-1/f*d^3/b/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+2/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*a-6/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)^2*c+2/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*a^2-6/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))*a*c+6/f*d/b*arctan(tan(1/2*f*x+1/2*e))*c^2+1/f*d^3/b*arctan(tan(1/2*f*x+1/2*e))-2/f/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*d^3+6/f/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c*d^2-6/f/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^2*d+2/f/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^3","B"
700,1,226,88,0.189000," ","int((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e)),x)","-\frac{2 d^{2}}{f b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{2 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{2}}+\frac{4 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f b}+\frac{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) a^{2} d^{2}}{f \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{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) a c d}{f b \sqrt{a^{2}-b^{2}}}+\frac{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) c^{2}}{f \sqrt{a^{2}-b^{2}}}"," ",0,"-2/f*d^2/b/(1+tan(1/2*f*x+1/2*e)^2)-2/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))*a+4/f*d/b*arctan(tan(1/2*f*x+1/2*e))*c+2/f/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*d^2-4/f/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c*d+2/f/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2","B"
701,1,119,60,0.119000," ","int((c+d*sin(f*x+e))/(a+b*sin(f*x+e)),x)","\frac{2 d \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f b}-\frac{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) d a}{f b \sqrt{a^{2}-b^{2}}}+\frac{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) c}{f \sqrt{a^{2}-b^{2}}}"," ",0,"2/f*d/b*arctan(tan(1/2*f*x+1/2*e))-2/f/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*d*a+2/f/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c","A"
702,1,47,42,0.103000," ","int(1/(a+b*sin(f*x+e)),x)","\frac{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)}{f \sqrt{a^{2}-b^{2}}}"," ",0,"2/f/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))","A"
703,1,116,107,0.296000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\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)}{f \left(d a -c b \right) \sqrt{c^{2}-d^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{f \left(d a -c b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"2/f/(a*d-b*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))-2/f*b/(a*d-b*c)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))","A"
704,1,514,175,0.335000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\frac{2 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a}{f \left(d a -c b \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) c \left(c^{2}-d^{2}\right)}-\frac{2 d^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b}{f \left(d a -c b \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^{2}-d^{2}\right)}+\frac{2 d^{3} a}{f \left(d a -c b \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^{2}-d^{2}\right)}-\frac{2 d^{2} c b}{f \left(d a -c b \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^{2}-d^{2}\right)}+\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 c}{f \left(d a -c b \right)^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{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 \left(d a -c b \right)^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{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 \left(d a -c b \right)^{2} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{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)}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"2/f*d^4/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/c/(c^2-d^2)*tan(1/2*f*x+1/2*e)*a-2/f*d^3/(a*d-b*c)^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)*tan(1/2*f*x+1/2*e)*b+2/f*d^3/(a*d-b*c)^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)*a-2/f*d^2/(a*d-b*c)^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*b+2/f*d^2/(a*d-b*c)^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*c-4/f*d/(a*d-b*c)^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*c^2+2/f*d^3/(a*d-b*c)^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+2/f*b^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))","B"
705,1,2644,270,0.376000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-2/f*b^3/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))+6/f*d^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^3*a*b+17/f*d^3/(a*d-b*c)^3/(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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^2-8/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^2-10/f*d^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c^3+4/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c+5/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*a^2-2/f*d^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^3*a^2+7/f*d^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^3*b^2-4/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*b^2+10/f*d^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b+6/f*d/(a*d-b*c)^3/(c^4-2*c^2*d^2+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^2*c^4-5/f*d^3/(a*d-b*c)^3/(c^4-2*c^2*d^2+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^2*c^2+2/f*d^3/(a*d-b*c)^3/(c^4-2*c^2*d^2+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))*a^2*c^2+4/f*d^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a^2-2/f*d^8/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2*a^2+6/f*d^2/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^4*tan(1/2*f*x+1/2*e)^2*b^2+9/f*d^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*b^2+11/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2*c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2-2/f*d^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/c/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2-6/f*d^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*b^2+4/f*d^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2*c^2+2/f*d^5/(a*d-b*c)^3/(c^4-2*c^2*d^2+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^2+1/f*d^5/(a*d-b*c)^3/(c^4-2*c^2*d^2+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))*a^2+6/f*d^2/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*b^2*c^4-3/f*d^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*b^2*c^2+7/f*d^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a^2-6/f*d^2/(a*d-b*c)^3/(c^4-2*c^2*d^2+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))*a*b*c^3-12/f*d^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^3*a*b-10/f*d^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*a*b-16/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*a*b+8/f*d^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^2*a*b-28/f*d^4/(a*d-b*c)^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/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b-1/f*d^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2","B"
706,1,1303,297,0.318000," ","int((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^2,x)","\frac{d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,b^{2}}+\frac{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) a \,c^{4}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{6 d^{4} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}}{f \,b^{4}}+\frac{2 b \,c^{4}}{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{d^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{12 a^{2} c^{2} d^{2}}{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} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{4}}{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{8 b \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{3} d}{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 b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{4}}{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) a}-\frac{8 a^{3} c \,d^{3}}{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{8 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c \,d^{3}}{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{12 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c^{2}}{f \,b^{2}}+\frac{12 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{2} d^{2}}{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{16 \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^{4} c \,d^{3}}{f \,b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{12 \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^{3} c^{2} d^{2}}{f \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{24 \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^{2} c \,d^{3}}{f b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}+\frac{4 d^{4} a}{f \,b^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{8 d^{3} c}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{16 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a c}{f \,b^{3}}+\frac{24 \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 \,c^{2} d^{2}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 \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^{5} d^{4}}{f \,b^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{8 \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^{3} d^{4}}{f \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{8 b \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c^{3} d}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{8 a \,c^{3} d}{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^{4} d^{4}}{f \,b^{3} \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{4 d^{4} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{3} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}-\frac{8 d^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)^{2}}"," ",0,"1/f*d^4/b^2*arctan(tan(1/2*f*x+1/2*e))+2/f*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)*c^4+2/f/(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*c^4+1/f*d^4/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-1/f*d^4/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+4/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*a-8/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*c+6/f*d^4/b^4*arctan(tan(1/2*f*x+1/2*e))*a^2-8/f/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*tan(1/2*f*x+1/2*e)*c*d^3+12/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))*c^2+12/f/(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*tan(1/2*f*x+1/2*e)*c^2*d^2+12/f/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*c^2*d^2+16/f/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))*a^4*c*d^3-12/f/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^3*c^2*d^2-24/f/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))*a^2*c*d^3+2/f/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)*a^3*tan(1/2*f*x+1/2*e)*d^4-8/f*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)*c^3*d+2/f*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)/a*tan(1/2*f*x+1/2*e)*c^4-8/f/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)*a^3*c*d^3-16/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*a*c-8/f/(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*c^3*d+24/f/(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*c^2*d^2+2/f/b^3/(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^4*d^4+4/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*a-6/f/b^4/(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^5*d^4+8/f/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^3*d^4-8/f*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))*c^3*d-8/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c","B"
707,1,842,200,0.293000," ","int((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^2,x)","-\frac{2 d^{3}}{f \,b^{2} \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{4 d^{3} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) a}{f \,b^{3}}+\frac{6 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{f \,b^{2}}-\frac{2 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{3}}{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{6 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c \,d^{2}}{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{6 b \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{2} d}{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 b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{3}}{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) a}-\frac{2 a^{3} d^{3}}{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{6 a^{2} c \,d^{2}}{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{6 a \,c^{2} d}{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 b \,c^{3}}{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{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) a^{4} d^{3}}{f \,b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 \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^{3} c \,d^{2}}{f \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 \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^{2} d^{3}}{f b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{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) a \,c^{3}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{12 \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 c \,d^{2}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 b \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c^{2} d}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/f*d^3/b^2/(1+tan(1/2*f*x+1/2*e)^2)-4/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*a+6/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))*c-2/f/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*tan(1/2*f*x+1/2*e)*d^3+6/f/(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*tan(1/2*f*x+1/2*e)*c*d^2-6/f*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)*c^2*d+2/f*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)/a*tan(1/2*f*x+1/2*e)*c^3-2/f/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)*a^3*d^3+6/f/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*c*d^2-6/f/(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*c^2*d+2/f*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)*c^3+4/f/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))*a^4*d^3-6/f/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^3*c*d^2-6/f/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))*a^2*d^3+2/f/(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*c^3+12/f/(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*c*d^2-6/f*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))*c^2*d","B"
708,1,556,124,0.323000," ","int((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^2,x)","\frac{2 d^{2} \arctan \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f \,b^{2}}+\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{2}}{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{4 b \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c d}{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 b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c^{2}}{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) a}+\frac{2 a^{2} d^{2}}{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{4 a c d}{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 b \,c^{2}}{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 \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^{3} d^{2}}{f \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{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) a \,c^{2}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{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) a \,d^{2}}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c d}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/f*d^2/b^2*arctan(tan(1/2*f*x+1/2*e))+2/f/(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*tan(1/2*f*x+1/2*e)*d^2-4/f*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)*c*d+2/f*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)/a*tan(1/2*f*x+1/2*e)*c^2+2/f/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*d^2-4/f/(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*c*d+2/f*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)*c^2-2/f/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^3*d^2+2/f/(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*c^2+4/f/(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*d^2-4/f*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))*c*d","B"
709,1,309,92,0.245000," ","int((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^2,x)","-\frac{2 b \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{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 b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{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) a}-\frac{2 d 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 c b}{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 \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) c a}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{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 d}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b/(a^2-b^2)*tan(1/2*f*x+1/2*e)*d+2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b^2/(a^2-b^2)/a*tan(1/2*f*x+1/2*e)*c-2/f/(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)*d*a+2/f/(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)*c*b+2/f/(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))*c*a-2/f/(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*d","B"
710,1,155,78,0.204000," ","int(1/(a+b*sin(f*x+e))^2,x)","\frac{2 b^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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) a \left(a^{2}-b^{2}\right)}+\frac{2 b}{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 \arctan \left(\frac{2 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{f \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b^2/a/(a^2-b^2)*tan(1/2*f*x+1/2*e)+2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)*b/(a^2-b^2)+2/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"
711,1,514,171,0.380000," ","int(1/(a+b*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)}{f \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{c^{2}-d^{2}}}-\frac{2 b^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{f \left(d a -c b \right)^{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 b^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{f \left(d a -c b \right)^{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) a \left(a^{2}-b^{2}\right)}-\frac{2 b^{2} d a}{f \left(d a -c b \right)^{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 b^{3} c}{f \left(d a -c b \right)^{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{4 b \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^{2} d}{f \left(d a -c b \right)^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{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) a c}{f \left(d a -c b \right)^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{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) d}{f \left(d a -c b \right)^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/f*d^2/(a^2*d^2-2*a*b*c*d+b^2*c^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))-2/f*b^3/(a*d-b*c)^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)*tan(1/2*f*x+1/2*e)*d+2/f*b^4/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/a/(a^2-b^2)*tan(1/2*f*x+1/2*e)*c-2/f*b^2/(a*d-b*c)^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)*d*a+2/f*b^3/(a*d-b*c)^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)*c-4/f*b/(a*d-b*c)^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^2*d+2/f*b^2/(a*d-b*c)^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*c+2/f*b^3/(a*d-b*c)^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))*d","B"
712,1,886,280,0.380000," ","int(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x)","\frac{2 d^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) a}{f \left(d a -c b \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) c \left(c^{2}-d^{2}\right)}-\frac{2 d^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b}{f \left(d a -c b \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^{2}-d^{2}\right)}+\frac{2 d^{4} a}{f \left(d a -c b \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^{2}-d^{2}\right)}-\frac{2 d^{3} c b}{f \left(d a -c b \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^{2}-d^{2}\right)}+\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 c}{f \left(d a -c b \right)^{3} \left(c^{2}-d^{2}\right)^{\frac{3}{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 \left(d a -c b \right)^{3} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{4 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 \left(d a -c b \right)^{3} \left(c^{2}-d^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{f \left(d a -c b \right)^{3} \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 b^{5} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{f \left(d a -c b \right)^{3} \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) a \left(a^{2}-b^{2}\right)}+\frac{2 b^{3} d a}{f \left(d a -c b \right)^{3} \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 b^{4} c}{f \left(d a -c b \right)^{3} \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{6 b^{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) a^{2} d}{f \left(d a -c b \right)^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{2 b^{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 c}{f \left(d a -c b \right)^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{4 b^{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) d}{f \left(d a -c b \right)^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/f*d^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/c/(c^2-d^2)*tan(1/2*f*x+1/2*e)*a-2/f*d^4/(a*d-b*c)^3/(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+2/f*d^4/(a*d-b*c)^3/(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/f*d^3/(a*d-b*c)^3/(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*b+2/f*d^3/(a*d-b*c)^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))*a*c-6/f*d^2/(a*d-b*c)^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*c^2+4/f*d^4/(a*d-b*c)^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+2/f*b^4/(a*d-b*c)^3/(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)*d-2/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/a/(a^2-b^2)*tan(1/2*f*x+1/2*e)*c+2/f*b^3/(a*d-b*c)^3/(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)*d*a-2/f*b^4/(a*d-b*c)^3/(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)*c+6/f*b^2/(a*d-b*c)^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))*a^2*d-2/f*b^3/(a*d-b*c)^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))*a*c-4/f*b^4/(a*d-b*c)^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))*d","B"
713,1,4023,444,0.439000," ","int(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-2/f*d^9/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c^2*tan(1/2*f*x+1/2*e)^2*a^2+8/f*d^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^4*tan(1/2*f*x+1/2*e)^2*b^2-15/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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^2*c^2+12/f*d^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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^2*c^4+11/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*b^2+11/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2+2/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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))*a^2*c^2+8/f*d^7/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^3*a*b+16/f*d^7/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b+5/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*a^2+2/f*b^6/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)/a/(a^2-b^2)*tan(1/2*f*x+1/2*e)*c+2/f*b^4/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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*c-5/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*b^2*c^2+7/f*d^7/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*a^2-10/f*d^7/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)^2*b^2+1/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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))*a^2+6/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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^2+4/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2*c^2+8/f*d^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*b^2*c^4-2/f*b^5/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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)*tan(1/2*f*x+1/2*e)*d-2/f*b^4/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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)*d*a-8/f*b^3/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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^2*d-18/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^2*a*b+12/f*d^8/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^2*a*b-34/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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/(c^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a*b-8/f*d^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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))*a*b*c^3+2/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(c^4-2*c^2*d^2+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))*a*b*c-14/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^3*a*b-12/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^2*a*b-1/f*d^7/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a^2+2/f*b^5/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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)*c+6/f*b^5/(a*d-b*c)^2/(a^2*d^2-2*a*b*c*d+b^2*c^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))*d-2/f*d^8/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*a^2+23/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^2-14/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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^4-2*c^2*d^2+d^4)*tan(1/2*f*x+1/2*e)*b^2-12/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c^3+6/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*a*b*c-2/f*d^8/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)/c*tan(1/2*f*x+1/2*e)^3*a^2+9/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^3*tan(1/2*f*x+1/2*e)^3*b^2-6/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c*tan(1/2*f*x+1/2*e)^3*b^2+4/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)^2/(c^4-2*c^2*d^2+d^4)*c^2*tan(1/2*f*x+1/2*e)^2*a^2","B"
714,1,4767,519,0.355000," ","int((c+d*sin(f*x+e))^5/(a+b*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"1/f*d^5/b^3*arctan(tan(1/2*f*x+1/2*e))-15/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c^4*d-40/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c^2*d^3+20/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^3*d^2-20/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^6*tan(1/2*f*x+1/2*e)^2*c*d^4+20/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^2*c^2*d^3-5/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^2*c*d^4+30/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^3*d^2+100/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3*d^2-160/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d^3+10/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^3*c^2*d^3-15/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^3*c*d^4+70/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d^3-25/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^4*d+30/f/b^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^6*c*d^4-20/f/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^5*c^2*d^3-75/f/b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^4*c*d^4+50/f/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*c^2*d^3-15/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^4*d-60/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^2*d^3+70/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c*d^4-25/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c^4*d-100/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c^2*d^3-10/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*c^4*d-65/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^5/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^4+60/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c*d^4-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*c^5+6/f/b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^7*tan(1/2*f*x+1/2*e)^2*d^5+3/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^2*d^5+10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*c^3*d^2+30/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*c*d^4-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c^4*d-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c^2*d^3-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3*d^2+110/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^4+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^5-2/f*b^5/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*c^5+19/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^6/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^5-28/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^5+11/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^5-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^5-20/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^6*c*d^4+20/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*c^2*d^3+35/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*c*d^4+60/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^3*d^2-20/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^4*d+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^5-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c^4*d-50/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c^2*d^3+6/f*d^5/b^4/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*a-10/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^2*c-30/f*d^4/b^4*arctan(tan(1/2*f*x+1/2*e))*a*c-1/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^5+1/f*d^5/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)^3-1/f*d^5/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*tan(1/2*f*x+1/2*e)+6/f*d^5/b^4/(1+tan(1/2*f*x+1/2*e)^2)^2*a-10/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)^2*c+12/f*d^5/b^5*arctan(tan(1/2*f*x+1/2*e))*a^2+20/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*c^2-18/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*d^5+6/f/b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^7*d^5-9/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*d^5+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c^5+7/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^5+1/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^5+20/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^3*d^2-12/f/b^5/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^7*d^5+29/f/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^5*d^5-20/f/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*d^5+10/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^3*d^2+30/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c^3*d^2-5/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*c^4*d+5/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^6*tan(1/2*f*x+1/2*e)^3*d^5-8/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^3*d^5+5/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^5","B"
715,1,3683,307,0.345000," ","int((c+d*sin(f*x+e))^4/(a+b*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"-2/f*d^4/b^3/(1+tan(1/2*f*x+1/2*e)^2)-12/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^3*d-24/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c*d^3-8/f/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^5*c*d^3+20/f/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*c*d^3+8/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^2*c*d^3+18/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^2*d^2-20/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c^3*d-40/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c*d^3+28/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^3+60/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d^2-12/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c^3*d-16/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c*d^3+12/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^2*d^2-20/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3*d-64/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^3-8/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*c^3*d+4/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^3*c*d^3+6/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^2*d^2-3/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^3*d^4-6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d^2+5/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^4-1/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^4-6/f*d^4/b^4*arctan(tan(1/2*f*x+1/2*e))*a+8/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))*c-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*c^4-4/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^6*tan(1/2*f*x+1/2*e)^2*d^4-1/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^2*d^4+6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*c^2*d^2-8/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c^3*d-4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c*d^3-15/f/b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^4*d^4+12/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2*d^2+6/f/b^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^6*d^4+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^4+36/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^2*d^2-16/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3*d+14/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*d^4-2/f*b^5/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*c^4-13/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^5/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^4+11/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^4-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^4+8/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*c*d^3+18/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c^2*d^2-4/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*c^3*d+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^4+22/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^4-8/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c^3*d-20/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c*d^3+1/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^4-4/f/b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^6*d^4+7/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*d^4+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c^4+7/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^4+6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*d^4+12/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*d^4","B"
716,1,2785,239,0.306000," ","int((c+d*sin(f*x+e))^3/(a+b*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"-5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*d^3+2/f*d^3/b^3*arctan(tan(1/2*f*x+1/2*e))+6/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c*d^2-9/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c^2*d-6/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*c^2*d-15/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d+30/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^2+9/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c*d^2-15/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c^2*d-9/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c^2*d+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c^3+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^3-6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c^2*d-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*d^3+7/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^3+1/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^3+2/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*d^3-1/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^3+9/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*c*d^2-3/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*c^2*d+11/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^3+2/f/b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^5*tan(1/2*f*x+1/2*e)^2*d^3+4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^3-10/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*d^3-2/f*b^5/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*c^3+18/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c*d^2-12/f*b^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2*d+1/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^3*d^3-3/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d^2+5/f*b^2/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^3-2/f*b^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*c^3+7/f/b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^4/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^3-16/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^3-6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c^2*d+3/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*c*d^2+3/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c*d^2+5/f/b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*d^3-2/f/b^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^5*d^3-6/f*b/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*d^3+6/f*b^2/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c*d^2-4/f*b/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*d^3","B"
717,1,1923,187,0.267000," ","int((c+d*sin(f*x+e))^2/(a+b*sin(f*x+e))^3,x)","-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{5} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{11 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{2} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{10 a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{2} d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{8 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{3} c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{4} c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}-\frac{6 a^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{b^{3} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 \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 b c d}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{4 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b \,c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b^{4} c^{2}}{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)^{2} a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a \,b^{2} c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{4} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}+\frac{5 a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{3 a^{2} \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) a +2 \tan \left(\frac{f x}{2}+\frac{e}{2}\right) b +a \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 a^{3} c d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 a^{2} b \,c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{3 a^{2} b \,d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{\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^{2} d^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{\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^{2} c^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{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^{2} d^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{a^{3} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{3} c^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{6 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{3} d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{a^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{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) a^{2} c^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"-4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c*d+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*b*c^2-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*b^2*c*d-10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*b*c*d-4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*b^4*c*d-6/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*b*c*d-6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*b*c*d-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*b^3*c^2+5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*b^2*c^2+2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*b^2*d^2+3/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*b*d^2-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*b^5*c^2+11/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*b^2*c^2+10/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*b^2*d^2-8/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*b^3*c*d-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*b^4*c^2-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*b^2*c*d-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*b^4*c^2+1/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*d^2+1/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b^2*c^2+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b^2*d^2+1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*d^2+7/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*b^3*c^2+6/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*b^3*d^2-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^2-4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c*d+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*b*c^2+3/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*b*d^2+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c^2","B"
718,1,1291,153,0.243000," ","int((c+d*sin(f*x+e))/(a+b*sin(f*x+e))^3,x)","-\frac{3 b \,a^{2} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{5 b^{2} a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) c}{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)^{2} a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{5 a \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2} d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{3} c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{4} d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}-\frac{2 \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{5} c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a^{2}}-\frac{5 b \,a^{2} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{11 b^{2} a \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{4 b^{3} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right) c}{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)^{2} a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 a^{3} d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 a^{2} b c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{a \,b^{2} d}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{b^{3} c}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{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) a^{2} c}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}-\frac{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 b d}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{\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^{2} c}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"-3/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^3*d+5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^3*c-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^4/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^3*c-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*d+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*b*c-5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*b^2*d+7/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*b^3*c-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*b^4*d-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*b^5*c-5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d+11/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c-4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^4/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*d+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*b*c-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*b^2*d-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*b^3*c+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*c-3/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*b*d+1/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b^2*c","B"
719,1,705,122,0.200000," ","int(1/(a+b*sin(f*x+e))^3,x)","\frac{5 b^{2} a \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4} \left(\tan^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a}+\frac{4 b \,a^{2} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 b^{3} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{5} \left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{11 b^{2} a \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{2 b^{4} \tan \left(\frac{f x}{2}+\frac{e}{2}\right)}{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)^{2} a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{4 b \,a^{2}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{b^{3}}{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)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{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) a^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}+\frac{\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^{2}}{f \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}-b^{2}}}"," ",0,"5/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^4/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2+7/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^5/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2+11/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)-2/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^4/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)+4/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b/(a^4-2*a^2*b^2+b^4)*a^2-1/f/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*b^3/(a^4-2*a^2*b^2+b^4)+2/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2+1/f/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
720,1,2644,271,0.367000," ","int(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"16/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c*d-8/f*b^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*c*d+28/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d+1/f*b^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^2-6/f*b^2/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^2*d^2-4/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^2-9/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*d^2+2/f*b^8/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*c^2+4/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*d^2-17/f*b^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^2-11/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2+8/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^2+2/f*b^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2+10/f*b^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c*d-4/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*c*d-6/f*b^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^3*c*d-2/f*b^3/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2*a^2-10/f*b^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d+2/f*b^7/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*c^2+5/f*b^3/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*d^2-6/f*b/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^4*d^2-7/f*b^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*d^2-5/f*b^5/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^2-7/f*b^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^2+6/f*b^6/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*d^2-6/f*b^2/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*d^2-4/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^2*a^2+3/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*d^2-1/f*b^5/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2-2/f*b^5/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*d^2+6/f*b^2/(a*d-b*c)^3/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*c*d+12/f*b^4/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c*d+10/f*b^3/(a*d-b*c)^3/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c*d+2/f*d^3/(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^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"
721,1,3241,438,0.442000," ","int(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x)","\text{output too large to display}"," ",0,"8/f*b^7/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^3*c*d+16/f*b^7/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d+2/f*b^4/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2*a^2-15/f*b^4/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^2*d^2+9/f*b^4/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^3*d^2+5/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*c^2-6/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^3*d^2-2/f*b^8/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^3*c^2+8/f*b^3/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*tan(1/2*f*x+1/2*e)^2*d^2+4/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*c^2+11/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^2*d^2-2/f*b^9/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a^2*tan(1/2*f*x+1/2*e)^2*c^2+23/f*b^4/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^3/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^2+11/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2-14/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*d^2-2/f*b^8/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/a/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c^2-12/f*b^4/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*c*d+6/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*c*d+12/f*b^2/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^4*d^2-2/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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)*tan(1/2*f*x+1/2*e)*b-2/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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*b+2/f*d^4/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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*c-8/f*d^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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*c^2-1/f*b^7/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^2-18/f*b^6/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a*tan(1/2*f*x+1/2*e)^2*c*d+12/f*b^8/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)/a*tan(1/2*f*x+1/2*e)^2*c*d+2/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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)*a+6/f*d^5/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^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-5/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*d^2+6/f*b^6/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*d^2+7/f*b^7/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*c^2-10/f*b^7/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)^2*d^2+8/f*b^3/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^4*d^2+4/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*c^2*a^2+1/f*b^6/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*c^2-34/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2*a^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*f*x+1/2*e)*c*d-8/f*b^3/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a^3*c*d+2/f*b^5/(a*d-b*c)^4/(a^4-2*a^2*b^2+b^4)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*f*x+1/2*e)+2*b)/(a^2-b^2)^(1/2))*a*c*d+2/f*d^6/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)^2/(tan(1/2*f*x+1/2*e)^2*c+2*tan(1/2*f*x+1/2*e)*d+c)/c/(c^2-d^2)*tan(1/2*f*x+1/2*e)*a-14/f*b^5/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^2*tan(1/2*f*x+1/2*e)^3*c*d-12/f*b^4/(a*d-b*c)^4/(tan(1/2*f*x+1/2*e)^2*a+2*tan(1/2*f*x+1/2*e)*b+a)^2/(a^4-2*a^2*b^2+b^4)*a^3*tan(1/2*f*x+1/2*e)^2*c*d","B"
722,1,7348,651,0.520000," ","int(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
723,1,1839,340,1.506000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(5/2),x)","\frac{\frac{28 a c \,d^{4} \left(\sin^{3}\left(f x +e \right)\right)}{15}+\frac{12 b \,c^{2} d^{3} \left(\sin^{3}\left(f x +e \right)\right)}{7}+\frac{22 a \,c^{2} d^{3} \left(\sin^{2}\left(f x +e \right)\right)}{15}-\frac{28 a c \,d^{4} \sin \left(f x +e \right)}{15}-\frac{12 b \,c^{2} d^{3} \sin \left(f x +e \right)}{7}-\frac{22 a \,c^{2} d^{3}}{15}-\frac{6 b \,c^{3} d^{2}}{7}-\frac{10 b c \,d^{4}}{21}+\frac{6 b \,c^{3} d^{2} \left(\sin^{2}\left(f x +e \right)\right)}{7}-\frac{2 b c \,d^{4} \left(\sin^{2}\left(f x +e \right)\right)}{3}+\frac{8 b c \,d^{4} \left(\sin^{4}\left(f x +e \right)\right)}{7}-\frac{10 b \,d^{5} \sin \left(f x +e \right)}{21}-\frac{2 a \,d^{5} \left(\sin^{2}\left(f x +e \right)\right)}{5}+\frac{2 b \,d^{5} \left(\sin^{5}\left(f x +e \right)\right)}{7}+\frac{4 b \,d^{5} \left(\sin^{3}\left(f x +e \right)\right)}{21}+\frac{2 a \,d^{5} \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{58 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c \,d^{4}}{21}+2 a \,c^{4} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d +\frac{16 a \,c^{3} \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}}{15}-\frac{4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,c^{2} d^{3}}{5}-\frac{16 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a c \,d^{4}}{15}+\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{4} d}{7}+\frac{16 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{3} d^{2}}{7}+\frac{4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{2} d^{3}}{21}-\frac{16 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c \,d^{4}}{7}-\frac{46 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,c^{4} d}{15}+\frac{28 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,c^{2} d^{3}}{15}-\frac{52 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{3} d^{2}}{21}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{5}}{7}+\frac{6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,d^{5}}{5}-\frac{6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,d^{5}}{5}-\frac{10 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,d^{5}}{21}}{d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/105*(-15*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^5+45*b*c^3*d^2*sin(f*x+e)^2-35*b*c*d^4*sin(f*x+e)^2-98*a*c*d^4*sin(f*x+e)-90*b*c^2*d^3*sin(f*x+e)+60*b*c*d^4*sin(f*x+e)^4+98*a*c*d^4*sin(f*x+e)^3+90*b*c^2*d^3*sin(f*x+e)^3+77*a*c^2*d^3*sin(f*x+e)^2-77*a*c^2*d^3-45*b*c^3*d^2-25*b*c*d^4+15*b*d^5*sin(f*x+e)^5+21*a*d^5*sin(f*x+e)^4+10*b*d^5*sin(f*x+e)^3-21*a*d^5*sin(f*x+e)^2-25*b*d^5*sin(f*x+e)+63*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*d^5-63*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*d^5+145*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c*d^4+105*a*c^4*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d+56*a*c^3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2-42*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c^2*d^3-56*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c*d^4+15*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^4*d+120*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^3*d^2+10*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^2*d^3-120*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c*d^4-161*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c^4*d+98*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c^2*d^3-130*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^3*d^2-25*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d^5)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
724,1,1449,281,1.536000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x)","\frac{2 c^{3} a \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d +\frac{2 c^{2} a \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d^{2}}{3}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a c \,d^{3}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,d^{4}}{3}+\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{3} d}{5}+\frac{6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{2} d^{2}}{5}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c \,d^{3}}{5}-\frac{6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,d^{4}}{5}-\frac{8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,c^{3} d}{3}+\frac{8 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a c \,d^{3}}{3}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{4}}{5}-\frac{4 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{2} d^{2}}{5}+\frac{6 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,d^{4}}{5}+\frac{2 b \,d^{4} \left(\sin^{4}\left(f x +e \right)\right)}{5}+\frac{2 a \,d^{4} \left(\sin^{3}\left(f x +e \right)\right)}{3}+\frac{6 b c \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)}{5}+\frac{2 a c \,d^{3} \left(\sin^{2}\left(f x +e \right)\right)}{3}+\frac{4 b \,c^{2} d^{2} \left(\sin^{2}\left(f x +e \right)\right)}{5}-\frac{2 b \,d^{4} \left(\sin^{2}\left(f x +e \right)\right)}{5}-\frac{2 a \,d^{4} \sin \left(f x +e \right)}{3}-\frac{6 b c \,d^{3} \sin \left(f x +e \right)}{5}-\frac{2 a c \,d^{3}}{3}-\frac{4 b \,c^{2} d^{2}}{5}}{d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/15*(15*c^3*a*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d+5*c^2*a*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d^2-15*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c*d^3-5*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*d^4+3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^3*d+9*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^2*d^2-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c*d^3-9*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d^4-20*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c^3*d+20*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c*d^3-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^4-6*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^2*d^2+9*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d^4+3*b*d^4*sin(f*x+e)^4+5*a*d^4*sin(f*x+e)^3+9*b*c*d^3*sin(f*x+e)^3+5*a*c*d^3*sin(f*x+e)^2+6*b*c^2*d^2*sin(f*x+e)^2-3*b*d^4*sin(f*x+e)^2-5*a*d^4*sin(f*x+e)-9*b*c*d^3*sin(f*x+e)-5*a*c*d^3-6*b*c^2*d^2)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
725,1,862,231,1.249000," ","int((a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x)","\frac{2 c^{2} a \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d -2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,d^{3}+\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{2} d}{3}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,d^{3}}{3}-2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,c^{2} d +2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) a \,d^{3}-\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b \,c^{3}}{3}+\frac{2 \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c \,d^{2}}{3}+\frac{2 b \,d^{3} \left(\sin^{3}\left(f x +e \right)\right)}{3}+\frac{2 b c \,d^{2} \left(\sin^{2}\left(f x +e \right)\right)}{3}-\frac{2 b \,d^{3} \sin \left(f x +e \right)}{3}-\frac{2 c \,d^{2} b}{3}}{d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2/3*(3*c^2*a*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*d^3+((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^2*d-((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d^3-3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*c^2*d+3*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*a*d^3-((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c^3+((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c*d^2+b*d^3*sin(f*x+e)^3+b*c*d^2*sin(f*x+e)^2-b*d^3*sin(f*x+e)-c*d^2*b)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
726,1,243,198,1.328000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","-\frac{2 \left(c -d \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \left(\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c +\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b d -a \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d -\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b d \right)}{d^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2*(c-d)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c+EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d-a*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d-EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d)/d^2/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
727,1,567,251,3.274000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(d a -c b \right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*b/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+(a*d-b*c)/d*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
728,1,887,331,5.127000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\left(d a -c b \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}+\frac{b \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((a*d-b*c)/d*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+b/d*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
729,1,1049,411,7.602000," ","int((a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\left(d a -c b \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}+\frac{b \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((a*d-b*c)/d*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+b/d*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
730,1,2112,489,7.077000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{2} d^{3} \left(-\frac{2 \left(\sin^{3}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{9 d}+\frac{16 c \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{63 d^{2}}-\frac{2 \left(\frac{7}{9}+\frac{16 c^{2}}{21 d^{2}}\right) \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}-\frac{2 \left(-64 c^{3}-62 c \,d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{315 d^{4}}+\frac{2 \left(32 c^{3}+36 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{315 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(128 c^{4}+108 c^{2} d^{2}+147 d^{4}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{315 d^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) \left(-\frac{2 \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 d}+\frac{12 c \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 d^{2}}-\frac{2 \left(\frac{5}{7}+\frac{24 c^{2}}{35 d^{2}}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(-\frac{4 c^{2}}{35 d^{2}}+\frac{5}{21}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(-48 c^{3}-44 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c^{3} a^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^2*d^3*(-2/9/d*sin(f*x+e)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+16/63*c/d^2*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/5*(7/9+16/21*c^2/d^2)/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/315*(-64*c^3-62*c*d^2)/d^4*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/315*(32*c^3+36*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/315*(128*c^4+108*c^2*d^2+147*d^4)/d^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(2*a*b*d^3+3*b^2*c*d^2)*(-2/7/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+12/35*c/d^2*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3*(5/7+24/35*c^2/d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(-4/35*c^2/d^2+5/21)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/105*(-48*c^3-44*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(3*a^2*c^2*d+2*a*b*c^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*c^3*a^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
731,1,1575,389,5.135000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{2} d^{2} \left(-\frac{2 \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 d}+\frac{12 c \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 d^{2}}-\frac{2 \left(\frac{5}{7}+\frac{24 c^{2}}{35 d^{2}}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(-\frac{4 c^{2}}{35 d^{2}}+\frac{5}{21}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(-48 c^{3}-44 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(2 a b \,d^{2}+2 b^{2} c d \right) \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(2 a^{2} c d +2 a b \,c^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{2} c^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^2*d^2*(-2/7/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+12/35*c/d^2*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3*(5/7+24/35*c^2/d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(-4/35*c^2/d^2+5/21)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/105*(-48*c^3-44*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(2*a*b*d^2+2*b^2*c*d)*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(a^2*d^2+4*a*b*c*d+b^2*c^2)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(2*a^2*c*d+2*a*b*c^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^2*c^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
732,1,1100,300,4.434000," ","int((a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{2} d \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(2 a b d +b^{2} c \right) \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(a^{2} d +2 a b c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{2} c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^2*d*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(2*a*b*d+b^2*c)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(a^2*d+2*a*b*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^2*c*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
733,1,695,253,2.998000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{2} \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{4 a b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+4*a*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
734,1,888,284,3.989000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{b \left(\frac{2 b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{4 d a \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{2 c b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b/d^2*(2*b*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+4*d*a*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-2*c*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(a^2*d^2-2*a*b*c*d+b^2*c^2)/d^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
735,1,1043,375,6.034000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 b^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{d^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}+\frac{2 b \left(d a -c b \right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*b^2/d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+1/d^2*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*b/d^2*(a*d-b*c)*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
736,1,1450,502,8.367000," ","int((a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}+\frac{2 b \left(d a -c b \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}+\frac{b^{2} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((a^2*d^2-2*a*b*c*d+b^2*c^2)/d^2*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*b*(a*d-b*c)/d^2*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+b^2/d^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
737,1,2728,676,9.399000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^3*d^3*(-2/11/d*sin(f*x+e)^4*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+20/99*c/d^2*sin(f*x+e)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/7*(9/11+80/99*c^2/d^2)/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3465*(-480*c^3-472*c*d^2)/d^4*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3465*(640*c^4+596*c^2*d^2+675*d^4)/d^5*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3465*(-320*c^4-348*c^2*d^2+675*d^4)/d^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/3465*(-1280*c^5-1032*c^3*d^2-1146*c*d^4)/d^5*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a*b^2*d^3+3*b^3*c*d^2)*(-2/9/d*sin(f*x+e)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+16/63*c/d^2*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/5*(7/9+16/21*c^2/d^2)/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/315*(-64*c^3-62*c*d^2)/d^4*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/315*(32*c^3+36*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/315*(128*c^4+108*c^2*d^2+147*d^4)/d^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a^2*b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*(-2/7/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+12/35*c/d^2*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3*(5/7+24/35*c^2/d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(-4/35*c^2/d^2+5/21)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/105*(-48*c^3-44*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3)*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a^3*c*d^2+9*a^2*b*c^2*d+3*a*b^2*c^3)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(3*a^3*c^2*d+3*a^2*b*c^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*c^3*a^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
738,1,2112,534,7.027000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{3} d^{2} \left(-\frac{2 \left(\sin^{3}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{9 d}+\frac{16 c \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{63 d^{2}}-\frac{2 \left(\frac{7}{9}+\frac{16 c^{2}}{21 d^{2}}\right) \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}-\frac{2 \left(-64 c^{3}-62 c \,d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{315 d^{4}}+\frac{2 \left(32 c^{3}+36 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{315 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(128 c^{4}+108 c^{2} d^{2}+147 d^{4}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{315 d^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(3 d^{2} a \,b^{2}+2 b^{3} c d \right) \left(-\frac{2 \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 d}+\frac{12 c \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 d^{2}}-\frac{2 \left(\frac{5}{7}+\frac{24 c^{2}}{35 d^{2}}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(-\frac{4 c^{2}}{35 d^{2}}+\frac{5}{21}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(-48 c^{3}-44 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(3 a^{2} b \,d^{2}+6 a \,b^{2} c d +b^{3} c^{2}\right) \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(a^{3} d^{2}+6 a^{2} b c d +3 c^{2} a \,b^{2}\right) \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(2 a^{3} c d +3 a^{2} b \,c^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c^{2} a^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^3*d^2*(-2/9/d*sin(f*x+e)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+16/63*c/d^2*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/5*(7/9+16/21*c^2/d^2)/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/315*(-64*c^3-62*c*d^2)/d^4*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/315*(32*c^3+36*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/315*(128*c^4+108*c^2*d^2+147*d^4)/d^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a*b^2*d^2+2*b^3*c*d)*(-2/7/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+12/35*c/d^2*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3*(5/7+24/35*c^2/d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(-4/35*c^2/d^2+5/21)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/105*(-48*c^3-44*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a^2*b*d^2+6*a*b^2*c*d+b^3*c^2)*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(a^3*d^2+6*a^2*b*c*d+3*a*b^2*c^2)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(2*a^3*c*d+3*a^2*b*c^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*c^2*a^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
739,1,1561,417,5.820000," ","int((a+b*sin(f*x+e))^3*(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{3} d \left(-\frac{2 \left(\sin^{2}\left(f x +e \right)\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 d}+\frac{12 c \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 d^{2}}-\frac{2 \left(\frac{5}{7}+\frac{24 c^{2}}{35 d^{2}}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(-\frac{4 c^{2}}{35 d^{2}}+\frac{5}{21}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(-48 c^{3}-44 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(3 a \,b^{2} d +b^{3} c \right) \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\left(3 a^{2} b d +3 a \,b^{2} c \right) \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(a^{3} d +3 a^{2} b c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{3} c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^3*d*(-2/7/d*sin(f*x+e)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+12/35*c/d^2*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)-2/3*(5/7+24/35*c^2/d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(-4/35*c^2/d^2+5/21)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/105*(-48*c^3-44*c*d^2)/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a*b^2*d+b^3*c)*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+(3*a^2*b*d+3*a*b^2*c)*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(a^3*d+3*a^2*b*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^3*c*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
740,1,1085,348,4.182000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(b^{3} \left(-\frac{2 \sin \left(f x +e \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 d}+\frac{8 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 d^{2}}+\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{15 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(\frac{3}{5}+\frac{8 c^{2}}{15 d^{2}}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+3 a \,b^{2} \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{6 a^{2} b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^3*(-2/5/d*sin(f*x+e)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+8/15*c/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+4/15*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*(3/5+8/15*c^2/d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*a*b^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+6*a^2*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
741,1,1398,409,5.200000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{b \left(b^{2} d^{2} \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(3 a b \,d^{2}-b^{2} c d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 a^{2} d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{6 a b c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 b^{2} c^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(1/d^3*b*(b^2*d^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(3*a*b*d^2-b^2*c*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+6*a^2*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-6*a*b*c*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2*b^2*c^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/d^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
742,1,1379,437,6.790000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{b^{2} \left(\frac{2 b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 d a \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 b \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(b^2/d^3*(2*b*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+6*d*a*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4*c*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/d^3*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*b/d^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
743,1,1621,574,9.591000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(7/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 b^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{d^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{3 b \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 b^{2} \left(d a -c b \right) \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*b^3/d^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+3*b/d^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+1/d^3*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*b^2/d^3*(a*d-b*c)*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
744,1,2111,754,14.084000," ","int((a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(9/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{7 \left(c^{2}-d^{2}\right) d^{3} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{4}}+\frac{24 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{35 \left(c^{2}-d^{2}\right)^{2} d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{2 \left(71 c^{2}+25 d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{105 d \left(c^{2}-d^{2}\right)^{3} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{32 d \left(\cos^{2}\left(f x +e \right)\right) c \left(11 c^{2}+13 d^{2}\right)}{105 \left(c^{2}-d^{2}\right)^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(105 c^{4}+254 c^{2} d^{2}+25 d^{4}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(105 c^{8}-420 c^{6} d^{2}+630 d^{4} c^{4}-420 c^{2} d^{6}+105 d^{8}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{32 c d \left(11 c^{2}+13 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{105 \left(c^{2}-d^{2}\right)^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 b^{2} \left(d a -c b \right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{3 b \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{5 \left(c^{2}-d^{2}\right) d^{2} \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{3}}+\frac{16 c \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{15 \left(c^{2}-d^{2}\right)^{2} d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{2 d \left(\cos^{2}\left(f x +e \right)\right) \left(23 c^{2}+9 d^{2}\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(15 c^{3}+17 c \,d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(15 c^{6}-45 c^{4} d^{2}+45 c^{2} d^{4}-15 d^{6}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(23 c^{2}+9 d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{15 \left(c^{2}-d^{2}\right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}+\frac{b^{3} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/d^3*(2/7/(c^2-d^2)/d^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^4+24/35/(c^2-d^2)^2/d^2*c*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+2/105*(71*c^2+25*d^2)/d/(c^2-d^2)^3*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+32/105*d*cos(f*x+e)^2/(c^2-d^2)^4*c*(11*c^2+13*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(105*c^4+254*c^2*d^2+25*d^4)/(105*c^8-420*c^6*d^2+630*c^4*d^4-420*c^2*d^6+105*d^8)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+32/105*c*d*(11*c^2+13*d^2)/(c^2-d^2)^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*b^2*(a*d-b*c)/d^3*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+3*b*(a^2*d^2-2*a*b*c*d+b^2*c^2)/d^3*(2/5/(c^2-d^2)/d^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^3+16/15*c/(c^2-d^2)^2/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+2/15*d*cos(f*x+e)^2/(c^2-d^2)^3*(23*c^2+9*d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(15*c^3+17*c*d^2)/(15*c^6-45*c^4*d^2+45*c^2*d^4-15*d^6)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/15*d*(23*c^2+9*d^2)/(c^2-d^2)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+b^3/d^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
745,1,1190,375,4.416000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{d \left(b^{2} d^{2} \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(-a b \,d^{2}+3 b^{2} c d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 a^{2} d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{6 a b c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 b^{2} c^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{b^{3}}+\frac{2 \left(-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,b^{2} c^{2} d +b^{3} c^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(d/b^3*(b^2*d^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(-a*b*d^2+3*b^2*c*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*a^2*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-6*a*b*c*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+6*b^2*c^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+2*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/b^4*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
746,1,391,316,1.515000," ","int((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","-\frac{2 \left(\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b c +\EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b d +a \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) d -2 c b \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)-\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right) b d -\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right) a d +\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right) b c \right) \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \left(c -d \right)}{b^{2} \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"-2*(EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*c+EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d+a*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*d-2*c*b*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))*b*d-EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2))*a*d+EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2))*b*c)/b^2*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(c-d)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
747,1,181,211,1.422000," ","int((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{2 \left(\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)-\EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right)\right) \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \left(c -d \right)}{b \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2*(EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2)))/b*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(c-d)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
748,1,151,104,1.554000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x)","\frac{2 \left(c -d \right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{-\frac{\left(\sin \left(f x +e \right)-1\right) d}{c +d}}\, \sqrt{-\frac{d \left(1+\sin \left(f x +e \right)\right)}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, -\frac{\left(c -d \right) b}{d a -c b}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right) \cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"2*(c-d)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(-(sin(f*x+e)-1)*d/(c+d))^(1/2)*(-d*(1+sin(f*x+e))/(c-d))^(1/2)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),-(c-d)*b/(a*d-b*c),((c-d)/(c+d))^(1/2))/(a*d-b*c)/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
749,1,610,276,3.766000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{d \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d a -c b}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(-2/(a*d-b*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+d/(a*d-b*c)*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
750,1,1072,474,6.198000," ","int(1/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{d \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{d a -c b}-\frac{d b \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(d a -c b \right)^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*b/(a*d-b*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+d/(a*d-b*c)*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-d*b/(a*d-b*c)^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
751,1,1886,612,7.199000," ","int((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{d^{2} \left(b^{2} d^{2} \left(-\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 d}+\frac{2 \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{3 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 d \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+\frac{2 \left(-2 a b \,d^{2}+4 b^{2} c d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 a^{2} d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{16 a b c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{12 b^{2} c^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{b^{4}}-\frac{8 d \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{5} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{4}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(d^2/b^4*(b^2*d^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(-2*a*b*d^2+4*b^2*c*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+6*a^2*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-16*a*b*c*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+12*b^2*c^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))-8/b^5*d*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^4*(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
752,1,1363,476,6.697000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{d^{2} \left(\frac{2 b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 d a \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{6 c b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{b^{3}}+\frac{6 d \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,b^{2} c^{2} d +b^{3} c^{3}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(d^2/b^3*(2*b*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))-4*d*a*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+6*c*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+6/b^4*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^3*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
753,1,1027,439,5.111000," ","int((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{4 d \left(d a -c b \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*d^2/b^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/b^3*d*(a*d-b*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^2*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
754,1,872,393,4.823000," ","int((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^2,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(-d a +c b \right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*d/b^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+(-a*d+b*c)/b*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
755,1,690,411,3.824000," ","int(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
756,1,1266,533,6.921000," ","int(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{d^{2} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(d a -c b \right)^{2}}-\frac{b \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{d a -c b}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(-2*d/(a*d-b*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+d^2/(a*d-b*c)^2*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-b/(a*d-b*c)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
757,1,1731,735,11.970000," ","int(1/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e))^(5/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{4 b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{d^{2} \left(\frac{2 \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{3 \left(c^{2}-d^{2}\right) d \left(\sin \left(f x +e \right)+\frac{c}{d}\right)^{2}}+\frac{8 d \left(\cos^{2}\left(f x +e \right)\right) c}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 \left(3 c^{2}+d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(3 c^{4}-6 c^{2} d^{2}+3 d^{4}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{3 \left(c^{2}-d^{2}\right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(d a -c b \right)^{2}}-\frac{2 d^{2} b \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(d a -c b \right)^{3}}+\frac{b^{2} \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{\left(d a -c b \right)^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(4*b/(a*d-b*c)^3*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+d^2/(a*d-b*c)^2*(2/3/(c^2-d^2)/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(sin(f*x+e)+c/d)^2+8/3*d*cos(f*x+e)^2/(c^2-d^2)^2*c/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*(3*c^2+d^2)/(3*c^4-6*c^2*d^2+3*d^4)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8/3*c*d/(c^2-d^2)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-2*d^2/(a*d-b*c)^3*b*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+b^2/(a*d-b*c)^2*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
758,1,2775,885,13.686000," ","int((c+d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e))^3,x)","\text{Expression too large to display}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(d^3/b^5*(b^2*d^2*(-2/3/d*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2/3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-4/3*c/d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))+2*(-3*a*b*d^2+5*b^2*c*d)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+12*a^2*d^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-30*a*b*c*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+20*b^2*c^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))-20/b^6*d^2*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^5*(-a^5*d^5+5*a^4*b*c*d^4-10*a^3*b^2*c^2*d^3+10*a^2*b^3*c^3*d^2-5*a*b^4*c^4*d+b^5*c^5)*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))+5/b^5*d*(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
759,1,2237,678,11.597000," ","int((c+d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{d^{3} \left(\frac{2 b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{6 d a \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{8 c b \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{b^{4}}+\frac{12 d^{2} \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{5} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{4}}-\frac{4 d \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{4}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(d^3/b^4*(2*b*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))-6*d*a*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+8*c*b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+12/b^5*d^2*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^4*(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))-4/b^4*d*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
760,1,1888,622,10.042000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{3} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{6 d^{2} \left(d a -c b \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{4} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,b^{2} c^{2} d +b^{3} c^{3}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{3}}+\frac{3 d \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{3}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*d^3/b^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-6/b^4*d^2*(a*d-b*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+1/b^3*(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))+3/b^3*d*(a^2*d^2-2*a*b*c*d+b^2*c^2)*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
761,1,1718,545,9.957000," ","int((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{b^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{2}}-\frac{2 d \left(d a -c b \right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(2*d^2/b^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))+(a^2*d^2-2*a*b*c*d+b^2*c^2)/b^2*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))-2*d*(a*d-b*c)/b^2*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
762,1,1525,560,9.439000," ","int((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^3,x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\left(-d a +c b \right) \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b}+\frac{d \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{b}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-a*d+b*c)/b*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))+d/b*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
763,1,867,576,6.336000," ","int(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","A"
764,1,2099,751,13.150000," ","int(1/(a+b*sin(f*x+e))^3/(c+d*sin(f*x+e))^(3/2),x)","\frac{\sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{2 d^{2} \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(d a -c b \right)^{3} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}-\frac{b \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{2} \left(3 a^{2} d -2 a b c -b^{2} d \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \left(a +b \sin \left(f x +e \right)\right)}-\frac{d \left(7 a^{3} d -4 a^{2} b c -a \,b^{2} d -2 b^{3} c \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{3 b d \left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(15 a^{4} d^{2}-20 a^{3} b c d +8 a^{2} b^{2} c^{2}-6 a^{2} b^{2} d^{2}-4 a \,b^{3} c d +4 b^{4} c^{2}+3 b^{4} d^{2}\right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{4 \left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right)^{2} b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{d a -c b}+\frac{d^{3} \left(\frac{2 d \left(\cos^{2}\left(f x +e \right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 c \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{2 d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(c^{2}-d^{2}\right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\left(d a -c b \right)^{3}}-\frac{b d \left(-\frac{b^{2} \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \left(a +b \sin \left(f x +e \right)\right)}-\frac{a d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{b d \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \left(\left(-\frac{c}{d}-1\right) \EllipticE \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)+\EllipticF \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \sqrt{\frac{c -d}{c +d}}\right)\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{\left(3 a^{2} d -2 a b c -b^{2} d \right) \left(\frac{c}{d}-1\right) \sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}\, \sqrt{\frac{d \left(1-\sin \left(f x +e \right)\right)}{c +d}}\, \sqrt{\frac{\left(-\sin \left(f x +e \right)-1\right) d}{c -d}}\, \EllipticPi \left(\sqrt{\frac{c +d \sin \left(f x +e \right)}{c -d}}, \frac{-\frac{c}{d}+1}{-\frac{c}{d}+\frac{a}{b}}, \sqrt{\frac{c -d}{c +d}}\right)}{\left(a^{3} d -a^{2} b c -a \,b^{2} d +b^{3} c \right) b \sqrt{-\left(-d \sin \left(f x +e \right)-c \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{c}{d}+\frac{a}{b}\right)}\right)}{\left(d a -c b \right)^{2}}\right)}{\cos \left(f x +e \right) \sqrt{c +d \sin \left(f x +e \right)}\, f}"," ",0,"(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*(-2*d^2/(a*d-b*c)^3*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))-b/(a*d-b*c)*(-1/2*b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))^2-3/4*b^2*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-1/4*d*(7*a^3*d-4*a^2*b*c-a*b^2*d-2*b^3*c)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-3/4*b*d*(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+1/4*(15*a^4*d^2-20*a^3*b*c*d+8*a^2*b^2*c^2-6*a^2*b^2*d^2-4*a*b^3*c*d+4*b^4*c^2+3*b^4*d^2)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)^2/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2)))+d^3/(a*d-b*c)^3*(2*d*cos(f*x+e)^2/(c^2-d^2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)+2*c/(c^2-d^2)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+2/(c^2-d^2)*d*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))))-b*d/(a*d-b*c)^2*(-b^2/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e))-a*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))-b*d/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)*((-c/d-1)*EllipticE(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2))+EllipticF(((c+d*sin(f*x+e))/(c-d))^(1/2),((c-d)/(c+d))^(1/2)))+(3*a^2*d-2*a*b*c-b^2*d)/(a^3*d-a^2*b*c-a*b^2*d+b^3*c)/b*(c/d-1)*((c+d*sin(f*x+e))/(c-d))^(1/2)*(d*(1-sin(f*x+e))/(c+d))^(1/2)*((-sin(f*x+e)-1)*d/(c-d))^(1/2)/(-(-d*sin(f*x+e)-c)*cos(f*x+e)^2)^(1/2)/(-c/d+a/b)*EllipticPi(((c+d*sin(f*x+e))/(c-d))^(1/2),(-c/d+1)/(-c/d+a/b),((c-d)/(c+d))^(1/2))))/cos(f*x+e)/(c+d*sin(f*x+e))^(1/2)/f","B"
765,1,404501,819,17.169000," ","int((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
766,1,277000,715,6.806000," ","int((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
767,1,146762,579,1.850000," ","int((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
768,1,248299,183,5.864000," ","int((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
769,1,46827,379,1.060000," ","int((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
770,1,196704,449,4.500000," ","int((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
771,1,577718,1005,27.128000," ","int((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"
772,1,409354,801,17.433000," ","int((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","C"
773,1,278658,677,8.967000," ","int((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","C"
774,1,529691,595,10.601000," ","int((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"
775,1,2626418,555,133.542000," ","int((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"
776,1,190874,457,3.432000," ","int((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"
777,1,755109,1214,79.797000," ","int((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
778,1,577725,996,28.455000," ","int((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
779,1,410016,825,19.753000," ","int((a+b*sin(f*x+e))^(5/2)*(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
780,1,730813,682,22.141000," ","int((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
781,1,3436958,727,51.243000," ","int((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
782,-1,0,682,180.000000," ","int((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x)","F"
783,1,731601,709,24.280000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
784,1,544151,595,10.947000," ","int((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
785,1,248841,183,4.645000," ","int((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
786,1,1233,177,0.694000," ","int(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x)","-\frac{4 \EllipticF \left(\sqrt{-\frac{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}-c \sin \left(f x +e \right)-d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}-d \right) \left(c \sqrt{-a^{2}+b^{2}}-a \sqrt{-c^{2}+d^{2}}-d a +c b \right)}{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}+c \sin \left(f x +e \right)+d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}+d \right) \left(a \sqrt{-c^{2}+d^{2}}+c \sqrt{-a^{2}+b^{2}}-d a +c b \right)}}, \sqrt{\frac{\left(a \sqrt{-c^{2}+d^{2}}+c \sqrt{-a^{2}+b^{2}}+d a -c b \right) \left(a \sqrt{-c^{2}+d^{2}}+c \sqrt{-a^{2}+b^{2}}-d a +c b \right)}{\left(a \sqrt{-c^{2}+d^{2}}-c \sqrt{-a^{2}+b^{2}}-d a +c b \right) \left(a \sqrt{-c^{2}+d^{2}}-c \sqrt{-a^{2}+b^{2}}+d a -c b \right)}}\right) \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}-c \sin \left(f x +e \right)-d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}-d \right) \left(a \sqrt{-c^{2}+d^{2}}-c \sqrt{-a^{2}+b^{2}}+d a -c b \right)}{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}+c \sin \left(f x +e \right)+d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}+d \right) \left(a \sqrt{-c^{2}+d^{2}}+c \sqrt{-a^{2}+b^{2}}-d a +c b \right)}}\, \sqrt{\frac{\left(\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}+a \sin \left(f x +e \right)+b \cos \left(f x +e \right)+\sqrt{-a^{2}+b^{2}}+b \right) \sqrt{-c^{2}+d^{2}}\, c}{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}+c \sin \left(f x +e \right)+d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}+d \right) \left(a \sqrt{-c^{2}+d^{2}}+c \sqrt{-a^{2}+b^{2}}-d a +c b \right)}}\, \sqrt{-\frac{\left(\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}-a \sin \left(f x +e \right)-b \cos \left(f x +e \right)+\sqrt{-a^{2}+b^{2}}-b \right) \sqrt{-c^{2}+d^{2}}\, c}{\left(\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}+c \sin \left(f x +e \right)+d \cos \left(f x +e \right)+\sqrt{-c^{2}+d^{2}}+d \right) \left(a \sqrt{-c^{2}+d^{2}}-c \sqrt{-a^{2}+b^{2}}-d a +c b \right)}}\, \sqrt{a +b \sin \left(f x +e \right)}\, \sqrt{c +d \sin \left(f x +e \right)}\, \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(c \sqrt{-c^{2}+d^{2}}\, \sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)+b c \sqrt{-c^{2}+d^{2}}\, \sin \left(f x +e \right)+c d \sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-a \,c^{2} \sin \left(f x +e \right)+b c d \sin \left(f x +e \right)+\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}\, \sqrt{-a^{2}+b^{2}}\, d -\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}\, a c +\cos \left(f x +e \right) \sqrt{-c^{2}+d^{2}}\, b d -\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}\, c^{2}+\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}\, d^{2}-\cos \left(f x +e \right) b \,c^{2}+\cos \left(f x +e \right) b \,d^{2}+d \sqrt{-c^{2}+d^{2}}\, \sqrt{-a^{2}+b^{2}}+b d \sqrt{-c^{2}+d^{2}}+d^{2} \sqrt{-a^{2}+b^{2}}-a c d +d^{2} b \right)}{f \sin \left(f x +e \right)^{4} \left(-\left(\cos^{2}\left(f x +e \right)\right) b d +a d \sin \left(f x +e \right)+b c \sin \left(f x +e \right)+c a +b d \right) \sqrt{-c^{2}+d^{2}}\, \left(a \sqrt{-c^{2}+d^{2}}-c \sqrt{-a^{2}+b^{2}}+d a -c b \right)}"," ",0,"-4/f*EllipticF((-(cos(f*x+e)*(-c^2+d^2)^(1/2)-c*sin(f*x+e)-d*cos(f*x+e)+(-c^2+d^2)^(1/2)-d)*(c*(-a^2+b^2)^(1/2)-a*(-c^2+d^2)^(1/2)-d*a+c*b)/(cos(f*x+e)*(-c^2+d^2)^(1/2)+c*sin(f*x+e)+d*cos(f*x+e)+(-c^2+d^2)^(1/2)+d)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b))^(1/2),((a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)+d*a-c*b)*(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b)/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)-d*a+c*b)/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b))^(1/2))*((cos(f*x+e)*(-c^2+d^2)^(1/2)-c*sin(f*x+e)-d*cos(f*x+e)+(-c^2+d^2)^(1/2)-d)/(cos(f*x+e)*(-c^2+d^2)^(1/2)+c*sin(f*x+e)+d*cos(f*x+e)+(-c^2+d^2)^(1/2)+d)*(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b)/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b))^(1/2)*((cos(f*x+e)*(-a^2+b^2)^(1/2)+a*sin(f*x+e)+b*cos(f*x+e)+(-a^2+b^2)^(1/2)+b)/(cos(f*x+e)*(-c^2+d^2)^(1/2)+c*sin(f*x+e)+d*cos(f*x+e)+(-c^2+d^2)^(1/2)+d)*(-c^2+d^2)^(1/2)*c/(a*(-c^2+d^2)^(1/2)+c*(-a^2+b^2)^(1/2)-d*a+c*b))^(1/2)*(-(cos(f*x+e)*(-a^2+b^2)^(1/2)-a*sin(f*x+e)-b*cos(f*x+e)+(-a^2+b^2)^(1/2)-b)/(cos(f*x+e)*(-c^2+d^2)^(1/2)+c*sin(f*x+e)+d*cos(f*x+e)+(-c^2+d^2)^(1/2)+d)*(-c^2+d^2)^(1/2)*c/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)-d*a+c*b))^(1/2)*(a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(c*(-c^2+d^2)^(1/2)*(-a^2+b^2)^(1/2)*sin(f*x+e)+b*c*(-c^2+d^2)^(1/2)*sin(f*x+e)+c*d*(-a^2+b^2)^(1/2)*sin(f*x+e)-a*c^2*sin(f*x+e)+b*c*d*sin(f*x+e)+cos(f*x+e)*(-c^2+d^2)^(1/2)*(-a^2+b^2)^(1/2)*d-cos(f*x+e)*(-c^2+d^2)^(1/2)*a*c+cos(f*x+e)*(-c^2+d^2)^(1/2)*b*d-cos(f*x+e)*(-a^2+b^2)^(1/2)*c^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*d^2-cos(f*x+e)*b*c^2+cos(f*x+e)*b*d^2+d*(-c^2+d^2)^(1/2)*(-a^2+b^2)^(1/2)+b*d*(-c^2+d^2)^(1/2)+d^2*(-a^2+b^2)^(1/2)-a*c*d+d^2*b)/sin(f*x+e)^4/(-cos(f*x+e)^2*b*d+a*d*sin(f*x+e)+b*c*sin(f*x+e)+c*a+b*d)/(-c^2+d^2)^(1/2)/(a*(-c^2+d^2)^(1/2)-c*(-a^2+b^2)^(1/2)+d*a-c*b)","B"
787,1,41868,375,1.134000," ","int(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
788,1,218898,481,5.595000," ","int(1/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
789,1,3904542,769,59.718000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
790,1,2948827,555,142.722000," ","int((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"
791,1,47019,379,0.969000," ","int((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"
792,1,40621,375,1.021000," ","int(1/(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"
793,1,119964,461,2.083000," ","int(1/(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"
794,1,415383,637,10.108000," ","int(1/(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"
795,-1,0,681,180.000000," ","int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(5/2),x)","\int \frac{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}{\left(a +b \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c+d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))^(5/2),x)","F"
796,1,195220,457,4.101000," ","int((c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
797,1,212259,449,4.683000," ","int((c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
798,1,242318,476,5.832000," ","int(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
799,1,438748,642,10.676000," ","int(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
800,1,1123217,889,30.727000," ","int(1/(a+b*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
801,0,0,27,1.625000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
802,0,0,283,1.309000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","F"
803,0,0,201,0.412000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e)),x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e)),x)","F"
804,0,0,90,0.649000," ","int((a+b*sin(f*x+e))^m,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*sin(f*x+e))^m,x)","F"
805,0,0,27,1.422000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","F"
806,0,0,27,1.578000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","F"
807,0,0,27,1.908000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","F"
808,0,0,27,0.314000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(5/2),x)","F"
809,0,0,27,0.257000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2),x)","F"
810,0,0,27,0.244000," ","int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \sqrt{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2),x)","F"
811,0,0,27,0.228000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{\sqrt{c +d \sin \left(f x +e \right)}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(1/2),x)","F"
812,0,0,27,0.220000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(3/2),x)","F"
813,0,0,27,0.239000," ","int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x)","\int \frac{\left(a +b \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*sin(f*x+e))^m/(c+d*sin(f*x+e))^(5/2),x)","F"
814,0,0,240,5.857000," ","int((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^3,x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^3,x)","F"
815,0,0,179,8.406000," ","int((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^2,x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+a*sin(f*x+e))^2,x)","F"
816,0,0,129,1.866000," ","int((d*csc(f*x+e))^n*(a+a*sin(f*x+e)),x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+a*sin(f*x+e)),x)","F"
817,0,0,153,0.852000," ","int((d*csc(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(d \csc \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((d*csc(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
818,0,0,205,1.946000," ","int((d*csc(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(d \csc \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*csc(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
819,0,0,100,0.878000," ","int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^m,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^m,x)","F"
820,0,0,283,1.418000," ","int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^3,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^3,x)","F"
821,0,0,206,1.435000," ","int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^2,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e))^2,x)","F"
822,0,0,147,0.503000," ","int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e)),x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +a \sin \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+a*sin(f*x+e)),x)","F"
823,0,0,174,0.336000," ","int((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e)),x)","F"
824,0,0,264,1.426000," ","int((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n/(a+a*sin(f*x+e))^2,x)","F"
825,0,0,266,6.323000," ","int((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^3,x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +b \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^3,x)","F"
826,0,0,189,7.819000," ","int((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^2,x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +b \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+b*sin(f*x+e))^2,x)","F"
827,0,0,129,2.382000," ","int((d*csc(f*x+e))^n*(a+b*sin(f*x+e)),x)","\int \left(d \csc \left(f x +e \right)\right)^{n} \left(a +b \sin \left(f x +e \right)\right)\, dx"," ",0,"int((d*csc(f*x+e))^n*(a+b*sin(f*x+e)),x)","F"
828,0,0,188,0.877000," ","int((d*csc(f*x+e))^n/(a+b*sin(f*x+e)),x)","\int \frac{\left(d \csc \left(f x +e \right)\right)^{n}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((d*csc(f*x+e))^n/(a+b*sin(f*x+e)),x)","F"
829,0,0,297,1.917000," ","int((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(d \csc \left(f x +e \right)\right)^{n}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^2,x)","F"
830,0,0,400,2.061000," ","int((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^3,x)","\int \frac{\left(d \csc \left(f x +e \right)\right)^{n}}{\left(a +b \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((d*csc(f*x+e))^n/(a+b*sin(f*x+e))^3,x)","F"
831,0,0,56,0.365000," ","int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^m,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^m,x)","F"
832,0,0,307,1.269000," ","int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^3,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^3,x)","F"
833,0,0,215,1.422000," ","int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^2,x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e))^2,x)","F"
834,0,0,147,0.400000," ","int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e)),x)","\int \left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n} \left(a +b \sin \left(f x +e \right)\right)\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n*(a+b*sin(f*x+e)),x)","F"
835,0,0,186,0.312000," ","int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e)),x)","\int \frac{\left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e)),x)","F"
836,0,0,292,1.144000," ","int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^2,x)","F"
837,0,0,390,1.270000," ","int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^3,x)","\int \frac{\left(c \left(d \sin \left(f x +e \right)\right)^{p}\right)^{n}}{\left(a +b \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((c*(d*sin(f*x+e))^p)^n/(a+b*sin(f*x+e))^3,x)","F"