1,1,32,41,0.709000," ","int((a*sin(x)^2)^(5/2),x)","-\frac{a^{3} \sin \left(x \right) \cos \left(x \right) \left(3 \left(\sin^{4}\left(x \right)\right)+4 \left(\sin^{2}\left(x \right)\right)+8\right)}{15 \sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/15*a^3*sin(x)*cos(x)*(3*sin(x)^4+4*sin(x)^2+8)/(a*sin(x)^2)^(1/2)","A"
2,1,24,26,0.819000," ","int((a*sin(x)^2)^(3/2),x)","-\frac{a^{2} \sin \left(x \right) \cos \left(x \right) \left(2+\sin^{2}\left(x \right)\right)}{3 \sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/3*a^2*sin(x)*cos(x)*(2+sin(x)^2)/(a*sin(x)^2)^(1/2)","A"
3,1,16,12,0.614000," ","int((a*sin(x)^2)^(1/2),x)","-\frac{a \cos \left(x \right) \sin \left(x \right)}{\sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/(a*sin(x)^2)^(1/2)*a*cos(x)*sin(x)","A"
4,1,49,15,0.905000," ","int(1/(a*sin(x)^2)^(1/2),x)","-\frac{\sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}\, \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(x \right)\right)}+2 a}{\sin \left(x \right)}\right)}{\sqrt{a}\, \cos \left(x \right) \sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-sin(x)*(a*cos(x)^2)^(1/2)/a^(1/2)*ln(2*(a^(1/2)*(a*cos(x)^2)^(1/2)+a)/sin(x))/cos(x)/(a*sin(x)^2)^(1/2)","B"
5,1,70,34,1.558000," ","int(1/(a*sin(x)^2)^(3/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(x \right)\right)}\, \left(\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(x \right)\right)}+2 a}{\sin \left(x \right)}\right) \left(\sin^{2}\left(x \right)\right) a +\sqrt{a}\, \sqrt{a \left(\cos^{2}\left(x \right)\right)}\right)}{2 a^{\frac{5}{2}} \sin \left(x \right) \cos \left(x \right) \sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/2/a^(5/2)/sin(x)*(a*cos(x)^2)^(1/2)*(ln(2*(a^(1/2)*(a*cos(x)^2)^(1/2)+a)/sin(x))*sin(x)^2*a+a^(1/2)*(a*cos(x)^2)^(1/2))/cos(x)/(a*sin(x)^2)^(1/2)","B"
6,1,89,49,1.454000," ","int(1/(a*sin(x)^2)^(5/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(x \right)\right)}\, \left(3 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(x \right)\right)}+2 a}{\sin \left(x \right)}\right) a \left(\sin^{4}\left(x \right)\right)+3 \sqrt{a \left(\cos^{2}\left(x \right)\right)}\, \left(\sin^{2}\left(x \right)\right) \sqrt{a}+2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(x \right)\right)}\right)}{8 a^{\frac{7}{2}} \sin \left(x \right)^{3} \cos \left(x \right) \sqrt{a \left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/8/a^(7/2)/sin(x)^3*(a*cos(x)^2)^(1/2)*(3*ln(2*(a^(1/2)*(a*cos(x)^2)^(1/2)+a)/sin(x))*a*sin(x)^4+3*(a*cos(x)^2)^(1/2)*sin(x)^2*a^(1/2)+2*a^(1/2)*(a*cos(x)^2)^(1/2))/cos(x)/(a*sin(x)^2)^(1/2)","A"
7,1,155,122,0.427000," ","int((a*sin(x)^3)^(5/2),x)","-\frac{\left(-154 \left(\cos^{8}\left(x \right)\right)+195 i \sqrt{2}\, \sin \left(x \right) \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}+154 \left(\cos^{7}\left(x \right)\right)+644 \left(\cos^{6}\left(x \right)\right)-644 \left(\cos^{5}\left(x \right)\right)-1060 \left(\cos^{4}\left(x \right)\right)+1060 \left(\cos^{3}\left(x \right)\right)+960 \left(\cos^{2}\left(x \right)\right)-960 \cos \left(x \right)\right) \left(a \left(1-\left(\cos^{2}\left(x \right)\right)\right) \sin \left(x \right)\right)^{\frac{5}{2}}}{1155 \sin \left(x \right)^{7} \left(-1+\cos \left(x \right)\right)}"," ",0,"-1/1155*(-154*cos(x)^8+195*I*2^(1/2)*sin(x)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)+154*cos(x)^7+644*cos(x)^6-644*cos(x)^5-1060*cos(x)^4+1060*cos(x)^3+960*cos(x)^2-960*cos(x))*(a*(1-cos(x)^2)*sin(x))^(5/2)/sin(x)^7/(-1+cos(x))","C"
8,1,337,80,0.507000," ","int((a*sin(x)^3)^(3/2),x)","\frac{\left(21 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \cos \left(x \right)-42 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \cos \left(x \right)+21 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}-42 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}-10 \left(\cos^{5}\left(x \right)\right)+34 \left(\cos^{3}\left(x \right)\right)-66 \cos \left(x \right)+42\right) \left(a \left(\sin^{3}\left(x \right)\right)\right)^{\frac{3}{2}}}{45 \sin \left(x \right)^{5}}"," ",0,"1/45*(21*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)-42*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)+21*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)-42*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)-10*cos(x)^5+34*cos(x)^3-66*cos(x)+42)*(a*sin(x)^3)^(3/2)/sin(x)^5","C"
9,1,124,61,0.482000," ","int((a*sin(x)^3)^(1/2),x)","-\frac{\left(i \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sin \left(x \right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(x \right)\right) \sqrt{2}-\cos \left(x \right) \sqrt{2}\right) \sqrt{a \left(1-\left(\cos^{2}\left(x \right)\right)\right) \sin \left(x \right)}\, \sqrt{8}}{6 \sin \left(x \right) \left(-1+\cos \left(x \right)\right)}"," ",0,"-1/6*(I*(-I*(-1+cos(x))/sin(x))^(1/2)*sin(x)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))+cos(x)^2*2^(1/2)-cos(x)*2^(1/2))*(a*(1-cos(x)^2)*sin(x))^(1/2)/sin(x)/(-1+cos(x))*8^(1/2)","C"
10,1,330,63,0.392000," ","int(1/(a*sin(x)^3)^(1/2),x)","\frac{\left(2 \sqrt{2}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \cos \left(x \right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \cos \left(x \right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{2}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \cos \left(x \right)-\sin \left(x \right)-i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)-2\right) \sin \left(x \right)}{\sqrt{a \left(\sin^{3}\left(x \right)\right)}}"," ",0,"(2*2^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*cos(x)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))-2^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*cos(x)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))+2*2^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))-2^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*(-(I*cos(x)-sin(x)-I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))-2)*sin(x)/(a*sin(x)^3)^(1/2)","C"
11,1,360,84,0.458000," ","int(1/(a*sin(x)^3)^(3/2),x)","-\frac{\left(\cos \left(x \right)+1\right)^{2} \left(-1+\cos \left(x \right)\right)^{2} \left(5 i \sqrt{2}\, \sin \left(x \right) \left(\cos^{3}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)+5 i \sqrt{2}\, \sin \left(x \right) \left(\cos^{2}\left(x \right)\right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)-5 i \sqrt{2}\, \sin \left(x \right) \cos \left(x \right) \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)-5 i \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{2}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(x \right)-10 \left(\cos^{3}\left(x \right)\right)+16 \cos \left(x \right)\right)}{21 \left(a \left(\sin^{3}\left(x \right)\right)\right)^{\frac{3}{2}} \sin \left(x \right)^{3}}"," ",0,"-1/21*(cos(x)+1)^2*(-1+cos(x))^2*(5*I*2^(1/2)*sin(x)*cos(x)^3*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))+5*I*2^(1/2)*sin(x)*cos(x)^2*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))-5*I*2^(1/2)*sin(x)*cos(x)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))-5*I*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*2^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*sin(x)-10*cos(x)^3+16*cos(x))/(a*sin(x)^3)^(3/2)/sin(x)^3","C"
12,1,1301,122,0.400000," ","int(1/(a*sin(x)^3)^(5/2),x)","\frac{\left(231 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{7}\left(x \right)\right)-462 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{7}\left(x \right)\right)+231 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{6}\left(x \right)\right)-462 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{6}\left(x \right)\right)-693 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{5}\left(x \right)\right)+1386 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{5}\left(x \right)\right)-693 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{4}\left(x \right)\right)+1386 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{4}\left(x \right)\right)+693 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{3}\left(x \right)\right)-1386 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{3}\left(x \right)\right)+693 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(x \right)\right)-1386 \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \left(\cos^{2}\left(x \right)\right)-231 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \cos \left(x \right)+462 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}\, \cos \left(x \right)+462 \left(\cos^{6}\left(x \right)\right)-231 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}+462 \sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}\, \sqrt{\frac{-i \cos \left(x \right)+\sin \left(x \right)+i}{\sin \left(x \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(x \right)+\sin \left(x \right)-i}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{2}-154 \left(\cos^{5}\left(x \right)\right)-1386 \left(\cos^{4}\left(x \right)\right)+418 \left(\cos^{3}\left(x \right)\right)+1386 \left(\cos^{2}\left(x \right)\right)-354 \cos \left(x \right)-462\right) \sin \left(x \right)}{585 \left(a \left(\sin^{3}\left(x \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/585*(231*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^7-462*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^7+231*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^6-462*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^6-693*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^5+1386*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^5-693*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^4+1386*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^4+693*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^3-1386*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^3+693*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^2-1386*(-I*(-1+cos(x))/sin(x))^(1/2)*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)^2-231*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)+462*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)*cos(x)+462*cos(x)^6-231*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticF(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)+462*((I*cos(x)+sin(x)-I)/sin(x))^(1/2)*((-I*cos(x)+sin(x)+I)/sin(x))^(1/2)*(-I*(-1+cos(x))/sin(x))^(1/2)*EllipticE(((I*cos(x)+sin(x)-I)/sin(x))^(1/2),1/2*2^(1/2))*2^(1/2)-154*cos(x)^5-1386*cos(x)^4+418*cos(x)^3+1386*cos(x)^2-354*cos(x)-462)*sin(x)/(a*sin(x)^3)^(5/2)","C"
13,1,63,108,0.472000," ","int((a*sin(x)^4)^(5/2),x)","-\frac{\left(a \left(1-\left(\cos^{2}\left(x \right)\right)\right)^{2}\right)^{\frac{5}{2}} \left(128 \left(\cos^{9}\left(x \right)\right) \sin \left(x \right)-656 \left(\cos^{7}\left(x \right)\right) \sin \left(x \right)+1368 \left(\cos^{5}\left(x \right)\right) \sin \left(x \right)-1490 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)+965 \sin \left(x \right) \cos \left(x \right)-315 x \right)}{1280 \sin \left(x \right)^{10}}"," ",0,"-1/1280*(a*(1-cos(x)^2)^2)^(5/2)*(128*cos(x)^9*sin(x)-656*cos(x)^7*sin(x)+1368*cos(x)^5*sin(x)-1490*cos(x)^3*sin(x)+965*sin(x)*cos(x)-315*x)/sin(x)^10","A"
14,1,47,62,0.280000," ","int((a*sin(x)^4)^(3/2),x)","-\frac{\left(a \left(1-\left(\cos^{2}\left(x \right)\right)\right)^{2}\right)^{\frac{3}{2}} \left(8 \left(\cos^{5}\left(x \right)\right) \sin \left(x \right)-26 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right)+33 \sin \left(x \right) \cos \left(x \right)-15 x \right)}{48 \sin \left(x \right)^{6}}"," ",0,"-1/48*(a*(1-cos(x)^2)^2)^(3/2)*(8*cos(x)^5*sin(x)-26*cos(x)^3*sin(x)+33*sin(x)*cos(x)-15*x)/sin(x)^6","A"
15,1,33,28,0.278000," ","int((a*sin(x)^4)^(1/2),x)","-\frac{\sqrt{a \left(1-\left(\cos^{2}\left(x \right)\right)\right)^{2}}\, \left(\sin \left(x \right) \cos \left(x \right)-x \right) \sqrt{16}}{8 \sin \left(x \right)^{2}}"," ",0,"-1/8*(a*(1-cos(x)^2)^2)^(1/2)*(sin(x)*cos(x)-x)/sin(x)^2*16^(1/2)","A"
16,1,15,14,0.261000," ","int(1/(a*sin(x)^4)^(1/2),x)","-\frac{\cos \left(x \right) \sin \left(x \right)}{\sqrt{a \left(\sin^{4}\left(x \right)\right)}}"," ",0,"-cos(x)*sin(x)/(a*sin(x)^4)^(1/2)","A"
17,1,29,58,0.227000," ","int(1/(a*sin(x)^4)^(3/2),x)","-\frac{\left(8 \left(\cos^{4}\left(x \right)\right)-20 \left(\cos^{2}\left(x \right)\right)+15\right) \sin \left(x \right) \cos \left(x \right)}{15 \left(a \left(\sin^{4}\left(x \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/15*(8*cos(x)^4-20*cos(x)^2+15)*sin(x)*cos(x)/(a*sin(x)^4)^(3/2)","A"
18,1,41,100,0.303000," ","int(1/(a*sin(x)^4)^(5/2),x)","-\frac{\left(128 \left(\cos^{8}\left(x \right)\right)-576 \left(\cos^{6}\left(x \right)\right)+1008 \left(\cos^{4}\left(x \right)\right)-840 \left(\cos^{2}\left(x \right)\right)+315\right) \sin \left(x \right) \cos \left(x \right)}{315 \left(a \left(\sin^{4}\left(x \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/315*(128*cos(x)^8-576*cos(x)^6+1008*cos(x)^4-840*cos(x)^2+315)*sin(x)*cos(x)/(a*sin(x)^4)^(5/2)","A"
19,0,0,77,6.446000," ","int((c*sin(b*x+a)^m)^(5/2),x)","\int \left(c \left(\sin^{m}\left(b x +a \right)\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((c*sin(b*x+a)^m)^(5/2),x)","F"
20,0,0,73,0.550000," ","int((c*sin(b*x+a)^m)^(3/2),x)","\int \left(c \left(\sin^{m}\left(b x +a \right)\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((c*sin(b*x+a)^m)^(3/2),x)","F"
21,0,0,66,0.665000," ","int((c*sin(b*x+a)^m)^(1/2),x)","\int \sqrt{c \left(\sin^{m}\left(b x +a \right)\right)}\, dx"," ",0,"int((c*sin(b*x+a)^m)^(1/2),x)","F"
22,0,0,68,0.542000," ","int(1/(c*sin(b*x+a)^m)^(1/2),x)","\int \frac{1}{\sqrt{c \left(\sin^{m}\left(b x +a \right)\right)}}\, dx"," ",0,"int(1/(c*sin(b*x+a)^m)^(1/2),x)","F"
23,0,0,77,0.551000," ","int(1/(c*sin(b*x+a)^m)^(3/2),x)","\int \frac{1}{\left(c \left(\sin^{m}\left(b x +a \right)\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c*sin(b*x+a)^m)^(3/2),x)","F"
24,0,0,77,0.535000," ","int(1/(c*sin(b*x+a)^m)^(5/2),x)","\int \frac{1}{\left(c \left(\sin^{m}\left(b x +a \right)\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(c*sin(b*x+a)^m)^(5/2),x)","F"
25,0,0,69,0.865000," ","int((b*sin(d*x+c)^n)^p,x)","\int \left(b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int((b*sin(d*x+c)^n)^p,x)","F"
26,0,0,63,1.844000," ","int((c*sin(b*x+a)^2)^p,x)","\int \left(c \left(\sin^{2}\left(b x +a \right)\right)\right)^{p}\, dx"," ",0,"int((c*sin(b*x+a)^2)^p,x)","F"
27,0,0,67,1.714000," ","int((c*sin(b*x+a)^3)^p,x)","\int \left(c \left(\sin^{3}\left(b x +a \right)\right)\right)^{p}\, dx"," ",0,"int((c*sin(b*x+a)^3)^p,x)","F"
28,0,0,67,2.094000," ","int((c*sin(b*x+a)^4)^p,x)","\int \left(c \left(\sin^{4}\left(b x +a \right)\right)\right)^{p}\, dx"," ",0,"int((c*sin(b*x+a)^4)^p,x)","F"
29,0,0,25,0.851000," ","int((c*sin(b*x+a)^n)^(1/n),x)","\int \left(c \left(\sin^{n}\left(b x +a \right)\right)\right)^{\frac{1}{n}}\, dx"," ",0,"int((c*sin(b*x+a)^n)^(1/n),x)","F"
30,0,0,71,1.021000," ","int((a*(b*sin(d*x+c))^p)^n,x)","\int \left(a \left(b \sin \left(d x +c \right)\right)^{p}\right)^{n}\, dx"," ",0,"int((a*(b*sin(d*x+c))^p)^n,x)","F"
31,1,18,12,0.072000," ","int(a-a*sin(x)^2,x)","a x -a \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)"," ",0,"a*x-a*(-1/2*sin(x)*cos(x)+1/2*x)","A"
32,1,43,27,0.337000," ","int((a-a*sin(x)^2)^2,x)","a^{2} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)-2 a^{2} \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{2} x"," ",0,"a^2*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)-2*a^2*(-1/2*sin(x)*cos(x)+1/2*x)+a^2*x","A"
33,1,72,38,0.436000," ","int((a-a*sin(x)^2)^3,x)","-a^{3} \left(-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{5 x}{16}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)-3 a^{3} \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{3} x"," ",0,"-a^3*(-1/6*(sin(x)^5+5/4*sin(x)^3+15/8*sin(x))*cos(x)+5/16*x)+3*a^3*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)-3*a^3*(-1/2*sin(x)*cos(x)+1/2*x)+a^3*x","A"
34,1,105,49,0.544000," ","int((a-a*sin(x)^2)^4,x)","a^{4} \left(-\frac{\left(\sin^{7}\left(x \right)+\frac{7 \left(\sin^{5}\left(x \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(x \right)\right)}{24}+\frac{35 \sin \left(x \right)}{16}\right) \cos \left(x \right)}{8}+\frac{35 x}{128}\right)-4 a^{4} \left(-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{5 x}{16}\right)+6 a^{4} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)-4 a^{4} \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{4} x"," ",0,"a^4*(-1/8*(sin(x)^7+7/6*sin(x)^5+35/24*sin(x)^3+35/16*sin(x))*cos(x)+35/128*x)-4*a^4*(-1/6*(sin(x)^5+5/4*sin(x)^3+15/8*sin(x))*cos(x)+5/16*x)+6*a^4*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)-4*a^4*(-1/2*sin(x)*cos(x)+1/2*x)+a^4*x","B"
35,1,45,60,0.326000," ","int(sin(d*x+c)^7/(a-a*sin(d*x+c)^2),x)","\frac{\frac{\left(\cos^{5}\left(d x +c \right)\right)}{5}-\left(\cos^{3}\left(d x +c \right)\right)+3 \cos \left(d x +c \right)+\frac{1}{\cos \left(d x +c \right)}}{d a}"," ",0,"1/d/a*(1/5*cos(d*x+c)^5-cos(d*x+c)^3+3*cos(d*x+c)+1/cos(d*x+c))","A"
36,1,35,44,0.306000," ","int(sin(d*x+c)^5/(a-a*sin(d*x+c)^2),x)","\frac{-\frac{\left(\cos^{3}\left(d x +c \right)\right)}{3}+2 \cos \left(d x +c \right)+\frac{1}{\cos \left(d x +c \right)}}{d a}"," ",0,"1/d/a*(-1/3*cos(d*x+c)^3+2*cos(d*x+c)+1/cos(d*x+c))","A"
37,1,23,27,0.296000," ","int(sin(d*x+c)^3/(a-a*sin(d*x+c)^2),x)","\frac{\cos \left(d x +c \right)+\frac{1}{\cos \left(d x +c \right)}}{d a}"," ",0,"1/d/a*(cos(d*x+c)+1/cos(d*x+c))","A"
38,1,16,13,0.192000," ","int(sin(d*x+c)/(a-a*sin(d*x+c)^2),x)","\frac{1}{d a \cos \left(d x +c \right)}"," ",0,"1/d/a/cos(d*x+c)","A"
39,1,51,29,0.442000," ","int(csc(d*x+c)/(a-a*sin(d*x+c)^2),x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 a d}+\frac{1}{d a \cos \left(d x +c \right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 a d}"," ",0,"1/2/a/d*ln(cos(d*x+c)-1)+1/d/a/cos(d*x+c)-1/2/a/d*ln(1+cos(d*x+c))","A"
40,1,87,52,0.507000," ","int(csc(d*x+c)^3/(a-a*sin(d*x+c)^2),x)","\frac{1}{4 a d \left(\cos \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\cos \left(d x +c \right)-1\right)}{4 a d}+\frac{1}{d a \cos \left(d x +c \right)}+\frac{1}{4 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right)}{4 a d}"," ",0,"1/4/a/d/(cos(d*x+c)-1)+3/4/a/d*ln(cos(d*x+c)-1)+1/d/a/cos(d*x+c)+1/4/a/d/(1+cos(d*x+c))-3/4/a/d*ln(1+cos(d*x+c))","A"
41,1,123,74,0.490000," ","int(csc(d*x+c)^5/(a-a*sin(d*x+c)^2),x)","-\frac{1}{16 a d \left(\cos \left(d x +c \right)-1\right)^{2}}+\frac{7}{16 a d \left(\cos \left(d x +c \right)-1\right)}+\frac{15 \ln \left(\cos \left(d x +c \right)-1\right)}{16 a d}+\frac{1}{d a \cos \left(d x +c \right)}+\frac{1}{16 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{7}{16 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{15 \ln \left(1+\cos \left(d x +c \right)\right)}{16 a d}"," ",0,"-1/16/a/d/(cos(d*x+c)-1)^2+7/16/a/d/(cos(d*x+c)-1)+15/16/a/d*ln(cos(d*x+c)-1)+1/d/a/cos(d*x+c)+1/16/a/d/(1+cos(d*x+c))^2+7/16/a/d/(1+cos(d*x+c))-15/16/a/d*ln(1+cos(d*x+c))","A"
42,1,84,65,0.323000," ","int(sin(d*x+c)^6/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{a d}+\frac{9 \left(\tan^{3}\left(d x +c \right)\right)}{8 a d \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{7 \tan \left(d x +c \right)}{8 a d \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{15 \arctan \left(\tan \left(d x +c \right)\right)}{8 a d}"," ",0,"tan(d*x+c)/a/d+9/8/a/d/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3+7/8/a/d/(tan(d*x+c)^2+1)^2*tan(d*x+c)-15/8/a/d*arctan(tan(d*x+c))","A"
43,1,56,43,0.317000," ","int(sin(d*x+c)^4/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{a d}+\frac{\tan \left(d x +c \right)}{2 a d \left(\tan^{2}\left(d x +c \right)+1\right)}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right)}{2 a d}"," ",0,"tan(d*x+c)/a/d+1/2/a/d*tan(d*x+c)/(tan(d*x+c)^2+1)-3/2/a/d*arctan(tan(d*x+c))","A"
44,1,30,20,0.232000," ","int(sin(d*x+c)^2/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{a d}-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{a d}"," ",0,"tan(d*x+c)/a/d-1/a/d*arctan(tan(d*x+c))","A"
45,1,14,13,0.319000," ","int(1/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{a d}"," ",0,"tan(d*x+c)/a/d","A"
46,1,25,28,0.456000," ","int(csc(d*x+c)^2/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)-\frac{1}{\tan \left(d x +c \right)}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/tan(d*x+c))","A"
47,1,35,44,0.470000," ","int(csc(d*x+c)^4/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)-\frac{2}{\tan \left(d x +c \right)}-\frac{1}{3 \tan \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-2/tan(d*x+c)-1/3/tan(d*x+c)^3)","A"
48,1,45,60,0.509000," ","int(csc(d*x+c)^6/(a-a*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)-\frac{3}{\tan \left(d x +c \right)}-\frac{1}{5 \tan \left(d x +c \right)^{5}}-\frac{1}{\tan \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-3/tan(d*x+c)-1/5/tan(d*x+c)^5-1/tan(d*x+c)^3)","A"
49,1,47,61,0.304000," ","int(sin(d*x+c)^7/(a-a*sin(d*x+c)^2)^2,x)","\frac{\frac{\left(\cos^{3}\left(d x +c \right)\right)}{3}-3 \cos \left(d x +c \right)-\frac{3}{\cos \left(d x +c \right)}+\frac{1}{3 \cos \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/3*cos(d*x+c)^3-3*cos(d*x+c)-3/cos(d*x+c)+1/3/cos(d*x+c)^3)","A"
50,1,37,45,0.276000," ","int(sin(d*x+c)^5/(a-a*sin(d*x+c)^2)^2,x)","\frac{-\cos \left(d x +c \right)-\frac{2}{\cos \left(d x +c \right)}+\frac{1}{3 \cos \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-cos(d*x+c)-2/cos(d*x+c)+1/3/cos(d*x+c)^3)","A"
51,1,29,31,0.244000," ","int(sin(d*x+c)^3/(a-a*sin(d*x+c)^2)^2,x)","\frac{-\frac{1}{\cos \left(d x +c \right)}+\frac{1}{3 \cos \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/cos(d*x+c)+1/3/cos(d*x+c)^3)","A"
52,1,17,16,0.147000," ","int(sin(d*x+c)/(a-a*sin(d*x+c)^2)^2,x)","\frac{1}{3 d \,a^{2} \cos \left(d x +c \right)^{3}}"," ",0,"1/3/d/a^2/cos(d*x+c)^3","A"
53,1,67,45,0.427000," ","int(csc(d*x+c)/(a-a*sin(d*x+c)^2)^2,x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d \,a^{2}}+\frac{1}{3 d \,a^{2} \cos \left(d x +c \right)^{3}}+\frac{1}{d \,a^{2} \cos \left(d x +c \right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d \,a^{2}}"," ",0,"1/2/d/a^2*ln(cos(d*x+c)-1)+1/3/d/a^2/cos(d*x+c)^3+1/d/a^2/cos(d*x+c)-1/2/d/a^2*ln(1+cos(d*x+c))","A"
54,1,104,70,0.520000," ","int(csc(d*x+c)^3/(a-a*sin(d*x+c)^2)^2,x)","\frac{1}{4 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)}+\frac{5 \ln \left(\cos \left(d x +c \right)-1\right)}{4 d \,a^{2}}+\frac{1}{3 d \,a^{2} \cos \left(d x +c \right)^{3}}+\frac{2}{d \,a^{2} \cos \left(d x +c \right)}+\frac{1}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{5 \ln \left(1+\cos \left(d x +c \right)\right)}{4 d \,a^{2}}"," ",0,"1/4/d/a^2/(cos(d*x+c)-1)+5/4/d/a^2*ln(cos(d*x+c)-1)+1/3/d/a^2/cos(d*x+c)^3+2/d/a^2/cos(d*x+c)+1/4/d/a^2/(1+cos(d*x+c))-5/4/d/a^2*ln(1+cos(d*x+c))","A"
55,1,73,61,0.354000," ","int(sin(d*x+c)^6/(a-a*sin(d*x+c)^2)^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 a^{2} d}-\frac{2 \tan \left(d x +c \right)}{a^{2} d}-\frac{\tan \left(d x +c \right)}{2 d \,a^{2} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{2 d \,a^{2}}"," ",0,"1/3*tan(d*x+c)^3/a^2/d-2*tan(d*x+c)/a^2/d-1/2/d/a^2*tan(d*x+c)/(tan(d*x+c)^2+1)+5/2/d/a^2*arctan(tan(d*x+c))","A"
56,1,46,36,0.287000," ","int(sin(d*x+c)^4/(a-a*sin(d*x+c)^2)^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 a^{2} d}-\frac{\tan \left(d x +c \right)}{a^{2} d}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/3*tan(d*x+c)^3/a^2/d-tan(d*x+c)/a^2/d+1/d/a^2*arctan(tan(d*x+c))","A"
57,1,17,16,0.205000," ","int(sin(d*x+c)^2/(a-a*sin(d*x+c)^2)^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 a^{2} d}"," ",0,"1/3*tan(d*x+c)^3/a^2/d","A"
58,1,25,30,0.298000," ","int(1/(a-a*sin(d*x+c)^2)^2,x)","\frac{\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)}{d \,a^{2}}"," ",0,"1/d/a^2*(1/3*tan(d*x+c)^3+tan(d*x+c))","A"
59,1,37,45,0.448000," ","int(csc(d*x+c)^2/(a-a*sin(d*x+c)^2)^2,x)","\frac{\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+2 \tan \left(d x +c \right)-\frac{1}{\tan \left(d x +c \right)}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/3*tan(d*x+c)^3+2*tan(d*x+c)-1/tan(d*x+c))","A"
60,1,47,61,0.506000," ","int(csc(d*x+c)^4/(a-a*sin(d*x+c)^2)^2,x)","\frac{\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+3 \tan \left(d x +c \right)-\frac{3}{\tan \left(d x +c \right)}-\frac{1}{3 \tan \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/3*tan(d*x+c)^3+3*tan(d*x+c)-3/tan(d*x+c)-1/3/tan(d*x+c)^3)","A"
61,1,20,25,0.161000," ","int(1/(a-a*sin(x)^2)^3,x)","\frac{\frac{\left(\tan^{5}\left(x \right)\right)}{5}+\frac{2 \left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)}{a^{3}}"," ",0,"1/a^3*(1/5*tan(x)^5+2/3*tan(x)^3+tan(x))","A"
62,1,24,33,0.161000," ","int(1/(a-a*sin(x)^2)^4,x)","\frac{\frac{\left(\tan^{7}\left(x \right)\right)}{7}+\frac{3 \left(\tan^{5}\left(x \right)\right)}{5}+\tan^{3}\left(x \right)+\tan \left(x \right)}{a^{4}}"," ",0,"1/a^4*(1/7*tan(x)^7+3/5*tan(x)^5+tan(x)^3+tan(x))","A"
63,1,32,43,0.157000," ","int(1/(a-a*sin(x)^2)^5,x)","\frac{\frac{\left(\tan^{9}\left(x \right)\right)}{9}+\frac{4 \left(\tan^{7}\left(x \right)\right)}{7}+\frac{6 \left(\tan^{5}\left(x \right)\right)}{5}+\frac{4 \left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)}{a^{5}}"," ",0,"1/a^5*(1/9*tan(x)^9+4/7*tan(x)^7+6/5*tan(x)^5+4/3*tan(x)^3+tan(x))","A"
64,1,54,47,0.442000," ","int(sin(d*x+c)^3*(a+b*sin(d*x+c)^2),x)","\frac{-\frac{b \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}-\frac{a \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/5*b*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)-1/3*a*(2+sin(d*x+c)^2)*cos(d*x+c))","A"
65,1,34,29,0.329000," ","int(sin(d*x+c)*(a+b*sin(d*x+c)^2),x)","\frac{-\frac{b \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}-a \cos \left(d x +c \right)}{d}"," ",0,"1/d*(-1/3*b*(2+sin(d*x+c)^2)*cos(d*x+c)-a*cos(d*x+c))","A"
66,1,35,26,0.309000," ","int(csc(d*x+c)*(a+b*sin(d*x+c)^2),x)","-\frac{b \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-b*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
67,1,63,36,0.518000," ","int(csc(d*x+c)^3*(a+b*sin(d*x+c)^2),x)","-\frac{a \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
68,1,86,81,0.459000," ","int(sin(d*x+c)^4*(a+b*sin(d*x+c)^2),x)","\frac{b \left(-\frac{\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)+a \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b*(-1/6*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/16*d*x+5/16*c)+a*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c))","A"
69,1,65,55,0.345000," ","int(sin(d*x+c)^2*(a+b*sin(d*x+c)^2),x)","\frac{b \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+a*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
70,1,32,26,0.070000," ","int(a+b*sin(d*x+c)^2,x)","a x +\frac{b \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"a*x+b/d*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)","A"
71,1,22,16,0.431000," ","int(csc(d*x+c)^2*(a+b*sin(d*x+c)^2),x)","\frac{-\cot \left(d x +c \right) a +\left(d x +c \right) b}{d}"," ",0,"1/d*(-cot(d*x+c)*a+(d*x+c)*b)","A"
72,1,35,39,0.588000," ","int(csc(d*x+c)^4*(a+b*sin(d*x+c)^2),x)","\frac{a \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)-b \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c)-b*cot(d*x+c))","A"
73,1,56,59,0.576000," ","int(csc(d*x+c)^6*(a+b*sin(d*x+c)^2),x)","\frac{a \left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(d x +c \right)\right)}{15}\right) \cot \left(d x +c \right)+b \left(-\frac{2}{3}-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{3}\right) \cot \left(d x +c \right)}{d}"," ",0,"1/d*(a*(-8/15-1/5*csc(d*x+c)^4-4/15*csc(d*x+c)^2)*cot(d*x+c)+b*(-2/3-1/3*csc(d*x+c)^2)*cot(d*x+c))","A"
74,1,17,15,0.062000," ","int(a+b*sin(x)^2,x)","a x +b \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)"," ",0,"a*x+b*(-1/2*sin(x)*cos(x)+1/2*x)","A"
75,1,42,44,0.344000," ","int((a+b*sin(x)^2)^2,x)","b^{2} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)+2 a b \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{2} x"," ",0,"b^2*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)+2*a*b*(-1/2*sin(x)*cos(x)+1/2*x)+a^2*x","A"
76,1,73,79,0.467000," ","int((a+b*sin(x)^2)^3,x)","b^{3} \left(-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{5 x}{16}\right)+3 a \,b^{2} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)+3 a^{2} b \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{3} x"," ",0,"b^3*(-1/6*(sin(x)^5+5/4*sin(x)^3+15/8*sin(x))*cos(x)+5/16*x)+3*a*b^2*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)+3*a^2*b*(-1/2*sin(x)*cos(x)+1/2*x)+a^3*x","A"
77,1,110,130,0.563000," ","int((a+b*sin(x)^2)^4,x)","b^{4} \left(-\frac{\left(\sin^{7}\left(x \right)+\frac{7 \left(\sin^{5}\left(x \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(x \right)\right)}{24}+\frac{35 \sin \left(x \right)}{16}\right) \cos \left(x \right)}{8}+\frac{35 x}{128}\right)+4 a \,b^{3} \left(-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{5 x}{16}\right)+6 a^{2} b^{2} \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)+4 a^{3} b \left(-\frac{\sin \left(x \right) \cos \left(x \right)}{2}+\frac{x}{2}\right)+a^{4} x"," ",0,"b^4*(-1/8*(sin(x)^7+7/6*sin(x)^5+35/24*sin(x)^3+35/16*sin(x))*cos(x)+35/128*x)+4*a*b^3*(-1/6*(sin(x)^5+5/4*sin(x)^3+15/8*sin(x))*cos(x)+5/16*x)+6*a^2*b^2*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)+4*a^3*b*(-1/2*sin(x)*cos(x)+1/2*x)+a^4*x","A"
78,1,110,94,0.324000," ","int(sin(d*x+c)^7/(a+b*sin(d*x+c)^2),x)","\frac{-\frac{\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{3}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{3}+a^{2} \cos \left(d x +c \right)-a b \cos \left(d x +c \right)+\cos \left(d x +c \right) b^{2}}{b^{3}}+\frac{a^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b^{3} \sqrt{\left(a +b \right) b}}}{d}"," ",0,"1/d*(-1/b^3*(1/5*b^2*cos(d*x+c)^5+1/3*a*b*cos(d*x+c)^3-2/3*cos(d*x+c)^3*b^2+a^2*cos(d*x+c)-a*b*cos(d*x+c)+cos(d*x+c)*b^2)+a^3/b^3/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2)))","A"
79,1,70,67,0.298000," ","int(sin(d*x+c)^5/(a+b*sin(d*x+c)^2),x)","\frac{\frac{\frac{\left(\cos^{3}\left(d x +c \right)\right) b}{3}+a \cos \left(d x +c \right)-b \cos \left(d x +c \right)}{b^{2}}-\frac{a^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b^{2} \sqrt{\left(a +b \right) b}}}{d}"," ",0,"1/d*(1/b^2*(1/3*cos(d*x+c)^3*b+a*cos(d*x+c)-b*cos(d*x+c))-a^2/b^2/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2)))","A"
80,1,45,44,0.269000," ","int(sin(d*x+c)^3/(a+b*sin(d*x+c)^2),x)","\frac{-\frac{\cos \left(d x +c \right)}{b}+\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b \sqrt{\left(a +b \right) b}}}{d}"," ",0,"1/d*(-1/b*cos(d*x+c)+a/b/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2)))","A"
81,1,29,29,0.195000," ","int(sin(d*x+c)/(a+b*sin(d*x+c)^2),x)","-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \sqrt{\left(a +b \right) b}}"," ",0,"-1/d/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))","A"
82,1,67,47,0.459000," ","int(csc(d*x+c)/(a+b*sin(d*x+c)^2),x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 a d}+\frac{b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d a \sqrt{\left(a +b \right) b}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 a d}"," ",0,"1/2/a/d*ln(cos(d*x+c)-1)+1/d/a*b/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))-1/2/a/d*ln(1+cos(d*x+c))","A"
83,1,142,73,0.554000," ","int(csc(d*x+c)^3/(a+b*sin(d*x+c)^2),x)","\frac{1}{4 a d \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{4 a d}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{2 d \,a^{2}}-\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{2} \sqrt{\left(a +b \right) b}}+\frac{1}{4 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{4 a d}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{2 d \,a^{2}}"," ",0,"1/4/a/d/(cos(d*x+c)-1)+1/4/a/d*ln(cos(d*x+c)-1)-1/2/d/a^2*ln(cos(d*x+c)-1)*b-1/d*b^2/a^2/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))+1/4/a/d/(1+cos(d*x+c))-1/4/a/d*ln(1+cos(d*x+c))+1/2/d/a^2*ln(1+cos(d*x+c))*b","A"
84,1,255,111,0.523000," ","int(csc(d*x+c)^5/(a+b*sin(d*x+c)^2),x)","-\frac{1}{16 a d \left(\cos \left(d x +c \right)-1\right)^{2}}+\frac{3}{16 a d \left(\cos \left(d x +c \right)-1\right)}-\frac{b}{4 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\cos \left(d x +c \right)-1\right)}{16 a d}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{4 d \,a^{2}}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) b^{2}}{2 d \,a^{3}}+\frac{b^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{3} \sqrt{\left(a +b \right) b}}+\frac{1}{16 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{3}{16 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{b}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right)}{16 a d}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{4 d \,a^{2}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{2 d \,a^{3}}"," ",0,"-1/16/a/d/(cos(d*x+c)-1)^2+3/16/a/d/(cos(d*x+c)-1)-1/4/d/a^2/(cos(d*x+c)-1)*b+3/16/a/d*ln(cos(d*x+c)-1)-1/4/d/a^2*ln(cos(d*x+c)-1)*b+1/2/d/a^3*ln(cos(d*x+c)-1)*b^2+1/d*b^3/a^3/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))+1/16/a/d/(1+cos(d*x+c))^2+3/16/a/d/(1+cos(d*x+c))-1/4/d/a^2/(1+cos(d*x+c))*b-3/16/a/d*ln(1+cos(d*x+c))+1/4/d/a^2*ln(1+cos(d*x+c))*b-1/2/d/a^3*ln(1+cos(d*x+c))*b^2","B"
85,1,361,147,0.306000," ","int(sin(d*x+c)^8/(a+b*sin(d*x+c)^2),x)","\frac{a^{4} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{4} \sqrt{a \left(a +b \right)}}-\frac{\left(\tan^{5}\left(d x +c \right)\right) a^{2}}{2 d \,b^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}+\frac{5 \left(\tan^{5}\left(d x +c \right)\right) a}{8 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{11 \left(\tan^{5}\left(d x +c \right)\right)}{16 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a}{d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right)}{6 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{\tan \left(d x +c \right) a^{2}}{2 d \,b^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}+\frac{3 \tan \left(d x +c \right) a}{8 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{5 \tan \left(d x +c \right)}{16 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \,b^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{2 d \,b^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a}{8 d \,b^{2}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{16 d b}"," ",0,"1/d*a^4/b^4/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/2/d/b^3/(tan(d*x+c)^2+1)^3*tan(d*x+c)^5*a^2+5/8/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)^5*a-11/16/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)^5-1/d/b^3/(tan(d*x+c)^2+1)^3*tan(d*x+c)^3*a^2+1/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)^3*a-5/6/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)^3-1/2/d/b^3/(tan(d*x+c)^2+1)^3*tan(d*x+c)*a^2+3/8/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)*a-5/16/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)-1/d/b^4*arctan(tan(d*x+c))*a^3+1/2/d/b^3*arctan(tan(d*x+c))*a^2-3/8/d/b^2*arctan(tan(d*x+c))*a+5/16/d/b*arctan(tan(d*x+c))","B"
86,1,196,103,0.325000," ","int(sin(d*x+c)^6/(a+b*sin(d*x+c)^2),x)","-\frac{a^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{3} \sqrt{a \left(a +b \right)}}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a}{2 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{\tan \left(d x +c \right) a}{2 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{3 \tan \left(d x +c \right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \,b^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{2 d \,b^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right)}{8 d b}"," ",0,"-1/d*a^3/b^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/2/d/b^2/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3*a-5/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3+1/2/d/b^2/(tan(d*x+c)^2+1)^2*tan(d*x+c)*a-3/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)+1/d/b^3*arctan(tan(d*x+c))*a^2-1/2/d/b^2*arctan(tan(d*x+c))*a+3/8/d/b*arctan(tan(d*x+c))","A"
87,1,94,65,0.248000," ","int(sin(d*x+c)^4/(a+b*sin(d*x+c)^2),x)","\frac{a^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{2} \sqrt{a \left(a +b \right)}}-\frac{\tan \left(d x +c \right)}{2 d b \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{2 d b}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{d \,b^{2}}"," ",0,"1/d*a^2/b^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/2/d/b*tan(d*x+c)/(tan(d*x+c)^2+1)+1/2/d/b*arctan(tan(d*x+c))-1/d/b^2*arctan(tan(d*x+c))*a","A"
88,1,50,38,0.242000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)^2),x)","-\frac{a \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d b \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d b}"," ",0,"-1/d*a/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/d/b*arctan(tan(d*x+c))","A"
89,1,30,28,0.381000," ","int(1/(a+b*sin(d*x+c)^2),x)","\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \sqrt{a \left(a +b \right)}}"," ",0,"1/d/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
90,1,52,45,0.539000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)^2),x)","-\frac{b \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d a \sqrt{a \left(a +b \right)}}-\frac{1}{d a \tan \left(d x +c \right)}"," ",0,"-1/d/a*b/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/d/a/tan(d*x+c)","A"
91,1,85,67,0.573000," ","int(csc(d*x+c)^4/(a+b*sin(d*x+c)^2),x)","\frac{b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,a^{2} \sqrt{a \left(a +b \right)}}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)}"," ",0,"1/d*b^2/a^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/3/d/a/tan(d*x+c)^3-1/d/a/tan(d*x+c)+1/d/a^2/tan(d*x+c)*b","A"
92,1,138,97,0.582000," ","int(csc(d*x+c)^6/(a+b*sin(d*x+c)^2),x)","-\frac{b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,a^{3} \sqrt{a \left(a +b \right)}}-\frac{1}{5 d a \tan \left(d x +c \right)^{5}}-\frac{2}{3 d a \tan \left(d x +c \right)^{3}}+\frac{b}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \tan \left(d x +c \right)}"," ",0,"-1/d*b^3/a^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/5/d/a/tan(d*x+c)^5-2/3/d/a/tan(d*x+c)^3+1/3/d/a^2/tan(d*x+c)^3*b-1/d/a/tan(d*x+c)+1/d/a^2/tan(d*x+c)*b-1/d/a^3/tan(d*x+c)*b^2","A"
93,1,207,126,0.605000," ","int(csc(d*x+c)^8/(a+b*sin(d*x+c)^2),x)","\frac{b^{4} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,a^{4} \sqrt{a \left(a +b \right)}}-\frac{1}{7 d a \tan \left(d x +c \right)^{7}}-\frac{3}{5 d a \tan \left(d x +c \right)^{5}}+\frac{b}{5 d \,a^{2} \tan \left(d x +c \right)^{5}}-\frac{1}{d a \tan \left(d x +c \right)^{3}}+\frac{2 b}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{b^{2}}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \tan \left(d x +c \right)}+\frac{b^{3}}{d \,a^{4} \tan \left(d x +c \right)}"," ",0,"1/d*b^4/a^4/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/7/d/a/tan(d*x+c)^7-3/5/d/a/tan(d*x+c)^5+1/5/d/a^2/tan(d*x+c)^5*b-1/d/a/tan(d*x+c)^3+2/3/d/a^2/tan(d*x+c)^3*b-1/3/d/a^3/tan(d*x+c)^3*b^2-1/d/a/tan(d*x+c)+1/d/a^2/tan(d*x+c)*b-1/d/a^3/tan(d*x+c)*b^2+1/d/a^4/tan(d*x+c)*b^3","A"
94,1,118,114,0.326000," ","int(sin(d*x+c)^7/(a+b*sin(d*x+c)^2)^2,x)","\frac{\frac{\frac{\left(\cos^{3}\left(d x +c \right)\right) b}{3}+2 a \cos \left(d x +c \right)-b \cos \left(d x +c \right)}{b^{3}}+\frac{a^{2} \left(-\frac{a \cos \left(d x +c \right)}{2 \left(a +b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}-\frac{\left(5 a +6 b \right) \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) b}}\right)}{b^{3}}}{d}"," ",0,"1/d*(1/b^3*(1/3*cos(d*x+c)^3*b+2*a*cos(d*x+c)-b*cos(d*x+c))+a^2/b^3*(-1/2*a/(a+b)*cos(d*x+c)/(b*cos(d*x+c)^2-a-b)-1/2*(5*a+6*b)/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))))","A"
95,1,94,90,0.325000," ","int(sin(d*x+c)^5/(a+b*sin(d*x+c)^2)^2,x)","\frac{-\frac{\cos \left(d x +c \right)}{b^{2}}-\frac{a \left(-\frac{a \cos \left(d x +c \right)}{2 \left(a +b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}-\frac{\left(3 a +4 b \right) \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) b}}\right)}{b^{2}}}{d}"," ",0,"1/d*(-1/b^2*cos(d*x+c)-a/b^2*(-1/2*a/(a+b)*cos(d*x+c)/(b*cos(d*x+c)^2-a-b)-1/2*(3*a+4*b)/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))))","A"
96,1,80,71,0.293000," ","int(sin(d*x+c)^3/(a+b*sin(d*x+c)^2)^2,x)","\frac{-\frac{a \cos \left(d x +c \right)}{2 \left(a +b \right) b \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}-\frac{\left(a +2 b \right) \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 \left(a +b \right) b \sqrt{\left(a +b \right) b}}}{d}"," ",0,"1/d*(-1/2*a/(a+b)/b*cos(d*x+c)/(b*cos(d*x+c)^2-a-b)-1/2*(a+2*b)/(a+b)/b/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2)))","A"
97,1,68,62,0.219000," ","int(sin(d*x+c)/(a+b*sin(d*x+c)^2)^2,x)","\frac{\frac{\cos \left(d x +c \right)}{2 \left(a +b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 \left(a +b \right) \sqrt{\left(a +b \right) b}}}{d}"," ",0,"1/d*(1/2*cos(d*x+c)/(a+b)/(b*cos(d*x+c)^2-a-b)-1/2/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2)))","A"
98,1,150,91,0.509000," ","int(csc(d*x+c)/(a+b*sin(d*x+c)^2)^2,x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d \,a^{2}}-\frac{b \cos \left(d x +c \right)}{2 d a \left(a +b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}+\frac{3 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 d a \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d \,a^{2}}"," ",0,"1/2/d/a^2*ln(cos(d*x+c)-1)-1/2/d/a*b/(a+b)*cos(d*x+c)/(b*cos(d*x+c)^2-a-b)+3/2/d/a*b/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))+1/d/a^2*b^2/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))-1/2/d/a^2*ln(1+cos(d*x+c))","A"
99,1,226,137,0.618000," ","int(csc(d*x+c)^3/(a+b*sin(d*x+c)^2)^2,x)","\frac{1}{4 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{4 d \,a^{2}}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{d \,a^{3}}+\frac{b^{2} \cos \left(d x +c \right)}{2 d \,a^{2} \left(a +b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}-\frac{5 b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{2 d \,a^{2} \left(a +b \right) \sqrt{\left(a +b \right) b}}-\frac{2 b^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(a +b \right) b}}\right)}{d \,a^{3} \left(a +b \right) \sqrt{\left(a +b \right) b}}+\frac{1}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{4 d \,a^{2}}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{d \,a^{3}}"," ",0,"1/4/d/a^2/(cos(d*x+c)-1)+1/4/d/a^2*ln(cos(d*x+c)-1)-1/d/a^3*ln(cos(d*x+c)-1)*b+1/2/d/a^2*b^2/(a+b)*cos(d*x+c)/(b*cos(d*x+c)^2-a-b)-5/2/d/a^2*b^2/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))-2/d/a^3*b^3/(a+b)/((a+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/((a+b)*b)^(1/2))+1/4/d/a^2/(1+cos(d*x+c))-1/4/d/a^2*ln(1+cos(d*x+c))+1/d/a^3*ln(1+cos(d*x+c))*b","A"
100,1,187,132,0.342000," ","int(sin(d*x+c)^6/(a+b*sin(d*x+c)^2)^2,x)","-\frac{a^{2} \tan \left(d x +c \right)}{2 d \,b^{2} \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}+\frac{2 a^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{3} \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{5 a^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \,b^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{\tan \left(d x +c \right)}{2 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{2 d \,b^{2}}-\frac{2 \arctan \left(\tan \left(d x +c \right)\right) a}{d \,b^{3}}"," ",0,"-1/2/d*a^2/b^2/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)+2/d*a^3/b^3/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+5/2/d*a^2/b^2/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/2/d/b^2*tan(d*x+c)/(tan(d*x+c)^2+1)+1/2/d/b^2*arctan(tan(d*x+c))-2/d/b^3*arctan(tan(d*x+c))*a","A"
101,1,140,81,0.274000," ","int(sin(d*x+c)^4/(a+b*sin(d*x+c)^2)^2,x)","\frac{a \tan \left(d x +c \right)}{2 d b \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}-\frac{a^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{3 a \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d b \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,b^{2}}"," ",0,"1/2/d*a/b/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)-1/d*a^2/b^2/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-3/2/d*a/b/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/d/b^2*arctan(tan(d*x+c))","A"
102,1,77,66,0.247000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)^2)^2,x)","-\frac{\tan \left(d x +c \right)}{2 d \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \left(a +b \right) \sqrt{a \left(a +b \right)}}"," ",0,"-1/2/d/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)+1/2/d/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
103,1,119,75,0.358000," ","int(1/(a+b*sin(d*x+c)^2)^2,x)","\frac{b \tan \left(d x +c \right)}{2 d a \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{2 d a \left(a +b \right) \sqrt{a \left(a +b \right)}}"," ",0,"1/2/d*b/a/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)+1/d/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/2/d/a/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b","A"
104,1,144,115,0.540000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)^2)^2,x)","-\frac{b^{2} \tan \left(d x +c \right)}{2 d \,a^{2} \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}-\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{3 b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \,a^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}"," ",0,"-1/2/d/a^2*b^2/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)-2/d/a/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b-3/2/d/a^2*b^2/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/d/a^2/tan(d*x+c)","A"
105,1,179,146,0.556000," ","int(csc(d*x+c)^4/(a+b*sin(d*x+c)^2)^2,x)","\frac{b^{3} \tan \left(d x +c \right)}{2 d \,a^{3} \left(a +b \right) \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)}+\frac{3 b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,a^{2} \left(a +b \right) \sqrt{a \left(a +b \right)}}+\frac{5 b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \,a^{3} \left(a +b \right) \sqrt{a \left(a +b \right)}}-\frac{1}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}+\frac{2 b}{d \,a^{3} \tan \left(d x +c \right)}"," ",0,"1/2/d*b^3/a^3/(a+b)*tan(d*x+c)/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)+3/d/a^2*b^2/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+5/2/d*b^3/a^3/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/3/d/a^2/tan(d*x+c)^3-1/d/a^2/tan(d*x+c)+2/d/a^3/tan(d*x+c)*b","A"
106,1,363,134,0.327000," ","int(sin(d*x+c)^6/(a+b*sin(d*x+c)^2)^3,x)","\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{2 d \,b^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a +b \right)}+\frac{9 a \left(\tan^{3}\left(d x +c \right)\right)}{8 d b \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a +b \right)}+\frac{a^{3} \tan \left(d x +c \right)}{2 d \,b^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{7 a^{2} \tan \left(d x +c \right)}{8 d b \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \,b^{3} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}-\frac{5 a^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \,b^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}-\frac{15 a \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{8 d b \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,b^{3}}"," ",0,"1/2/d*a^2/b^2/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a+b)*tan(d*x+c)^3+9/8/d*a/b/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a+b)*tan(d*x+c)^3+1/2/d*a^3/b^2/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a^2+2*a*b+b^2)*tan(d*x+c)+7/8/d*a^2/b/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a^2+2*a*b+b^2)*tan(d*x+c)-1/d*a^3/b^3/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-5/2/d*a^2/b^2/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-15/8/d*a/b/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/d/b^3*arctan(tan(d*x+c))","B"
107,1,136,96,0.265000," ","int(sin(d*x+c)^4/(a+b*sin(d*x+c)^2)^3,x)","-\frac{5 \left(\tan^{3}\left(d x +c \right)\right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{3 a \tan \left(d x +c \right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{8 d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}"," ",0,"-5/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a+b)*tan(d*x+c)^3-3/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2*a/(a^2+2*a*b+b^2)*tan(d*x+c)+3/8/d/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
108,1,278,117,0.260000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)^2)^3,x)","-\frac{\tan^{3}\left(d x +c \right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a +b \right)}+\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a \left(a +b \right)}-\frac{a \tan \left(d x +c \right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{\tan \left(d x +c \right) b}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{8 d \left(a^{2}+2 a b +b^{2}\right) a \sqrt{a \left(a +b \right)}}"," ",0,"-1/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a+b)*tan(d*x+c)^3+1/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/a/(a+b)*tan(d*x+c)^3*b-1/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2*a/(a^2+2*a*b+b^2)*tan(d*x+c)-1/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a^2+2*a*b+b^2)*tan(d*x+c)*b+1/2/d/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/8/d/(a^2+2*a*b+b^2)/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b","B"
109,1,334,130,0.398000," ","int(1/(a+b*sin(d*x+c)^2)^3,x)","\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a \left(a +b \right)}+\frac{3 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a^{2} \left(a +b \right)}+\frac{\tan \left(d x +c \right) b}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{5 b^{2} \tan \left(d x +c \right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d \left(a^{2}+2 a b +b^{2}\right) a \sqrt{a \left(a +b \right)}}+\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{8 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}"," ",0,"1/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/a/(a+b)*tan(d*x+c)^3*b+3/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/a^2*b^2/(a+b)*tan(d*x+c)^3+1/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a^2+2*a*b+b^2)*tan(d*x+c)*b+5/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2*b^2/a/(a^2+2*a*b+b^2)*tan(d*x+c)+1/d/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+1/d/(a^2+2*a*b+b^2)/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b+3/8/d/a^2/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2","B"
110,1,367,180,0.582000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)^2)^3,x)","-\frac{3 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a^{2} \left(a +b \right)}-\frac{7 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{8 d \,a^{3} \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a +b \right)}-\frac{3 b^{2} \tan \left(d x +c \right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} a \left(a^{2}+2 a b +b^{2}\right)}-\frac{9 b^{3} \tan \left(d x +c \right)}{8 d \,a^{2} \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d \left(a^{2}+2 a b +b^{2}\right) a \sqrt{a \left(a +b \right)}}-\frac{9 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{2 d \,a^{2} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}-\frac{15 b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{8 d \,a^{3} \left(a^{2}+2 a b +b^{2}\right) \sqrt{a \left(a +b \right)}}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}"," ",0,"-3/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/a^2*b^2/(a+b)*tan(d*x+c)^3-7/8/d*b^3/a^3/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a+b)*tan(d*x+c)^3-3/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2*b^2/a/(a^2+2*a*b+b^2)*tan(d*x+c)-9/8/d*b^3/a^2/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^2/(a^2+2*a*b+b^2)*tan(d*x+c)-3/d/(a^2+2*a*b+b^2)/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b-9/2/d/a^2/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2-15/8/d*b^3/a^3/(a^2+2*a*b+b^2)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/d/a^3/tan(d*x+c)","B"
111,1,705,190,0.396000," ","int(1/(a+b*sin(d*x+c)^2)^4,x)","\frac{3 b \left(\tan^{5}\left(d x +c \right)\right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a \left(a +b \right)}+\frac{9 b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a^{2} \left(a +b \right)}+\frac{5 b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{16 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a^{3} \left(a +b \right)}+\frac{3 b \left(\tan^{3}\left(d x +c \right)\right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a \left(a^{2}+2 a b +b^{2}\right)}+\frac{5 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{6 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b a \tan \left(d x +c \right)}{2 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{15 b^{2} \tan \left(d x +c \right)}{8 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{11 b^{3} \tan \left(d x +c \right)}{16 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{3} a \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right) \sqrt{a \left(a +b \right)}}+\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{2 d a \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right) \sqrt{a \left(a +b \right)}}+\frac{9 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{8 d \,a^{2} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right) \sqrt{a \left(a +b \right)}}+\frac{5 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{3}}{16 d \,a^{3} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right) \sqrt{a \left(a +b \right)}}"," ",0,"3/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3/a*b/(a+b)*tan(d*x+c)^5+9/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3/a^2*b^2/(a+b)*tan(d*x+c)^5+5/16/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3/a^3*b^3/(a+b)*tan(d*x+c)^5+3/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3*b/(a^2+2*a*b+b^2)*tan(d*x+c)^3+3/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3/a*b^2/(a^2+2*a*b+b^2)*tan(d*x+c)^3+5/6/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3/a^2*b^3/(a^2+2*a*b+b^2)*tan(d*x+c)^3+3/2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3*b*a/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)+15/8/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3*b^2/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)+11/16/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^3*b^3/a/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)+1/d/(a^3+3*a^2*b+3*a*b^2+b^3)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+3/2/d/a/(a^3+3*a^2*b+3*a*b^2+b^3)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b+9/8/d/a^2/(a^3+3*a^2*b+3*a*b^2+b^3)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2+5/16/d/a^3/(a^3+3*a^2*b+3*a*b^2+b^3)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^3","B"
112,1,1249,261,0.407000," ","int(1/(a+b*sin(d*x+c)^2)^5,x)","\frac{2 b \left(\tan^{7}\left(d x +c \right)\right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a \left(a +b \right)}+\frac{9 b^{2} \left(\tan^{7}\left(d x +c \right)\right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{2} \left(a +b \right)}+\frac{5 b^{3} \left(\tan^{7}\left(d x +c \right)\right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{3} \left(a +b \right)}+\frac{35 b^{4} \left(\tan^{7}\left(d x +c \right)\right)}{128 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{4} \left(a +b \right)}+\frac{6 b \left(\tan^{5}\left(d x +c \right)\right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{2}+2 a b +b^{2}\right)}+\frac{33 b^{2} \left(\tan^{5}\left(d x +c \right)\right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a \left(a^{2}+2 a b +b^{2}\right)}+\frac{55 b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{12 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{385 b^{4} \left(\tan^{5}\left(d x +c \right)\right)}{384 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{3} \left(a^{2}+2 a b +b^{2}\right)}+\frac{6 a b \left(\tan^{3}\left(d x +c \right)\right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{39 b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{73 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{12 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{511 b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{384 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a^{2} \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right)}+\frac{2 b \,a^{2} \tan \left(d x +c \right)}{d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right)}+\frac{15 b^{2} a \tan \left(d x +c \right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right)}+\frac{11 b^{3} \tan \left(d x +c \right)}{4 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right)}+\frac{93 b^{4} \tan \left(d x +c \right)}{128 d \left(a \left(\tan^{2}\left(d x +c \right)\right)+\left(\tan^{2}\left(d x +c \right)\right) b +a \right)^{4} a \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) \sqrt{a \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) \sqrt{a \left(a +b \right)}}+\frac{9 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{4 d \,a^{2} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) \sqrt{a \left(a +b \right)}}+\frac{5 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{3}}{4 d \,a^{3} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) \sqrt{a \left(a +b \right)}}+\frac{35 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{4}}{128 d \,a^{4} \left(a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) \sqrt{a \left(a +b \right)}}"," ",0,"2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b/a/(a+b)*tan(d*x+c)^7+9/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^2/a^2/(a+b)*tan(d*x+c)^7+5/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^3/a^3/(a+b)*tan(d*x+c)^7+35/128/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^4/a^4/(a+b)*tan(d*x+c)^7+6/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b/(a^2+2*a*b+b^2)*tan(d*x+c)^5+33/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4/a*b^2/(a^2+2*a*b+b^2)*tan(d*x+c)^5+55/12/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4/a^2*b^3/(a^2+2*a*b+b^2)*tan(d*x+c)^5+385/384/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4/a^3*b^4/(a^2+2*a*b+b^2)*tan(d*x+c)^5+6/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*a*b/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^3+39/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^2/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^3+73/12/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4/a*b^3/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^3+511/384/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4/a^2*b^4/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(d*x+c)^3+2/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b*a^2/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*tan(d*x+c)+15/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^2*a/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*tan(d*x+c)+11/4/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^3/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*tan(d*x+c)+93/128/d/(a*tan(d*x+c)^2+tan(d*x+c)^2*b+a)^4*b^4/a/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*tan(d*x+c)+1/d/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+2/d/a/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b+9/4/d/a^2/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2+5/4/d/a^3/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^3+35/128/d/a^4/(a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^4","B"
113,1,33,10,0.755000," ","int(sin(x)/(1+sin(x)^2)^(1/2),x)","\frac{\sqrt{\left(1+\sin^{2}\left(x \right)\right) \left(\cos^{2}\left(x \right)\right)}\, \arcsin \left(\sin^{2}\left(x \right)\right)}{2 \cos \left(x \right) \sqrt{1+\sin^{2}\left(x \right)}}"," ",0,"1/2*((1+sin(x)^2)*cos(x)^2)^(1/2)*arcsin(sin(x)^2)/cos(x)/(1+sin(x)^2)^(1/2)","B"
114,1,51,25,1.110000," ","int(sin(x)*(1+sin(x)^2)^(1/2),x)","-\frac{\sqrt{\left(1+\sin^{2}\left(x \right)\right) \left(\cos^{2}\left(x \right)\right)}\, \left(\sqrt{-\left(\cos^{4}\left(x \right)\right)+2 \left(\cos^{2}\left(x \right)\right)}+\arcsin \left(\cos^{2}\left(x \right)-1\right)\right)}{2 \cos \left(x \right) \sqrt{1+\sin^{2}\left(x \right)}}"," ",0,"-1/2*((1+sin(x)^2)*cos(x)^2)^(1/2)*((-cos(x)^4+2*cos(x)^2)^(1/2)+arcsin(cos(x)^2-1))/cos(x)/(1+sin(x)^2)^(1/2)","A"
115,1,57,11,1.158000," ","int(sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2),x)","-\frac{\sqrt{\left(3+\sin^{2}\left(7+3 x \right)\right) \left(\cos^{2}\left(7+3 x \right)\right)}\, \arcsin \left(-1+\frac{\left(\cos^{2}\left(7+3 x \right)\right)}{2}\right)}{6 \cos \left(7+3 x \right) \sqrt{3+\sin^{2}\left(7+3 x \right)}}"," ",0,"-1/6*((3+sin(7+3*x)^2)*cos(7+3*x)^2)^(1/2)*arcsin(-1+1/2*cos(7+3*x)^2)/cos(7+3*x)/(3+sin(7+3*x)^2)^(1/2)","B"
116,1,32,41,0.877000," ","int((a-a*sin(x)^2)^(5/2),x)","\frac{a^{3} \cos \left(x \right) \sin \left(x \right) \left(3 \left(\cos^{4}\left(x \right)\right)+4 \left(\cos^{2}\left(x \right)\right)+8\right)}{15 \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/15*a^3*cos(x)*sin(x)*(3*cos(x)^4+4*cos(x)^2+8)/(a*cos(x)^2)^(1/2)","A"
117,1,24,26,0.851000," ","int((a-a*sin(x)^2)^(3/2),x)","\frac{a^{2} \cos \left(x \right) \sin \left(x \right) \left(\cos^{2}\left(x \right)+2\right)}{3 \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/3*a^2*cos(x)*sin(x)*(cos(x)^2+2)/(a*cos(x)^2)^(1/2)","A"
118,1,15,11,0.525000," ","int((a-a*sin(x)^2)^(1/2),x)","\frac{a \cos \left(x \right) \sin \left(x \right)}{\sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"a*cos(x)*sin(x)/(a*cos(x)^2)^(1/2)","A"
119,1,20,14,0.120000," ","int(1/(a-a*sin(x)^2)^(1/2),x)","\frac{\cos \left(x \right) \mathrm{am}^{-1}\left(x | 1\right)}{\sqrt{a \left(\cos^{2}\left(x \right)\right)}\, \mathrm{csgn}\left(\cos \left(x \right)\right)}"," ",0,"1/(a*cos(x)^2)^(1/2)/csgn(cos(x))*cos(x)*InverseJacobiAM(x,1)","C"
120,1,70,34,1.339000," ","int(1/(a-a*sin(x)^2)^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}+2 a}{\cos \left(x \right)}\right) \left(\cos^{2}\left(x \right)\right) a +\sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}\right)}{2 a^{\frac{5}{2}} \cos \left(x \right) \sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/2/a^(5/2)/cos(x)*(a*sin(x)^2)^(1/2)*(ln(2/cos(x)*(a^(1/2)*(a*sin(x)^2)^(1/2)+a))*cos(x)^2*a+a^(1/2)*(a*sin(x)^2)^(1/2))/sin(x)/(a*cos(x)^2)^(1/2)","B"
121,1,89,49,1.391000," ","int(1/(a-a*sin(x)^2)^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(3 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}+2 a}{\cos \left(x \right)}\right) a \left(\cos^{4}\left(x \right)\right)+3 \sqrt{a \left(\sin^{2}\left(x \right)\right)}\, \left(\cos^{2}\left(x \right)\right) \sqrt{a}+2 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(x \right)\right)}\right)}{8 a^{\frac{7}{2}} \cos \left(x \right)^{3} \sin \left(x \right) \sqrt{a \left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/8/a^(7/2)/cos(x)^3*(a*sin(x)^2)^(1/2)*(3*ln(2/cos(x)*(a^(1/2)*(a*sin(x)^2)^(1/2)+a))*a*cos(x)^4+3*(a*sin(x)^2)^(1/2)*cos(x)^2*a^(1/2)+2*a^(1/2)*(a*sin(x)^2)^(1/2))/sin(x)/(a*cos(x)^2)^(1/2)","A"
122,1,311,109,1.904000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(-4 b^{\frac{5}{2}} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\cos^{2}\left(f x +e \right)\right)+10 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{5}{2}}+2 a \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{3}{2}}+\arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right) a^{2} b -2 a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right) b^{2}-3 b^{3} \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{16 b^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/16*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(-4*b^(5/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*cos(f*x+e)^2+10*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(5/2)+2*a*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(3/2)+arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))*a^2*b-2*a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))*b^2-3*b^3*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)))/b^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
123,1,182,66,1.327000," ","int(sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(b \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\right)}{4 \sqrt{b}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(b*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))+a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-2*b^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))/b^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
124,1,174,71,2.128000," ","int(csc(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sqrt{b}\, \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-\sqrt{a}\, \ln \left(\frac{-\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-a -b}{-1+\cos^{2}\left(f x +e \right)}\right)\right)}{2 \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/2*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(b^(1/2)*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-a^(1/2)*ln((-(a-b)*cos(f*x+e)^2-2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-a-b)/(-1+cos(f*x+e)^2)))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
125,1,227,72,1.794000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(a \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right)+b \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\right)}{4 \sqrt{a}\, \sin \left(f x +e \right)^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(a*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^2+b*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^2+2*a^(1/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/a^(1/2)/sin(f*x+e)^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
126,1,379,127,2.205000," ","int(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(3 a^{3} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{4}\left(f x +e \right)\right)+2 b \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{4}\left(f x +e \right)\right) a^{2}-\ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) b^{2} \left(\sin^{4}\left(f x +e \right)\right) a +6 \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{2}\left(f x +e \right)\right) a^{\frac{5}{2}}+2 b \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{2}\left(f x +e \right)\right) a^{\frac{3}{2}}+4 \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, a^{\frac{5}{2}}\right)}{16 \sin \left(f x +e \right)^{4} a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/16*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(3*a^3*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^4+2*b*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^4*a^2-ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*b^2*sin(f*x+e)^4*a+6*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^2*a^(5/2)+2*b*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^2*a^(3/2)+4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*a^(5/2))/sin(f*x+e)^4/a^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
127,1,413,237,1.550000," ","int(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{3 b^{3} \left(\sin^{7}\left(f x +e \right)\right)+4 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+b^{3} \left(\sin^{5}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-2 a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -4 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}+a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-4 b^{3} \left(\sin^{3}\left(f x +e \right)\right)-a^{2} b \sin \left(f x +e \right)-4 a \,b^{2} \sin \left(f x +e \right)}{15 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/15*(3*b^3*sin(f*x+e)^7+4*a*b^2*sin(f*x+e)^5+b^3*sin(f*x+e)^5+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3-2*a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-4*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2+a^2*b*sin(f*x+e)^3-4*b^3*sin(f*x+e)^3-a^2*b*sin(f*x+e)-4*a*b^2*sin(f*x+e))/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
128,1,266,185,1.453000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{-b^{2} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -a b \left(\sin^{3}\left(f x +e \right)\right)+b^{2} \left(\sin^{3}\left(f x +e \right)\right)+a b \sin \left(f x +e \right)}{3 b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(-b^2*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b-a*b*sin(f*x+e)^3+b^2*sin(f*x+e)^3+a*b*sin(f*x+e))/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
129,1,71,68,0.872000," ","int((a+b*sin(f*x+e)^2)^(1/2),x)","\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
130,1,156,162,1.318000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \right)+b \left(\cos^{4}\left(f x +e \right)\right)+\left(-a -b \right) \left(\cos^{2}\left(f x +e \right)\right)}{\sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(sin(f*x+e)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a)+b*cos(f*x+e)^4+(-a-b)*cos(f*x+e)^2)/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
131,1,342,212,1.487000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+2 b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+2 a b \left(\sin^{6}\left(f x +e \right)\right)+b^{2} \left(\sin^{6}\left(f x +e \right)\right)+2 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-b^{2} \left(\sin^{4}\left(f x +e \right)\right)-a^{2} \left(\sin^{2}\left(f x +e \right)\right)-2 a b \left(\sin^{2}\left(f x +e \right)\right)-a^{2}}{3 a \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+2*b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+2*a*b*sin(f*x+e)^6+b^2*sin(f*x+e)^6+2*a^2*sin(f*x+e)^4-b^2*sin(f*x+e)^4-a^2*sin(f*x+e)^2-2*a*b*sin(f*x+e)^2-a^2)/a/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
132,1,446,149,1.822000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(16 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{7}{2}} \left(\cos^{4}\left(f x +e \right)\right)-4 b^{\frac{5}{2}} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(13 b +7 a \right) \left(\cos^{2}\left(f x +e \right)\right)+66 b^{\frac{7}{2}} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+72 a \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{5}{2}}+6 a^{2} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{3}{2}}+3 \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right) a^{3} b -9 \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right) a^{2} b^{2}-27 b^{3} a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-15 b^{4} \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{96 b^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/96*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(16*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(7/2)*cos(f*x+e)^4-4*b^(5/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(13*b+7*a)*cos(f*x+e)^2+66*b^(7/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+72*a*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(5/2)+6*a^2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(3/2)+3*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))*a^3*b-9*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))*a^2*b^2-27*b^3*a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-15*b^4*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)))/b^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
133,1,309,98,1.684000," ","int(sin(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(4 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)-10 b^{\frac{3}{2}} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+3 \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right) a^{2}+6 b a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+3 b^{2} \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-10 a \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{b}\right)}{16 \sqrt{b}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/16*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(4*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(3/2)*cos(f*x+e)^2-10*b^(3/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+3*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))*a^2+6*b*a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))+3*b^2*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-10*a*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^(1/2))/b^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
134,1,255,104,2.080000," ","int(csc(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(b^{\frac{3}{2}} \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-2 a^{\frac{3}{2}} \ln \left(\frac{-\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)-2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-a -b}{-1+\cos^{2}\left(f x +e \right)}\right)+3 \sqrt{b}\, a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)-2 b \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\right)}{4 \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(b^(3/2)*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-2*a^(3/2)*ln((-(a-b)*cos(f*x+e)^2-2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-a-b)/(-1+cos(f*x+e)^2))+3*b^(1/2)*a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))-2*b*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
135,1,287,110,2.365000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(2 b^{\frac{3}{2}} \arctan \left(\frac{2 b \left(\sin^{2}\left(f x +e \right)\right)+a -b}{2 \sqrt{b}\, \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}}\right) \left(\sin^{2}\left(f x +e \right)\right)-a^{\frac{3}{2}} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right)-3 \sqrt{a}\, b \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right)-2 a \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\right)}{4 \sin \left(f x +e \right)^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(2*b^(3/2)*arctan(1/2/b^(1/2)*(2*b*sin(f*x+e)^2+a-b)/(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))*sin(f*x+e)^2-a^(3/2)*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^2-3*a^(1/2)*b*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^2-2*a*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/sin(f*x+e)^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
136,1,376,112,1.949000," ","int(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(3 a^{2} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{4}\left(f x +e \right)\right)+6 a b \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{4}\left(f x +e \right)\right)+3 b^{2} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{4}\left(f x +e \right)\right)+6 a^{\frac{3}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{2}\left(f x +e \right)\right)+10 b \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \sqrt{a}\, \left(\sin^{2}\left(f x +e \right)\right)+4 a^{\frac{3}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\right)}{16 \sqrt{a}\, \sin \left(f x +e \right)^{4} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/16*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(3*a^2*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^4+6*a*b*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^4+3*b^2*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^4+6*a^(3/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^2+10*b*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*a^(1/2)*sin(f*x+e)^2+4*a^(3/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/a^(1/2)/sin(f*x+e)^4/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
137,1,565,177,2.516000," ","int(csc(f*x+e)^7*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(15 a^{4} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{6}\left(f x +e \right)\right)+27 a^{3} b \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{6}\left(f x +e \right)\right)+9 b^{2} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{6}\left(f x +e \right)\right) a^{2}-3 b^{3} \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{6}\left(f x +e \right)\right) a +30 a^{\frac{7}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{4}\left(f x +e \right)\right)+44 b \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{4}\left(f x +e \right)\right) a^{\frac{5}{2}}+6 b^{2} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{4}\left(f x +e \right)\right) a^{\frac{3}{2}}+20 a^{\frac{7}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{2}\left(f x +e \right)\right)+28 b \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\sin^{2}\left(f x +e \right)\right) a^{\frac{5}{2}}+16 a^{\frac{7}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\right)}{96 \sin \left(f x +e \right)^{6} a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/96*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(15*a^4*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^6+27*a^3*b*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^6+9*b^2*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^6*a^2-3*b^3*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^6*a+30*a^(7/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^4+44*b*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^4*a^(5/2)+6*b^2*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^4*a^(3/2)+20*a^(7/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^2+28*b*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*sin(f*x+e)^2*a^(5/2)+16*a^(7/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/sin(f*x+e)^6/a^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
138,1,602,299,1.608000," ","int(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{5 b^{4} \left(\sin^{9}\left(f x +e \right)\right)+13 a \,b^{3} \left(\sin^{7}\left(f x +e \right)\right)+b^{4} \left(\sin^{7}\left(f x +e \right)\right)+9 a^{2} b^{2} \left(\sin^{5}\left(f x +e \right)\right)+4 a \,b^{3} \left(\sin^{5}\left(f x +e \right)\right)+2 b^{4} \left(\sin^{5}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}-3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b -13 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}+4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +24 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}+16 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}+a^{3} b \left(\sin^{3}\left(f x +e \right)\right)+2 a^{2} b^{2} \left(\sin^{3}\left(f x +e \right)\right)-9 a \,b^{3} \left(\sin^{3}\left(f x +e \right)\right)-8 b^{4} \left(\sin^{3}\left(f x +e \right)\right)-a^{3} b \sin \left(f x +e \right)-11 a^{2} b^{2} \sin \left(f x +e \right)-8 a \,b^{3} \sin \left(f x +e \right)}{35 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/35*(5*b^4*sin(f*x+e)^9+13*a*b^3*sin(f*x+e)^7+b^4*sin(f*x+e)^7+9*a^2*b^2*sin(f*x+e)^5+4*a*b^3*sin(f*x+e)^5+2*b^4*sin(f*x+e)^5+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^4-3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b-13*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^4+4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+24*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2+16*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3+a^3*b*sin(f*x+e)^3+2*a^2*b^2*sin(f*x+e)^3-9*a*b^3*sin(f*x+e)^3-8*b^4*sin(f*x+e)^3-a^3*b*sin(f*x+e)-11*a^2*b^2*sin(f*x+e)-8*a*b^3*sin(f*x+e))/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
139,1,429,240,1.408000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{-3 b^{3} \left(\sin^{7}\left(f x +e \right)\right)-9 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)-b^{3} \left(\sin^{5}\left(f x +e \right)\right)+3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+7 a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b +4 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-13 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-6 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)+5 a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)+4 b^{3} \left(\sin^{3}\left(f x +e \right)\right)+6 a^{2} b \sin \left(f x +e \right)+4 a \,b^{2} \sin \left(f x +e \right)}{15 b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/15*(-3*b^3*sin(f*x+e)^7-9*a*b^2*sin(f*x+e)^5-b^3*sin(f*x+e)^5+3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+7*a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b+4*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-13*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-6*a^2*b*sin(f*x+e)^3+5*a*b^2*sin(f*x+e)^3+4*b^3*sin(f*x+e)^3+6*a^2*b*sin(f*x+e)+4*a*b^2*sin(f*x+e))/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
140,1,266,180,1.435000," ","int((a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}-\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b}{3}+\frac{4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}+\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b}{3}+\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)}{3}+\frac{a b \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{b^{2} \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{a b \sin \left(f x +e \right)}{3}}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-1/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2-1/3*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b+4/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+1/3*b^2*sin(f*x+e)^5+1/3*a*b*sin(f*x+e)^3-1/3*b^2*sin(f*x+e)^3-1/3*a*b*sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
141,1,174,169,1.404000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{a \left(\sin \left(f x +e \right) \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right)+b \left(\cos^{4}\left(f x +e \right)\right)+\left(-a -b \right) \left(\cos^{2}\left(f x +e \right)\right)\right)}{\sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"a*(sin(f*x+e)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)+b*cos(f*x+e)^4+(-a-b)*cos(f*x+e)^2)/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
142,1,408,214,1.728000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+5 b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)+3 b^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \left(\sin^{3}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+2 a b \left(\sin^{6}\left(f x +e \right)\right)+4 b^{2} \left(\sin^{6}\left(f x +e \right)\right)+2 a^{2} \left(\sin^{4}\left(f x +e \right)\right)+3 a b \left(\sin^{4}\left(f x +e \right)\right)-4 b^{2} \left(\sin^{4}\left(f x +e \right)\right)-a^{2} \left(\sin^{2}\left(f x +e \right)\right)-5 a b \left(\sin^{2}\left(f x +e \right)\right)-a^{2}}{3 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+5*b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3+3*b^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*sin(f*x+e)^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+2*a*b*sin(f*x+e)^6+4*b^2*sin(f*x+e)^6+2*a^2*sin(f*x+e)^4+3*a*b*sin(f*x+e)^4-4*b^2*sin(f*x+e)^4-a^2*sin(f*x+e)^2-5*a*b*sin(f*x+e)^2-a^2)/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
143,1,437,232,1.619000," ","int((a+b*sin(d*x+c)^2)^(5/2),x)","\frac{-\frac{b^{3} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{5}+\frac{\left(14 a \,b^{2}+10 b^{3}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}+\frac{\left(-11 a^{2} b -18 a \,b^{2}-7 b^{3}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}-\frac{8 \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) a^{3}}{15}-\frac{4 a^{2} \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) b}{5}-\frac{4 a \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) b^{2}}{15}+\frac{23 \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) a^{3}}{15}+\frac{23 \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) a^{2} b}{15}+\frac{8 \sqrt{\frac{\cos \left(2 d x +2 c \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(d x +c \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{15}}{\cos \left(d x +c \right) \sqrt{a +b \left(\sin^{2}\left(d x +c \right)\right)}\, d}"," ",0,"(-1/5*b^3*sin(d*x+c)*cos(d*x+c)^6+1/15*(14*a*b^2+10*b^3)*cos(d*x+c)^4*sin(d*x+c)+1/15*(-11*a^2*b-18*a*b^2-7*b^3)*cos(d*x+c)^2*sin(d*x+c)-8/15*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticF(sin(d*x+c),(-1/a*b)^(1/2))*a^3-4/5*a^2*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticF(sin(d*x+c),(-1/a*b)^(1/2))*b-4/15*a*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticF(sin(d*x+c),(-1/a*b)^(1/2))*b^2+23/15*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticE(sin(d*x+c),(-1/a*b)^(1/2))*a^3+23/15*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticE(sin(d*x+c),(-1/a*b)^(1/2))*a^2*b+8/15*(cos(d*x+c)^2)^(1/2)*(-b/a*cos(d*x+c)^2+(a+b)/a)^(1/2)*EllipticE(sin(d*x+c),(-1/a*b)^(1/2))*a*b^2)/cos(d*x+c)/(a+b*sin(d*x+c)^2)^(1/2)/d","A"
144,1,186,71,1.476000," ","int(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(2 b^{\frac{3}{2}} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-b^{2} \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)+b a \arctan \left(\frac{-2 b \left(\cos^{2}\left(f x +e \right)\right)+a +b}{2 \sqrt{b}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)\right)}{4 b^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(2*b^(3/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-b^2*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2))+b*a*arctan(1/2*(-2*b*cos(f*x+e)^2+a+b)/b^(1/2)/(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)))/b^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
145,1,99,35,1.183000," ","int(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \arctan \left(\frac{2 b \left(\sin^{2}\left(f x +e \right)\right)+a -b}{2 \sqrt{b}\, \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}}\right)}{2 \sqrt{b}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/2*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)/b^(1/2)*arctan(1/2/b^(1/2)*(2*b*sin(f*x+e)^2+a-b)/(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
146,1,112,35,1.389000," ","int(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right)}{2 \sqrt{a}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/2*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)/a^(1/2)*ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
147,1,231,77,2.098000," ","int(csc(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\, \left(\ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right) a^{2}-\ln \left(\frac{\left(a -b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+a +b}{\sin \left(f x +e \right)^{2}}\right) b \left(\sin^{2}\left(f x +e \right)\right) a +2 a^{\frac{3}{2}} \sqrt{\left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)}\right)}{4 \sin \left(f x +e \right)^{2} a^{\frac{5}{2}} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/4*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2)*(ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*sin(f*x+e)^2*a^2-ln(((a-b)*cos(f*x+e)^2+2*a^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+a+b)/sin(f*x+e)^2)*b*sin(f*x+e)^2*a+2*a^(3/2)*(cos(f*x+e)^2*(a+b*sin(f*x+e)^2))^(1/2))/sin(f*x+e)^2/a^(5/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
148,1,268,188,1.436000," ","int(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +a b \left(\sin^{3}\left(f x +e \right)\right)-b^{2} \left(\sin^{3}\left(f x +e \right)\right)-a b \sin \left(f x +e \right)}{3 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(b^2*sin(f*x+e)^5+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+a*b*sin(f*x+e)^3-b^2*sin(f*x+e)^3-a*b*sin(f*x+e))/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
149,1,93,145,1.237000," ","int(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)\right)}{b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)/b*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
150,1,60,68,0.322000," ","int(1/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)-a -b}{a}}\, \mathrm{am}^{-1}\left(f x +e \bigg| \frac{i \sqrt{b}}{\sqrt{a}}\right)}{f \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}"," ",0,"1/f/(a+b-b*cos(f*x+e)^2)^(1/2)*(-(b*cos(f*x+e)^2-a-b)/a)^(1/2)*InverseJacobiAM(f*x+e,I/a^(1/2)*b^(1/2))","C"
151,1,140,165,1.526000," ","int(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)\right)+b \left(\cos^{4}\left(f x +e \right)\right)+\left(-a -b \right) \left(\cos^{2}\left(f x +e \right)\right)}{a \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(sin(f*x+e)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))+b*cos(f*x+e)^4+(-a-b)*cos(f*x+e)^2)/a/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
152,1,354,222,1.483000," ","int(csc(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)-b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+2 a b \left(\sin^{6}\left(f x +e \right)\right)-2 b^{2} \left(\sin^{6}\left(f x +e \right)\right)+2 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-3 a b \left(\sin^{4}\left(f x +e \right)\right)+2 b^{2} \left(\sin^{4}\left(f x +e \right)\right)-a^{2} \left(\sin^{2}\left(f x +e \right)\right)+a b \left(\sin^{2}\left(f x +e \right)\right)-a^{2}}{3 a^{2} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3-b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+2*a*b*sin(f*x+e)^6-2*b^2*sin(f*x+e)^6+2*a^2*sin(f*x+e)^4-3*a*b*sin(f*x+e)^4+2*b^2*sin(f*x+e)^4-a^2*sin(f*x+e)^2+a*b*sin(f*x+e)^2-a^2)/a^2/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
153,1,156,71,2.377000," ","int(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\arctan \left(\frac{\sqrt{b}\, \left(\sin^{2}\left(f x +e \right)-\frac{-a +b}{2 b}\right)}{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{2 b^{\frac{3}{2}}}+\frac{a \left(\cos^{2}\left(f x +e \right)\right)}{b \left(a +b \right) \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)*(1/2/b^(3/2)*arctan(b^(1/2)*(sin(f*x+e)^2-1/2*(-a+b)/b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))+a/b*cos(f*x+e)^2/(a+b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
154,1,31,32,0.885000," ","int(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\cos \left(f x +e \right)}{\left(a +b \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-cos(f*x+e)/(a+b)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
155,1,165,71,2.383000," ","int(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a \left(a +b \right) \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +\left(-a +b \right) \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)^{2}}\right)}{2 a^{\frac{3}{2}}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)*(1/a*b*cos(f*x+e)^2/(a+b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)-1/2/a^(3/2)*ln((2*a+(-a+b)*sin(f*x+e)^2+2*a^(1/2)*(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))/sin(f*x+e)^2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
156,1,274,118,2.803000," ","int(csc(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(-\frac{b^{2} \left(\cos^{2}\left(f x +e \right)\right)}{a^{2} \left(a +b \right) \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}+\frac{3 b \ln \left(\frac{2 a +\left(-a +b \right) \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)^{2}}\right)}{4 a^{\frac{5}{2}}}-\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{2 a^{2} \sin \left(f x +e \right)^{2}}-\frac{\ln \left(\frac{2 a +\left(-a +b \right) \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)^{2}}\right)}{4 a^{\frac{3}{2}}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)*(-b^2/a^2*cos(f*x+e)^2/(a+b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)+3/4/a^(5/2)*b*ln((2*a+(-a+b)*sin(f*x+e)^2+2*a^(1/2)*(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))/sin(f*x+e)^2)-1/2/a^2/sin(f*x+e)^2*(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)-1/4/a^(3/2)*ln((2*a+(-a+b)*sin(f*x+e)^2+2*a^(1/2)*(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))/sin(f*x+e)^2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
157,1,405,254,1.934000," ","int(sin(f*x+e)^6/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+b^{3} \left(\sin^{5}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+7 a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}+4 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-b^{3} \left(\sin^{3}\left(f x +e \right)\right)-4 a^{2} b \sin \left(f x +e \right)-a \,b^{2} \sin \left(f x +e \right)}{3 b^{3} \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(a*b^2*sin(f*x+e)^5+b^3*sin(f*x+e)^5+8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+7*a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2+4*a^2*b*sin(f*x+e)^3-b^3*sin(f*x+e)^3-4*a^2*b*sin(f*x+e)-a*b^2*sin(f*x+e))/b^3/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
158,1,241,190,1.671000," ","int(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{a \left(2 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b +b \left(\sin^{3}\left(f x +e \right)\right)-b \sin \left(f x +e \right)\right)}{b^{2} \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-a*(2*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b+b*sin(f*x+e)^3-b*sin(f*x+e))/b^2/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
159,1,191,185,1.517000," ","int(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+b \left(\sin^{3}\left(f x +e \right)\right)-b \sin \left(f x +e \right)}{b \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))+b*sin(f*x+e)^3-b*sin(f*x+e))/b/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
160,1,103,116,1.740000," ","int(1/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b}{a \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"((cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))+sin(f*x+e)*cos(f*x+e)^2*b)/a/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
161,1,199,221,1.795000," ","int(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right)+\left(a b +2 b^{2}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-a^{2}-2 a b -2 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)}{a^{2} \sin \left(f x +e \right) \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(sin(f*x+e)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)+(a*b+2*b^2)*cos(f*x+e)^4+(-a^2-2*a*b-2*b^2)*cos(f*x+e)^2)/a^2/sin(f*x+e)/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
162,1,243,123,3.285000," ","int(sin(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{\arctan \left(\frac{\sqrt{b}\, \left(\sin^{2}\left(f x +e \right)-\frac{-a +b}{2 b}\right)}{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}\right)}{2 b^{\frac{5}{2}}}+\frac{2 a \left(\cos^{2}\left(f x +e \right)\right)}{b^{2} \left(a +b \right) \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{a^{2} \left(2 b \left(\sin^{2}\left(f x +e \right)\right)+3 a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 b^{2} \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(a^{2}+2 a b +b^{2}\right)}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)*(1/2/b^(5/2)*arctan(b^(1/2)*(sin(f*x+e)^2-1/2*(-a+b)/b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))+2*a/b^2*cos(f*x+e)^2/(a+b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)-1/3*a^2/b^2*(2*b*sin(f*x+e)^2+3*a+b)*cos(f*x+e)^2/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e)^2)/(a^2+2*a*b+b^2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
163,1,64,73,1.314000," ","int(sin(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\left(a \left(\sin^{2}\left(f x +e \right)\right)+3 b \left(\sin^{2}\left(f x +e \right)\right)+2 a \right) \cos \left(f x +e \right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a^{2}+2 a b +b^{2}\right) f}"," ",0,"-1/3*(a*sin(f*x+e)^2+3*b*sin(f*x+e)^2+2*a)*cos(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2)/(a^2+2*a*b+b^2)/f","A"
164,1,55,65,1.311000," ","int(sin(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\left(2 b \left(\sin^{2}\left(f x +e \right)\right)+3 a +b \right) \cos \left(f x +e \right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a^{2}+2 a b +b^{2}\right) f}"," ",0,"-1/3*(2*b*sin(f*x+e)^2+3*a+b)*cos(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2)/(a^2+2*a*b+b^2)/f","A"
165,1,249,115,3.709000," ","int(csc(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a^{2} \left(a +b \right) \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +\left(-a +b \right) \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{a}\, \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)^{2}}\right)}{2 a^{\frac{5}{2}}}+\frac{b \left(2 b \left(\sin^{2}\left(f x +e \right)\right)+3 a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 a \sqrt{-\left(-b \left(\sin^{2}\left(f x +e \right)\right)-a \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(a^{2}+2 a b +b^{2}\right)}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)*(1/a^2*b*cos(f*x+e)^2/(a+b)/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)-1/2/a^(5/2)*ln((2*a+(-a+b)*sin(f*x+e)^2+2*a^(1/2)*(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2))/sin(f*x+e)^2)+1/3/a*b*(2*b*sin(f*x+e)^2+3*a+b)*cos(f*x+e)^2/(-(-b*sin(f*x+e)^2-a)*cos(f*x+e)^2)^(1/2)/(a+b*sin(f*x+e)^2)/(a^2+2*a*b+b^2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
166,1,698,263,1.883000," ","int(sin(f*x+e)^6/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\left(\left(5 a \,b^{2}+7 b^{3}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-4 a^{2} b -11 a \,b^{2}-7 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, b \left(8 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+17 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +9 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-13 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -3 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+25 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +26 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}+9 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-21 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -16 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}\right) a}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{2} b^{3} \cos \left(f x +e \right) f}"," ",0,"-1/3*((5*a*b^2+7*b^3)*sin(f*x+e)*cos(f*x+e)^4+(-4*a^2*b-11*a*b^2-7*b^3)*cos(f*x+e)^2*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*b*(8*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+17*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b+9*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-13*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b-3*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^2)*cos(f*x+e)^2+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+25*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+26*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2+9*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^3-8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-21*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-16*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-3*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^3)*a/(a+b*sin(f*x+e)^2)^(3/2)/(a+b)^2/b^3/cos(f*x+e)/f","B"
167,1,623,247,1.787000," ","int(sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\left(2 a \,b^{2}+4 b^{3}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-a^{2} b -5 a \,b^{2}-4 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, b \left(2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+5 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-4 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}+3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-6 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{2} b^{2} \cos \left(f x +e \right) f}"," ",0,"1/3*((2*a*b^2+4*b^3)*sin(f*x+e)*cos(f*x+e)^4+(-a^2*b-5*a*b^2-4*b^3)*cos(f*x+e)^2*sin(f*x+e)-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*b*(2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+5*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b+3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-4*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b)*cos(f*x+e)^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+7*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2+3*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^3-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-6*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-4*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/(a+b*sin(f*x+e)^2)^(3/2)/(a+b)^2/b^2/cos(f*x+e)/f","B"
168,1,483,243,1.751000," ","int(sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\left(a \,b^{2}-b^{3}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-2 a^{2} b -a \,b^{2}+b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a b \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{2} a b \cos \left(f x +e \right) f}"," ",0,"1/3*((a*b^2-b^3)*sin(f*x+e)*cos(f*x+e)^4+(-2*a^2*b-a*b^2+b^3)*cos(f*x+e)^2*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*b*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/(a+b*sin(f*x+e)^2)^(3/2)/(a+b)^2/a/b/cos(f*x+e)/f","A"
169,1,547,245,1.931000," ","int(1/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)+4 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+2 b^{3} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +5 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)-2 b^{3} \left(\sin^{3}\left(f x +e \right)\right)-5 a^{2} b \sin \left(f x +e \right)-3 a \,b^{2} \sin \left(f x +e \right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} a^{2} \left(a +b \right)^{2} \cos \left(f x +e \right) f}"," ",0,"-1/3*((cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2+4*a*b^2*sin(f*x+e)^5+2*b^3*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+5*a^2*b*sin(f*x+e)^3-a*b^2*sin(f*x+e)^3-2*b^3*sin(f*x+e)^3-5*a^2*b*sin(f*x+e)-3*a*b^2*sin(f*x+e))/(a+b*sin(f*x+e)^2)^(3/2)/a^2/(a+b)^2/cos(f*x+e)/f","B"
170,1,527,296,2.035000," ","int(csc(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a b \left(3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+7 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-3 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-13 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a \left(3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+10 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +11 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}+4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}-3 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-16 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -21 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}\right) \sin \left(f x +e \right)+\left(-3 a^{2} b^{2}-13 a \,b^{3}-8 b^{4}\right) \left(\cos^{6}\left(f x +e \right)\right)+\left(6 a^{3} b +26 a^{2} b^{2}+38 a \,b^{3}+16 b^{4}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-3 a^{4}-12 a^{3} b -26 a^{2} b^{2}-25 a \,b^{3}-8 b^{4}\right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{2} \sin \left(f x +e \right) a^{3} \cos \left(f x +e \right) f}"," ",0,"1/3*(-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*b*(3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+7*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-3*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-13*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^2)*sin(f*x+e)*cos(f*x+e)^2+(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*(3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+10*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+11*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^3-3*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-16*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-21*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^3)*sin(f*x+e)+(-3*a^2*b^2-13*a*b^3-8*b^4)*cos(f*x+e)^6+(6*a^3*b+26*a^2*b^2+38*a*b^3+16*b^4)*cos(f*x+e)^4+(-3*a^4-12*a^3*b-26*a^2*b^2-25*a*b^3-8*b^4)*cos(f*x+e)^2)/(a+b*sin(f*x+e)^2)^(3/2)/(a+b)^2/sin(f*x+e)/a^3/cos(f*x+e)/f","A"
171,0,0,110,2.651000," ","int((d*sin(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x)","\int \left(d \sin \left(f x +e \right)\right)^{m} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*sin(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x)","F"
172,0,0,214,4.564000," ","int(sin(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sin^{5}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","F"
173,0,0,129,8.256000," ","int(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sin^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","F"
174,0,0,72,2.605000," ","int(sin(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","\int \sin \left(f x +e \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","F"
175,0,0,79,2.433000," ","int(csc(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","\int \csc \left(f x +e \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","F"
176,0,0,79,2.212000," ","int(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","F"
177,0,0,79,1.332000," ","int(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\csc^{5}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","F"
178,0,0,91,4.422000," ","int(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sin^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","F"
179,0,0,93,5.342000," ","int(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sin^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","F"
180,0,0,89,1.686000," ","int(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","F"
181,0,0,91,1.189000," ","int(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\csc^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(csc(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","F"
182,1,366,244,0.562000," ","int(sin(d*x+c)^7/(a+b*sin(d*x+c)^3),x)","\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b}+\frac{2 a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R} \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \,b^{2}}"," ",0,"3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a+11/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a-11/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a-3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*a+3/4/d/b*arctan(tan(1/2*d*x+1/2*c))+2/3/d*a^2/b^2*sum((_R^3+_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
183,1,163,194,0.573000," ","int(sin(d*x+c)^5/(a+b*sin(d*x+c)^3),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{4 a \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d b}"," ",0,"1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+1/d/b*arctan(tan(1/2*d*x+1/2*c))-4/3/d*a/b*sum(_R^2/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
184,1,106,182,0.469000," ","int(sin(d*x+c)^3/(a+b*sin(d*x+c)^3),x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{a \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d b}"," ",0,"2/d/b*arctan(tan(1/2*d*x+1/2*c))-1/3/d*a/b*sum((_R^4+2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
185,1,78,182,0.530000," ","int(sin(d*x+c)/(a+b*sin(d*x+c)^3),x)","\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R} \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d}"," ",0,"2/3/d*sum((_R^3+_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
186,1,98,189,0.762000," ","int(csc(d*x+c)/(a+b*sin(d*x+c)^3),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{4 b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}"," ",0,"1/a/d*ln(tan(1/2*d*x+1/2*c))-4/3/d/a*b*sum(_R^2/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
187,1,144,206,0.803000," ","int(csc(d*x+c)^3/(a+b*sin(d*x+c)^3),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/2/a/d*ln(tan(1/2*d*x+1/2*c))-1/3/d/a*b*sum((_R^4+2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
188,1,217,253,0.824000," ","int(csc(d*x+c)^5/(a+b*sin(d*x+c)^3),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d a}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{1}{64 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 b^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R} \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \,a^{2}}"," ",0,"1/64/d/a*tan(1/2*d*x+1/2*c)^4+1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/64/d/a/tan(1/2*d*x+1/2*c)^4-1/8/a/d/tan(1/2*d*x+1/2*c)^2+3/8/a/d*ln(tan(1/2*d*x+1/2*c))+1/2/d*b/a^2/tan(1/2*d*x+1/2*c)+2/3/d*b^2/a^2*sum((_R^3+_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
189,1,166,214,0.578000," ","int(sin(d*x+c)^6/(a+b*sin(d*x+c)^3),x)","-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}+\frac{a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \,b^{2}}"," ",0,"-4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-4/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3-2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))+1/3/d*a^2/b^2*sum((_R^4+2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
190,1,106,196,0.561000," ","int(sin(d*x+c)^4/(a+b*sin(d*x+c)^3),x)","-\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 a \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R} \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d b}"," ",0,"-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)-2/3/d*a/b*sum((_R^3+_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
191,1,76,165,0.454000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)^3),x)","\frac{4 \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d}"," ",0,"4/3/d*sum(_R^2/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
192,1,83,168,0.529000," ","int(1/(a+b*sin(d*x+c)^3),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}}{3 d}"," ",0,"1/3/d*sum((_R^4+2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
193,1,119,196,0.763000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)^3),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{3}+\textit{\_R} \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d a}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-2/3/d/a*b*sum((_R^3+_R)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
194,1,176,219,0.788000," ","int(csc(d*x+c)^4/(a+b*sin(d*x+c)^3),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{1}{24 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{3}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4 b^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\textit{\_R}^{2} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \,a^{2}}"," ",0,"1/24/d/a*tan(1/2*d*x+1/2*c)^3+3/8/a/d*tan(1/2*d*x+1/2*c)-1/24/d/a/tan(1/2*d*x+1/2*c)^3-3/8/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+4/3/d*b^2/a^2*sum(_R^2/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
195,1,159,133,0.367000," ","int(sin(d*x+c)^9/(a-b*sin(d*x+c)^4),x)","\frac{\cos^{5}\left(d x +c \right)}{5 b d}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{3 b d}+\frac{a \cos \left(d x +c \right)}{b^{2} d}+\frac{\cos \left(d x +c \right)}{b d}-\frac{a^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{a^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/5*cos(d*x+c)^5/b/d-2/3*cos(d*x+c)^3/b/d+a*cos(d*x+c)/b^2/d+cos(d*x+c)/b/d-1/2/d*a^2/b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d*a^2/b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
196,1,115,110,0.306000," ","int(sin(d*x+c)^7/(a-b*sin(d*x+c)^4),x)","-\frac{\cos^{3}\left(d x +c \right)}{3 b d}+\frac{\cos \left(d x +c \right)}{b d}+\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d b \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d b \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/3*cos(d*x+c)^3/b/d+cos(d*x+c)/b/d+1/2/d*a/b/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d*a/b/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
197,1,103,98,0.355000," ","int(sin(d*x+c)^5/(a-b*sin(d*x+c)^4),x)","\frac{\cos \left(d x +c \right)}{b d}-\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"cos(d*x+c)/b/d-1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
198,1,78,79,0.236000," ","int(sin(d*x+c)^3/(a-b*sin(d*x+c)^4),x)","\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/2/d/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
199,1,90,85,0.365000," ","int(sin(d*x+c)/(a-b*sin(d*x+c)^4),x)","-\frac{b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/2*b/d/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2*b/d/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
200,1,120,100,0.489000," ","int(csc(d*x+c)/(a-b*sin(d*x+c)^4),x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 a d}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d a}+\frac{b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d a \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d a \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/2/a/d*ln(cos(d*x+c)-1)-1/2/d/a*ln(1+cos(d*x+c))+1/2/d/a*b/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d/a*b/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
201,1,170,138,0.568000," ","int(csc(d*x+c)^3/(a-b*sin(d*x+c)^4),x)","\frac{1}{4 d a \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{4 a d}+\frac{1}{4 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{4 d a}-\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d a \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d a \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/4/d/a/(cos(d*x+c)-1)+1/4/a/d*ln(cos(d*x+c)-1)+1/4/a/d/(1+cos(d*x+c))-1/4/d/a*ln(1+cos(d*x+c))-1/2/d/a*b^2/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d/a*b^2/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
202,1,232,183,0.539000," ","int(csc(d*x+c)^5/(a-b*sin(d*x+c)^4),x)","-\frac{1}{16 d a \left(\cos \left(d x +c \right)-1\right)^{2}}+\frac{3}{16 d a \left(\cos \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\cos \left(d x +c \right)-1\right)}{16 a d}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{2 d \,a^{2}}+\frac{1}{16 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{3}{16 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right)}{16 d a}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{2 d \,a^{2}}+\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \,a^{2} \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \,a^{2} \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/16/d/a/(cos(d*x+c)-1)^2+3/16/d/a/(cos(d*x+c)-1)+3/16/a/d*ln(cos(d*x+c)-1)+1/2/d/a^2*ln(cos(d*x+c)-1)*b+1/16/a/d/(1+cos(d*x+c))^2+3/16/a/d/(1+cos(d*x+c))-3/16/d/a*ln(1+cos(d*x+c))-1/2/d/a^2*ln(1+cos(d*x+c))*b+1/2/d*b^2/a^2/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d*b^2/a^2/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
203,1,605,142,0.346000," ","int(sin(d*x+c)^8/(a-b*sin(d*x+c)^4),x)","\frac{5 \left(\tan^{3}\left(d x +c \right)\right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{3 \tan \left(d x +c \right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right)}{8 d b}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{d \,b^{2}}+\frac{a^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \,b^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \,b^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"5/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3+3/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)-3/8/d/b*arctan(tan(d*x+c))-1/d/b^2*arctan(tan(d*x+c))*a+1/2/d*a^3/b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^3/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a^3/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a^3/b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
204,1,551,111,0.347000," ","int(sin(d*x+c)^6/(a-b*sin(d*x+c)^4),x)","\frac{\tan \left(d x +c \right)}{2 d b \left(\tan^{2}\left(d x +c \right)+1\right)}-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{2 d b}+\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/2/d/b*tan(d*x+c)/(tan(d*x+c)^2+1)-1/2/d/b*arctan(tan(d*x+c))+1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^3/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a^3/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
205,1,517,91,0.282000," ","int(sin(d*x+c)^4/(a-b*sin(d*x+c)^4),x)","-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d b}+\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/d/b*arctan(tan(d*x+c))+1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a^2/b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b-1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b-1/2/d*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
206,1,492,85,0.431000," ","int(sin(d*x+c)^2/(a-b*sin(d*x+c)^4),x)","\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/2/d*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b-1/2/d*b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b","B"
207,1,492,79,0.357000," ","int(1/(a-b*sin(d*x+c)^4),x)","\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/2/d*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b+1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b+1/2/d*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2-1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2-1/2/d*b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
208,1,518,99,0.493000," ","int(csc(d*x+c)^2/(a-b*sin(d*x+c)^4),x)","-\frac{1}{d a \tan \left(d x +c \right)}+\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/d/a/tan(d*x+c)+1/2/d*b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b+1/2/d*b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b-1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2-1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2","B"
209,1,542,111,0.531000," ","int(csc(d*x+c)^4/(a-b*sin(d*x+c)^4),x)","-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}+\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/3/d/a/tan(d*x+c)^3-1/d/a/tan(d*x+c)+1/2/d*b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2+1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2+1/2/d*b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
210,1,585,134,0.529000," ","int(csc(d*x+c)^6/(a-b*sin(d*x+c)^4),x)","-\frac{1}{5 d a \tan \left(d x +c \right)^{5}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2}{3 d a \tan \left(d x +c \right)^{3}}+\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/5/d/a/tan(d*x+c)^5-1/d/a/tan(d*x+c)-1/d/a^2/tan(d*x+c)*b-2/3/d/a/tan(d*x+c)^3+1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2+1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2-1/2/d*b^3/a^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b^3/a^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
211,1,624,155,0.554000," ","int(csc(d*x+c)^8/(a-b*sin(d*x+c)^4),x)","-\frac{1}{7 d a \tan \left(d x +c \right)^{7}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{1}{d a \tan \left(d x +c \right)^{3}}-\frac{b}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{3}{5 d a \tan \left(d x +c \right)^{5}}+\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{4} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{4} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/7/d/a/tan(d*x+c)^7-1/d/a/tan(d*x+c)-1/d/a^2/tan(d*x+c)*b-1/d/a/tan(d*x+c)^3-1/3/d/a^2/tan(d*x+c)^3*b-3/5/d/a/tan(d*x+c)^5+1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/a*b^3/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d/a*b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b^3/a^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*b^4/a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b^4/a^2/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b^3/a^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
212,1,482,186,0.342000," ","int(sin(d*x+c)^9/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\cos \left(d x +c \right)}{b^{2} d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{4 d b \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{a^{2} \cos \left(d x +c \right)}{4 d \,b^{2} \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{a \cos \left(d x +c \right)}{4 d b \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{4 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{5 a^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{4 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{5 a^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-cos(d*x+c)/b^2/d-1/4/d*a/b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)^3+1/4/d*a^2/b^2/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)+1/4/d*a/b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)+1/8/d*a/b/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-3/4/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+5/8/d*a^2/b/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/8/d*a/b/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-3/4/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))+5/8/d*a^2/b/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
213,1,394,164,0.315000," ","int(sin(d*x+c)^7/(a-b*sin(d*x+c)^4)^2,x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{4 d b \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{a \cos \left(d x +c \right)}{2 d b \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}-\frac{3 a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{3 a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/4/d*a/b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)^3+1/2/d*a/b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)-3/8/d*a/b/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/2/d/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/8/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+3/8/d*a/b/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/2/d/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/8/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
214,1,440,167,0.301000," ","int(sin(d*x+c)^5/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\cos^{3}\left(d x +c \right)}{4 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{a \cos \left(d x +c \right)}{4 d b \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{\cos \left(d x +c \right)}{4 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{4 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{a \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{4 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{a \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/4/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)^3+1/4/d*a/b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)+1/4/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)+1/8/d/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/4/d/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b+1/8/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/8/d/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/4/d/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b+1/8/d*a/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
215,1,213,144,0.260000," ","int(sin(d*x+c)^3/(a-b*sin(d*x+c)^4)^2,x)","\frac{\sqrt{a b}\, \cos \left(d x +c \right)}{8 d a \left(\sqrt{a b}+b \right) \left(-b \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{a b}+b \right)}+\frac{\sqrt{a b}\, \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d a \left(\sqrt{a b}+b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\sqrt{a b}\, \cos \left(d x +c \right)}{8 d a \left(\sqrt{a b}-b \right) \left(b \left(\cos^{2}\left(d x +c \right)\right)-b +\sqrt{a b}\right)}-\frac{\sqrt{a b}\, \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d a \left(\sqrt{a b}-b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/8/d*(a*b)^(1/2)/a*cos(d*x+c)/((a*b)^(1/2)+b)/(-b*cos(d*x+c)^2+(a*b)^(1/2)+b)+1/8/d*(a*b)^(1/2)/a/((a*b)^(1/2)+b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/8/d*(a*b)^(1/2)/a*cos(d*x+c)/((a*b)^(1/2)-b)/(b*cos(d*x+c)^2-b+(a*b)^(1/2))-1/8/d*(a*b)^(1/2)/a/((a*b)^(1/2)-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
216,1,488,171,0.517000," ","int(sin(d*x+c)/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\cos \left(d x +c \right)}{8 d a \left(a -b \right) \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)}-\frac{\cos \left(d x +c \right)}{8 d \sqrt{a b}\, \left(a -b \right) \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)}-\frac{b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{4 d \sqrt{a b}\, a \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\cos \left(d x +c \right)}{8 d a \left(a -b \right) \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)}+\frac{\cos \left(d x +c \right)}{8 d \sqrt{a b}\, \left(a -b \right) \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)}+\frac{b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{8 d \left(a -b \right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{4 d \sqrt{a b}\, a \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}"," ",0,"-1/8/d/a/(a-b)*cos(d*x+c)/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)-1/8/d/(a*b)^(1/2)/(a-b)*cos(d*x+c)/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)-1/8/d*b/a/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-3/8/d/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b+1/4/d*b^2/(a*b)^(1/2)/a/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/8/d/a/(a-b)*cos(d*x+c)/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)+1/8/d/(a*b)^(1/2)/(a-b)*cos(d*x+c)/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)+1/8/d*b/a/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-3/8/d/(a-b)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b+1/4/d*b^2/(a*b)^(1/2)/a/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))","B"
217,1,450,247,0.533000," ","int(csc(d*x+c)/(a-b*sin(d*x+c)^4)^2,x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d \,a^{2}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d \,a^{2}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{4 d a \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{b \cos \left(d x +c \right)}{2 d a \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right) \left(a -b \right)}+\frac{5 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d \sqrt{a b}\, a \left(a -b \right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{5 b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d \sqrt{a b}\, a \left(a -b \right) \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/2/d/a^2*ln(cos(d*x+c)-1)-1/2/d/a^2*ln(1+cos(d*x+c))-1/4/d/a*b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)^3+1/2/d/a*b/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)/(a-b)*cos(d*x+c)+5/8/d*b/a/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/2/d/a^2*b^2/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/8/d*b^2/(a*b)^(1/2)/a/(a-b)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-5/8/d*b/a/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))+1/2/d/a^2*b^2/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/8/d*b^2/(a*b)^(1/2)/a/(a-b)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","A"
218,1,644,240,0.314000," ","int(sin(d*x+c)^8/(a-b*sin(d*x+c)^4)^2,x)","\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d \,b^{2}}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{2 d b \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{a \tan \left(d x +c \right)}{4 d b \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \,b^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{4 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \,b^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{4 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{5 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/d/b^2*arctan(tan(d*x+c))-1/2/d*a/b/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d*a/b/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)-1/2/d*a^2/b^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/4/d*a/b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/8/d*a^2/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-5/8/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a^2/b^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/4/d*a/b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-3/8/d*a^2/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+5/8/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
219,1,674,181,0.323000," ","int(sin(d*x+c)^6/(a-b*sin(d*x+c)^4)^2,x)","-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{4 d b \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{\tan^{3}\left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{a \tan \left(d x +c \right)}{4 d b \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{4 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d b \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{4 d b \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/4/d*a/b/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d*a/b/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)-1/8/d*a/b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/8/d/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/4/d*a^2/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/8/d*a/b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/8/d/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/4/d*a^2/b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
220,1,478,151,0.269000," ","int(sin(d*x+c)^4/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\tan^{3}\left(d x +c \right)}{2 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{\tan \left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{4 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{4 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/2/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)-1/8/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/8/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b+1/4/d/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/8/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/8/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b+1/4/d/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
221,1,534,169,0.446000," ","int(sin(d*x+c)^2/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\tan^{3}\left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right) a}-\frac{\tan \left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}+\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{4 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{4 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)/a*tan(d*x+c)^3*b-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)+3/8/d/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/8/d/a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b-1/4/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/8/d/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/8/d/a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b+1/4/d*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
222,1,618,164,0.397000," ","int(1/(a-b*sin(d*x+c)^4)^2,x)","-\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{2 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right) a}-\frac{b \tan \left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) a \left(a -b \right)}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{4 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{8 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{4 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{5 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{8 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{8 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/2/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)/a*tan(d*x+c)^3*b-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)*b/a/(a-b)*tan(d*x+c)+1/2/d/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/4/d/a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b-5/8/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b+3/8/d/a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2+1/2/d/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/4/d/a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b+5/8/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b-3/8/d/a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2","B"
223,1,708,186,0.531000," ","int(csc(d*x+c)^2/(a-b*sin(d*x+c)^4)^2,x)","-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right) a}-\frac{b^{2} \left(\tan^{3}\left(d x +c \right)\right)}{4 d \,a^{2} \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) \left(a -b \right)}-\frac{b \tan \left(d x +c \right)}{4 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right) a \left(a -b \right)}+\frac{7 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{8 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b}{4 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{7 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{8 d a \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{8 d \,a^{2} \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b}{4 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d a \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/d/a^2/tan(d*x+c)-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)/a*tan(d*x+c)^3*b-1/4/d*b^2/a^2/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)/(a-b)*tan(d*x+c)^3-1/4/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)*b/a/(a-b)*tan(d*x+c)+7/8/d/a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b-5/8/d*b^2/a^2/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-3/4/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b+1/2/d/a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2+7/8/d/a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b-5/8/d*b^2/a^2/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/4/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b-1/2/d/a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2","B"
224,1,1164,263,0.425000," ","int(sin(d*x+c)^9/(a-b*sin(d*x+c)^4)^3,x)","\frac{\left(\cos^{7}\left(d x +c \right)\right) a}{8 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{5 \left(\cos^{7}\left(d x +c \right)\right) b}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{9 \left(\cos^{5}\left(d x +c \right)\right) a^{2}}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 \left(\cos^{5}\left(d x +c \right)\right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{15 b \left(\cos^{5}\left(d x +c \right)\right)}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \left(\cos^{3}\left(d x +c \right)\right) a^{2}}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 \left(\cos^{3}\left(d x +c \right)\right) a}{8 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{15 b \left(\cos^{3}\left(d x +c \right)\right)}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{5 \cos \left(d x +c \right) a^{2}}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b^{2} \left(a -b \right)}-\frac{15 \cos \left(d x +c \right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a -b \right)}-\frac{5 \cos \left(d x +c \right)}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right)}-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) a}{16 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{5 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{5 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{11 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) a}{16 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{5 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{5 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{11 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/8/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7*a-5/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7*b-9/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a^2-2*a*b+b^2)*cos(d*x+c)^5*a^2+3/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^5*a+15/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^5+9/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a^2-2*a*b+b^2)*cos(d*x+c)^3*a^2-3/8/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3*a-15/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^3+5/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b^2/(a-b)*cos(d*x+c)*a^2-15/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a-b)*cos(d*x+c)*a-5/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)*cos(d*x+c)-1/16/d/(a^2-2*a*b+b^2)/b/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*a+5/32/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-5/64/d/(a^2-2*a*b+b^2)/b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*a^2+11/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*a-3/16/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/16/d/(a^2-2*a*b+b^2)/b/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*a-5/32/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-5/64/d/(a^2-2*a*b+b^2)/b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*a^2+11/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*a-3/16/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
225,1,814,238,0.363000," ","int(sin(d*x+c)^7/(a-b*sin(d*x+c)^4)^3,x)","\frac{3 \left(\cos^{7}\left(d x +c \right)\right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{9 \left(\cos^{7}\left(d x +c \right)\right) b}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{11 \left(\cos^{5}\left(d x +c \right)\right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{35 b \left(\cos^{5}\left(d x +c \right)\right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{\left(\cos^{3}\left(d x +c \right)\right) a^{2}}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \left(\cos^{3}\left(d x +c \right)\right) a}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{43 b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 \cos \left(d x +c \right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a -b \right)}-\frac{17 \cos \left(d x +c \right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right)}-\frac{3 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{9 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{3 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) b \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{9 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"3/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7*a-9/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7*b-11/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^5*a+35/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^5+1/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a^2-2*a*b+b^2)*cos(d*x+c)^3*a^2+9/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3*a-43/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^3-3/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a-b)*cos(d*x+c)*a-17/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)*cos(d*x+c)-3/64/d/(a^2-2*a*b+b^2)/b/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*a+9/64/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-3/32/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+3/64/d/(a^2-2*a*b+b^2)/b/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*a-9/64/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-3/32/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
226,1,1167,261,0.388000," ","int(sin(d*x+c)^5/(a-b*sin(d*x+c)^4)^3,x)","-\frac{\left(\cos^{7}\left(d x +c \right)\right) b}{8 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\cos^{5}\left(d x +c \right)\right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{19 b \left(\cos^{5}\left(d x +c \right)\right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 \left(\cos^{5}\left(d x +c \right)\right) b^{2}}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}+\frac{5 \left(\cos^{3}\left(d x +c \right)\right) a}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{7 b \left(\cos^{3}\left(d x +c \right)\right)}{8 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 \cos \left(d x +c \right) a}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} b \left(a -b \right)}-\frac{15 \cos \left(d x +c \right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right)}-\frac{b \cos \left(d x +c \right)}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right) a}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{3 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{13 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b^{2}}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{3 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) a}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{13 b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b^{2}}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"-1/8/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7*b-1/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^7-1/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^5*a+19/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^5+3/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^5*b^2+5/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3*a-7/8/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^3-3/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^3*b^2-3/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/b/(a-b)*cos(d*x+c)*a-15/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)*cos(d*x+c)-1/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)/a*b*cos(d*x+c)+1/16/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/32/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b+3/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*a-13/64/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/16/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b^2-1/16/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/32/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b+3/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*a-13/64/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))+1/16/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b^2","B"
227,1,1153,236,0.519000," ","int(sin(d*x+c)^3/(a-b*sin(d*x+c)^4)^3,x)","-\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{64 d b \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos^{3}\left(d x +c \right)}{64 d a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos^{3}\left(d x +c \right)}{8 d \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{7 \cos \left(d x +c \right)}{64 d b \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}-\frac{5 \cos \left(d x +c \right)}{64 d b a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}+\frac{\cos \left(d x +c \right)}{32 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}-\frac{5 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{8 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b^{2}}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{64 d b \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\cos^{3}\left(d x +c \right)}{64 d a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{\cos^{3}\left(d x +c \right)}{8 d \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{7 \cos \left(d x +c \right)}{64 d b \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}-\frac{5 \cos \left(d x +c \right)}{64 d b a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}-\frac{\cos \left(d x +c \right)}{32 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}+\frac{5 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{8 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b^{2}}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}"," ",0,"-5/64/d/b/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-1/64/d/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-1/8/d/(a*b)^(1/2)/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+1/32/d*b/(a*b)^(1/2)/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-7/64/d/b/(a*b)^(1/2)/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)-5/64/d/b/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)+1/32/d/(a*b)^(1/2)/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)-5/64/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/64/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b-1/8/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))+1/32/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b^2-5/64/d/b/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-1/64/d/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+1/8/d/(a*b)^(1/2)/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-1/32/d*b/(a*b)^(1/2)/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+7/64/d/b/(a*b)^(1/2)/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)-5/64/d/b/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)-1/32/d/(a*b)^(1/2)/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)+5/64/d/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/64/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b-1/8/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/32/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b^2","B"
228,1,1281,261,0.635000," ","int(sin(d*x+c)/(a-b*sin(d*x+c)^4)^3,x)","-\frac{3 \left(\cos^{3}\left(d x +c \right)\right)}{16 d a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \,a^{2} \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{9 \left(\cos^{3}\left(d x +c \right)\right)}{64 d \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 b \left(\cos^{3}\left(d x +c \right)\right)}{64 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{11 \cos \left(d x +c \right)}{64 d b a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}+\frac{3 \cos \left(d x +c \right)}{32 d \,a^{2} \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}-\frac{5 \cos \left(d x +c \right)}{64 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)+\frac{\sqrt{a b}}{b}-1\right)^{2} \left(a -b \right)}-\frac{3 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{3 b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{32 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{21 b \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{27 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b^{2}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 b^{3} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{16 d \,a^{2} \sqrt{a b}\, \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{3 \left(\cos^{3}\left(d x +c \right)\right)}{16 d a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \,a^{2} \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \left(\cos^{3}\left(d x +c \right)\right)}{64 d \sqrt{a b}\, \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 b \left(\cos^{3}\left(d x +c \right)\right)}{64 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{11 \cos \left(d x +c \right)}{64 d b a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}+\frac{3 \cos \left(d x +c \right)}{32 d \,a^{2} \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}+\frac{5 \cos \left(d x +c \right)}{64 d \sqrt{a b}\, a \left(\cos^{2}\left(d x +c \right)-1-\frac{\sqrt{a b}}{b}\right)^{2} \left(a -b \right)}+\frac{3 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{32 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{21 b \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{27 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b^{2}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{3 b^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{16 d \,a^{2} \sqrt{a b}\, \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}"," ",0,"-3/16/d/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+3/32/d*b/a^2/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-9/64/d/(a*b)^(1/2)/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+3/64/d*b/(a*b)^(1/2)/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-11/64/d/b/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)+3/32/d/a^2/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)-5/64/d/(a*b)^(1/2)/a/(cos(d*x+c)^2+(a*b)^(1/2)/b-1)^2/(a-b)*cos(d*x+c)-3/16/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b+3/32/d*b^2/a^2/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-21/64/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))+27/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b^2-3/16/d*b^3/a^2/(a*b)^(1/2)/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-3/16/d/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+3/32/d*b/a^2/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3+9/64/d/(a*b)^(1/2)/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-3/64/d*b/(a*b)^(1/2)/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-11/64/d/b/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)+3/32/d/a^2/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)+5/64/d/(a*b)^(1/2)/a/(cos(d*x+c)^2-1-(a*b)^(1/2)/b)^2/(a-b)*cos(d*x+c)+3/16/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b-3/32/d*b^2/a^2/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-21/64/d/(a^2-2*a*b+b^2)*b/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+27/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b^2-3/16/d*b^3/a^2/(a*b)^(1/2)/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))","B"
229,1,1139,487,0.612000," ","int(csc(d*x+c)/(a-b*sin(d*x+c)^4)^3,x)","\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d \,a^{3}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d \,a^{3}}-\frac{13 b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}+\frac{7 b^{3} \left(\cos^{7}\left(d x +c \right)\right)}{32 d \,a^{2} \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{53 \left(\cos^{5}\left(d x +c \right)\right) b^{2}}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{29 b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{32 d \,a^{2} \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{17 b \left(\cos^{3}\left(d x +c \right)\right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{39 \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{16 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}+\frac{37 b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{32 d \,a^{2} \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{35 b \cos \left(d x +c \right)}{32 d \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right) a}+\frac{15 b^{2} \cos \left(d x +c \right)}{32 d \,a^{2} \left(b \left(\cos^{4}\left(d x +c \right)\right)-2 b \left(\cos^{2}\left(d x +c \right)\right)-a +b \right)^{2} \left(a -b \right)}+\frac{45 \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{71 b^{2} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{b^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{2 d \,a^{3} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right) b^{2}}{4 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+b \right) b}}+\frac{5 b^{3} \arctanh \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}+b \right) b}}\right)}{32 d \,a^{2} \sqrt{a b}\, \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}+b \right) b}}-\frac{45 \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{71 b^{2} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{b^{3} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{2 d \,a^{3} \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}-\frac{\arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right) b^{2}}{4 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-b \right) b}}+\frac{5 b^{3} \arctan \left(\frac{\cos \left(d x +c \right) b}{\sqrt{\left(\sqrt{a b}-b \right) b}}\right)}{32 d \,a^{2} \sqrt{a b}\, \left(a^{2}-2 a b +b^{2}\right) \sqrt{\left(\sqrt{a b}-b \right) b}}"," ",0,"1/2/d/a^3*ln(cos(d*x+c)-1)-1/2/d/a^3*ln(1+cos(d*x+c))-13/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^7+7/32/d/a^2*b^3/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^7+53/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^5*b^2-29/32/d/a^2*b^3/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^5+17/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2*b/(a^2-2*a*b+b^2)*cos(d*x+c)^3-39/16/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/a/(a^2-2*a*b+b^2)*cos(d*x+c)^3*b^2+37/32/d/a^2*b^3/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a^2-2*a*b+b^2)*cos(d*x+c)^3-35/32/d/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)/a*b*cos(d*x+c)+15/32/d/a^2*b^2/(b*cos(d*x+c)^4-2*b*cos(d*x+c)^2-a+b)^2/(a-b)*cos(d*x+c)+45/64/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b-71/64/d*b^2/a^2/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))+1/2/d/a^3*b^3/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-1/4/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))*b^2+5/32/d*b^3/a^2/(a*b)^(1/2)/(a^2-2*a*b+b^2)/(((a*b)^(1/2)+b)*b)^(1/2)*arctanh(cos(d*x+c)*b/(((a*b)^(1/2)+b)*b)^(1/2))-45/64/d/a/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b+71/64/d*b^2/a^2/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/2/d/a^3*b^3/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))-1/4/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))*b^2+5/32/d*b^3/a^2/(a*b)^(1/2)/(a^2-2*a*b+b^2)/(((a*b)^(1/2)-b)*b)^(1/2)*arctan(cos(d*x+c)*b/(((a*b)^(1/2)-b)*b)^(1/2))","B"
230,1,1634,263,0.377000," ","int(sin(d*x+c)^8/(a-b*sin(d*x+c)^4)^3,x)","-\frac{\left(\tan^{7}\left(d x +c \right)\right) a}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) b}-\frac{19 \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right)}-\frac{3 \left(\tan^{5}\left(d x +c \right)\right) a^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{15 \left(\tan^{5}\left(d x +c \right)\right) a}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 b \left(\tan^{5}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{21 a \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{2} \tan \left(d x +c \right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{5 a \tan \left(d x +c \right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{64 d b \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{7 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{3}}{32 d b \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{11 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{64 d b \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{7 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{3}}{32 d b \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{11 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{13 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{5 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{13 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/b*tan(d*x+c)^7*a-19/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)*tan(d*x+c)^7-3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a^2-15/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a+9/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5-3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)^3-21/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)^3-1/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)-5/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)-1/64/d/b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+7/32/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/32/d/b/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^3-11/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+1/16/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/64/d/b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+7/32/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/32/d/b/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^3+11/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2-1/16/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-13/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+5/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-13/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-5/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
231,1,1909,291,0.368000," ","int(sin(d*x+c)^6/(a-b*sin(d*x+c)^4)^3,x)","-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{3}}{16 d b \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{7 b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{3}}{16 d b \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{7 b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{15 \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right)}+\frac{19 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{32 d b \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{a^{2} \tan \left(d x +c \right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 b \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) a}+\frac{3 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{32 d b \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{19 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{7 \left(\tan^{5}\left(d x +c \right)\right) a}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{5 b \left(\tan^{5}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{19 a \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{a \tan \left(d x +c \right)}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(\tan^{7}\left(d x +c \right)\right) a}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) b}+\frac{b \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 \left(\tan^{5}\left(d x +c \right)\right) a^{2}}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} b \left(a^{2}-2 a b +b^{2}\right)}+\frac{19 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{5 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{19 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}"," ",0,"-1/16/d/b/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^3-7/32/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/16/d/b/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^3+7/32/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-15/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)*tan(d*x+c)^7+19/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+1/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/32/d/b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2-7/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a-1/32/d/b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2-19/64/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2-3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/a*b*tan(d*x+c)^7+1/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^3+3/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+5/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5-19/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)^3-1/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)-1/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/b*tan(d*x+c)^7*a-3/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a^2-3/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)^3-1/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a^2/b/(a^2-2*a*b+b^2)*tan(d*x+c)+19/64/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+19/64/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-5/16/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-5/16/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
232,1,1624,261,0.328000," ","int(sin(d*x+c)^4/(a-b*sin(d*x+c)^4)^3,x)","-\frac{17 \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right)}-\frac{3 b \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) a}-\frac{43 \left(\tan^{5}\left(d x +c \right)\right) a}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 b \left(\tan^{5}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{35 a \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{11 b \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{9 a \tan \left(d x +c \right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 \tan \left(d x +c \right) b}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{15 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{9 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{15 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{9 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-17/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)*tan(d*x+c)^7-3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/a*b*tan(d*x+c)^7-43/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a+9/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5+1/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^5*b^2-35/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)^3+11/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^3-9/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)+3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)*b+15/64/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-9/32/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-3/32/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2-3/64/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/16/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+15/64/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-9/32/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/32/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+3/64/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-3/16/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-3/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3+3/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3","B"
233,1,1906,295,0.468000," ","int(sin(d*x+c)^2/(a-b*sin(d*x+c)^4)^3,x)","\frac{\tan \left(d x +c \right) b}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{13 b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{13 b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 \left(\tan^{7}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right)}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{64 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{15 b \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) a}-\frac{5 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{5 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{16 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{5 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{16 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{15 \left(\tan^{5}\left(d x +c \right)\right) a}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 b \left(\tan^{5}\left(d x +c \right)\right)}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{15 a \left(\tan^{3}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}-\frac{5 a \tan \left(d x +c \right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 \left(\tan^{5}\left(d x +c \right)\right) b^{2}}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{3 b \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{11 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{37 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{11 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{37 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{5 \left(\tan^{7}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a^{2} \left(a -b \right)}"," ",0,"1/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3-13/64/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+13/64/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/64/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3-5/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)*tan(d*x+c)^7+3/16/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2-1/32/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-15/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)^5*a-3/16/d/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+1/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)*b-15/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/a*b*tan(d*x+c)^7+9/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^3*b^2-3/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^3+5/16/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+5/16/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-5/64/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3-5/64/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3+1/32/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+9/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^5*b^2+5/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a^2/(a-b)*tan(d*x+c)^7*b^2-3/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5-15/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)^3-5/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*a/(a^2-2*a*b+b^2)*tan(d*x+c)+11/32/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+11/32/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-37/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-37/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
234,1,1803,271,0.416000," ","int(1/(a-b*sin(d*x+c)^4)^3,x)","-\frac{17 \tan \left(d x +c \right) b}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{23 b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{23 b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{19 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{19 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{16 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{21 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{4}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{21 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{4}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{33 b \left(\tan^{7}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) a}-\frac{13 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{23 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{23 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{13 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{101 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{101 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{83 b \left(\tan^{5}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{43 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}+\frac{33 \left(\tan^{5}\left(d x +c \right)\right) b^{2}}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{67 b \left(\tan^{3}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{65 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{65 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{13 \left(\tan^{7}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a^{2} \left(a -b \right)}-\frac{7 b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{11 b^{2} \tan \left(d x +c \right)}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}"," ",0,"-19/16/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3+23/32/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-23/32/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+19/16/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3+101/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+21/64/d/a^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^4-21/64/d/a^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^4-17/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)*b-33/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/a*b*tan(d*x+c)^7+43/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^3*b^2-67/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^3+23/32/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+23/32/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-13/64/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3-13/64/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3-101/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+33/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^5*b^2+13/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a^2/(a-b)*tan(d*x+c)^7*b^2-83/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5-7/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a^2*b^3/(a^2-2*a*b+b^2)*tan(d*x+c)^5+1/2/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/(a^2-2*a*b+b^2)*a/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-65/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-65/64/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+11/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)","B"
235,1,1959,305,0.612000," ","int(csc(d*x+c)^2/(a-b*sin(d*x+c)^4)^3,x)","-\frac{9 \tan \left(d x +c \right) b}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{15 b a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{15 b a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{45 b^{4} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \,a^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{57 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{57 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{32 d a \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{33 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{4}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{33 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{4}}{64 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{9 b \left(\tan^{7}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right) a}+\frac{39 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{3}}{16 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{189 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{189 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d a \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{39 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{3}}{16 d \,a^{2} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{141 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{141 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{27 b \left(\tan^{5}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{13 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{45 b^{4} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{64 d \,a^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{13 b^{3} \left(\tan^{7}\left(d x +c \right)\right)}{32 d \,a^{3} \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a -b \right)}+\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{2}}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}-\frac{27 b \left(\tan^{3}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{39 b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{39 b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{32 d \left(a^{2}-2 a b +b^{2}\right) \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{15 \left(\tan^{7}\left(d x +c \right)\right) b^{2}}{32 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a^{2} \left(a -b \right)}+\frac{17 b^{3} \left(\tan^{3}\left(d x +c \right)\right)}{32 d \,a^{2} \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{13 b^{3} \left(\tan^{5}\left(d x +c \right)\right)}{16 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 b^{2} \tan \left(d x +c \right)}{8 d \left(\left(\tan^{4}\left(d x +c \right)\right) a -\left(\tan^{4}\left(d x +c \right)\right) b +2 a \left(\tan^{2}\left(d x +c \right)\right)+a \right)^{2} a \left(a^{2}-2 a b +b^{2}\right)}"," ",0,"-57/32/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3+15/16/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-15/16/d*b/(a^2-2*a*b+b^2)*a/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+57/32/d/a/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3+141/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+33/64/d/a^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^4-33/64/d/a^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^4-9/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)*b-9/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)/a*b*tan(d*x+c)^7+13/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^3*b^2-27/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^3-189/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-189/64/d/a*b^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+39/16/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^3+39/16/d/a^2/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^3-1/d/a^3/tan(d*x+c)-141/64/d*b^2/(a^2-2*a*b+b^2)/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-45/64/d*b^4/a^3/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-45/64/d*b^4/a^3/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)^5*b^2+17/32/d*b^3/a^2/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a^2-2*a*b+b^2)*tan(d*x+c)^3+13/32/d*b^3/a^3/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/(a-b)*tan(d*x+c)^7-15/32/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a^2/(a-b)*tan(d*x+c)^7*b^2-27/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b/(a^2-2*a*b+b^2)*tan(d*x+c)^5+13/16/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2/a^2*b^3/(a^2-2*a*b+b^2)*tan(d*x+c)^5+39/32/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+39/32/d*b/(a^2-2*a*b+b^2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/8/d/(tan(d*x+c)^4*a-tan(d*x+c)^4*b+2*a*tan(d*x+c)^2+a)^2*b^2/a/(a^2-2*a*b+b^2)*tan(d*x+c)","B"
236,1,18,17,0.170000," ","int(1/(1-sin(x)^4),x)","\frac{\arctan \left(\sqrt{2}\, \tan \left(x \right)\right) \sqrt{2}}{4}+\frac{\tan \left(x \right)}{2}"," ",0,"1/4*arctan(2^(1/2)*tan(x))*2^(1/2)+1/2*tan(x)","A"
237,1,1677,343,0.414000," ","int(1/(a+b*sin(x)^4),x)","\frac{\ln \left(-\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}-\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{8 b \sqrt{a +b}}+\frac{\ln \left(-\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}-\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{8 a b \sqrt{a +b}}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}-\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{8 a^{\frac{3}{2}} b}-\frac{\ln \left(-\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}-\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{8 \sqrt{a}\, b}-\frac{\arctan \left(\frac{-2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right)}{\sqrt{a}\, \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}-\frac{\arctan \left(\frac{-2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{4 b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}\, \sqrt{a +b}}-\frac{\arctan \left(\frac{-2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{4 a b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}\, \sqrt{a +b}}+\frac{\arctan \left(\frac{-2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{4 a^{\frac{3}{2}} b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}+\frac{\arctan \left(\frac{-2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{4 \sqrt{a}\, b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}-\frac{\ln \left(\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}+\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{8 b \sqrt{a +b}}-\frac{\ln \left(\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}+\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{8 a b \sqrt{a +b}}+\frac{\ln \left(\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}+\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{8 a^{\frac{3}{2}} b}+\frac{\ln \left(\sqrt{a +b}\, \left(\tan^{2}\left(x \right)\right)+\tan \left(x \right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}+\sqrt{a}\right) \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{8 \sqrt{a}\, b}+\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right)}{\sqrt{a}\, \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}+\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{4 b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}\, \sqrt{a +b}}+\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{4 a b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}\, \sqrt{a +b}}-\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}\, \sqrt{a^{2}+a b}}{4 a^{\frac{3}{2}} b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}-\frac{\arctan \left(\frac{2 \sqrt{a +b}\, \tan \left(x \right)+\sqrt{2 \sqrt{a \left(a +b \right)}-2 a}}{\sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}\right) \sqrt{2 \sqrt{a \left(a +b \right)}-2 a}\, \sqrt{2 \sqrt{a^{2}+a b}-2 a}}{4 \sqrt{a}\, b \sqrt{4 \sqrt{a}\, \sqrt{a +b}-2 \sqrt{a \left(a +b \right)}+2 a}}"," ",0,"1/8/b/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/a/b/(a+b)^(1/2)*ln(-(a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8/a^(3/2)/b*ln(-(a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8/a^(1/2)/b*ln(-(a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/a^(1/2)/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))-1/4/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)/(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/a/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)/(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(3/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(1/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8/b/(a+b)^(1/2)*ln((a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8/a/b/(a+b)^(1/2)*ln((a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/8/a^(3/2)/b*ln((a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/8/a^(1/2)/b*ln((a+b)^(1/2)*tan(x)^2+tan(x)*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+a^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/a^(1/2)/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))+1/4/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)/(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)/(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4/a^(3/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4/a^(1/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*(a+b)^(1/2)*tan(x)+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)","B"
238,1,239,227,0.454000," ","int(1/(1+sin(x)^4),x)","-\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(-\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \tan \left(x \right)+2 \left(\tan^{2}\left(x \right)\right)+\sqrt{2}\right)}{16}+\frac{\arctan \left(\frac{-\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}+4 \tan \left(x \right)}{2 \sqrt{1+\sqrt{2}}}\right) \sqrt{2}}{4 \sqrt{1+\sqrt{2}}}+\frac{\arctan \left(\frac{-\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}+4 \tan \left(x \right)}{2 \sqrt{1+\sqrt{2}}}\right)}{4 \sqrt{1+\sqrt{2}}}+\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\sqrt{2}+2 \left(\tan^{2}\left(x \right)\right)+\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \tan \left(x \right)\right)}{16}+\frac{\arctan \left(\frac{4 \tan \left(x \right)+\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right) \sqrt{2}}{4 \sqrt{1+\sqrt{2}}}+\frac{\arctan \left(\frac{4 \tan \left(x \right)+\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right)}{4 \sqrt{1+\sqrt{2}}}"," ",0,"-1/16*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(-(-2+2*2^(1/2))^(1/2)*2^(1/2)*tan(x)+2*tan(x)^2+2^(1/2))+1/4/(1+2^(1/2))^(1/2)*arctan(1/2*(-2^(1/2)*(-2+2*2^(1/2))^(1/2)+4*tan(x))/(1+2^(1/2))^(1/2))*2^(1/2)+1/4/(1+2^(1/2))^(1/2)*arctan(1/2*(-2^(1/2)*(-2+2*2^(1/2))^(1/2)+4*tan(x))/(1+2^(1/2))^(1/2))+1/16*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(2^(1/2)+2*tan(x)^2+(-2+2*2^(1/2))^(1/2)*2^(1/2)*tan(x))+1/4/(1+2^(1/2))^(1/2)*arctan(1/2*(4*tan(x)+2^(1/2)*(-2+2*2^(1/2))^(1/2))/(1+2^(1/2))^(1/2))*2^(1/2)+1/4/(1+2^(1/2))^(1/2)*arctan(1/2*(4*tan(x)+2^(1/2)*(-2+2*2^(1/2))^(1/2))/(1+2^(1/2))^(1/2))","A"
239,1,439,497,3.672000," ","int(sin(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\frac{4 \cos \left(d x +c \right) \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}{3}+\frac{4 \left(\frac{2 a}{3}+\frac{2 b}{3}\right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)}{\sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}+\frac{16 b \left(a +b \right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \left(\EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)-\EllipticE \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)\right)}{3 \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}\, \left(-2 b +2 i \sqrt{a}\, \sqrt{b}\right)}}{4 d}"," ",0,"-1/4/d*(4/3*cos(d*x+c)*(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)+4*(2/3*a+2/3*b)/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)*EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))+16/3*b*(a+b)/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)/(-2*b+2*I*a^(1/2)*b^(1/2))*(EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-EllipticE(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))))","C"
240,0,0,531,1.539000," ","int(csc(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x)","\int \csc \left(d x +c \right) \sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}\, dx"," ",0,"int(csc(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x)","F"
241,1,837,504,1.395000," ","int(sin(d*x+c)^5/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)}{d \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}-\frac{4 \left(a +b \right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \left(\EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)-\EllipticE \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)\right)}{d \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}\, \left(-2 b +2 i \sqrt{a}\, \sqrt{b}\right)}-\frac{4 \left(\frac{\cos \left(d x +c \right) \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}{12 b}-\frac{\left(a +b \right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)}{12 b \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}-\frac{2 \left(a +b \right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \left(\EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)-\EllipticE \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)\right)}{3 \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}\, \left(-2 b +2 i \sqrt{a}\, \sqrt{b}\right)}\right)}{d}"," ",0,"-1/d/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)*EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-4/d*(a+b)/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)/(-2*b+2*I*a^(1/2)*b^(1/2))*(EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-EllipticE(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2)))-4/d*(1/12/b*cos(d*x+c)*(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)-1/12*(a+b)/b/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)*EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-2/3*(a+b)/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)/(-2*b+2*I*a^(1/2)*b^(1/2))*(EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-EllipticE(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))))","C"
242,1,398,459,1.332000," ","int(sin(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)}{d \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}-\frac{2 \left(a +b \right) \sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \left(\EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)-\EllipticE \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)\right)}{d \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}\, \left(-2 b +2 i \sqrt{a}\, \sqrt{b}\right)}"," ",0,"-1/d/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)*EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-2/d*(a+b)/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)/(-2*b+2*I*a^(1/2)*b^(1/2))*(EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))-EllipticE(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2)))","C"
243,1,163,191,0.857000," ","int(sin(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{1-\frac{\left(i \sqrt{a}\, \sqrt{b}+b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \sqrt{1+\frac{\left(i \sqrt{a}\, \sqrt{b}-b \right) \left(\cos^{2}\left(d x +c \right)\right)}{a +b}}\, \EllipticF \left(\cos \left(d x +c \right) \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}, \sqrt{-1-\frac{2 \left(i \sqrt{a}\, \sqrt{b}-b \right)}{a +b}}\right)}{d \sqrt{\frac{i \sqrt{a}\, \sqrt{b}+b}{a +b}}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}"," ",0,"-1/d/((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2)*(1-(I*a^(1/2)*b^(1/2)+b)/(a+b)*cos(d*x+c)^2)^(1/2)*(1+(I*a^(1/2)*b^(1/2)-b)/(a+b)*cos(d*x+c)^2)^(1/2)/(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2)*EllipticF(cos(d*x+c)*((I*a^(1/2)*b^(1/2)+b)/(a+b))^(1/2),(-1-2*(I*a^(1/2)*b^(1/2)-b)/(a+b))^(1/2))","C"
244,0,0,483,1.543000," ","int(csc(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\csc \left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(csc(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
245,0,0,794,1.621000," ","int(csc(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\csc^{3}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(csc(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
246,1,881,507,7.356000," ","int(sin(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{\left(4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)\right) \left(\sin^{2}\left(2 d x +2 c \right)\right)}\, \sqrt{-a b}\, \sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \left(\cos \left(2 d x +2 c \right)+1\right)^{2} \sqrt{\frac{-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \sqrt{\frac{b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}, \sqrt{\frac{b +\sqrt{-a b}}{-b +\sqrt{-a b}}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}, \frac{\sqrt{-a b}}{-b +\sqrt{-a b}}, \sqrt{\frac{b +\sqrt{-a b}}{-b +\sqrt{-a b}}}\right)\right)}{2 \left(-b +\sqrt{-a b}\right) \sqrt{\frac{\left(-1+\cos \left(2 d x +2 c \right)\right) \left(\cos \left(2 d x +2 c \right)+1\right) \left(-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b \right) \left(b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b \right)}{b}}\, \sin \left(2 d x +2 c \right) \sqrt{4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)}\, d}-\frac{\sqrt{\left(4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)\right) \left(\sin^{2}\left(2 d x +2 c \right)\right)}\, \sqrt{-a b}\, \sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \left(\cos \left(2 d x +2 c \right)+1\right)^{2} \sqrt{\frac{-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \sqrt{\frac{b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}, \sqrt{\frac{b +\sqrt{-a b}}{-b +\sqrt{-a b}}}\right)}{2 \left(-b +\sqrt{-a b}\right) \sqrt{\frac{\left(-1+\cos \left(2 d x +2 c \right)\right) \left(\cos \left(2 d x +2 c \right)+1\right) \left(-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b \right) \left(b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b \right)}{b}}\, \sin \left(2 d x +2 c \right) \sqrt{4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)}\, d}"," ",0,"-1/2*((4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))*sin(2*d*x+2*c)^2)^(1/2)*(-a*b)^(1/2)*((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*(cos(2*d*x+2*c)+1)^2*((-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*((b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*(EllipticF(((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2),((b+(-a*b)^(1/2))/(-b+(-a*b)^(1/2)))^(1/2))-2*EllipticPi(((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2),(-a*b)^(1/2)/(-b+(-a*b)^(1/2)),((b+(-a*b)^(1/2))/(-b+(-a*b)^(1/2)))^(1/2)))/(-b+(-a*b)^(1/2))/(1/b*(-1+cos(2*d*x+2*c))*(cos(2*d*x+2*c)+1)*(-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)*(b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b))^(1/2)/sin(2*d*x+2*c)/(4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))^(1/2)/d-1/2*((4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))*sin(2*d*x+2*c)^2)^(1/2)*(-a*b)^(1/2)*((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*(cos(2*d*x+2*c)+1)^2*((-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*((b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*EllipticF(((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2),((b+(-a*b)^(1/2))/(-b+(-a*b)^(1/2)))^(1/2))/(-b+(-a*b)^(1/2))/(1/b*(-1+cos(2*d*x+2*c))*(cos(2*d*x+2*c)+1)*(-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)*(b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b))^(1/2)/sin(2*d*x+2*c)/(4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))^(1/2)/d","A"
247,1,396,181,2.941000," ","int(1/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{\left(4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)\right) \left(\sin^{2}\left(2 d x +2 c \right)\right)}\, \sqrt{-a b}\, \sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \left(\cos \left(2 d x +2 c \right)+1\right)^{2} \sqrt{\frac{-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \sqrt{\frac{b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}, \sqrt{\frac{b +\sqrt{-a b}}{-b +\sqrt{-a b}}}\right)}{\left(-b +\sqrt{-a b}\right) \sqrt{\frac{\left(-1+\cos \left(2 d x +2 c \right)\right) \left(\cos \left(2 d x +2 c \right)+1\right) \left(-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b \right) \left(b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b \right)}{b}}\, \sin \left(2 d x +2 c \right) \sqrt{4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)}\, d}"," ",0,"-((4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))*sin(2*d*x+2*c)^2)^(1/2)*(-a*b)^(1/2)*((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*(cos(2*d*x+2*c)+1)^2*((-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*((b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*EllipticF(((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2),((b+(-a*b)^(1/2))/(-b+(-a*b)^(1/2)))^(1/2))/(-b+(-a*b)^(1/2))/(1/b*(-1+cos(2*d*x+2*c))*(cos(2*d*x+2*c)+1)*(-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)*(b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b))^(1/2)/sin(2*d*x+2*c)/(4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))^(1/2)/d","B"
248,0,0,519,1.501000," ","int(csc(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\csc^{2}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(csc(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
249,1,109,246,0.260000," ","int(1/(a+b*sin(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{10}+5 a \,\textit{\_Z}^{8}+10 a \,\textit{\_Z}^{6}+32 b \,\textit{\_Z}^{5}+10 a \,\textit{\_Z}^{4}+5 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{8}+4 \textit{\_R}^{6}+6 \textit{\_R}^{4}+4 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a +4 \textit{\_R}^{7} a +6 \textit{\_R}^{5} a +16 \textit{\_R}^{4} b +4 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{5}"," ",0,"1/5*sum((_R^8+4*_R^6+6*_R^4+4*_R^2+1)/(_R^9*a+4*_R^7*a+6*_R^5*a+16*_R^4*b+4*_R^3*a+_R*a)*ln(tan(1/2*x)-_R),_R=RootOf(_Z^10*a+5*_Z^8*a+10*_Z^6*a+32*_Z^5*b+10*_Z^4*a+5*_Z^2*a+a))","C"
250,1,68,109,1.542000," ","int(1/(a+b*sin(x)^6),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +\textit{\_R}^{5} b +2 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{6}"," ",0,"1/6*sum((_R^4+2*_R^2+1)/(_R^5*a+_R^5*b+2*_R^3*a+_R*a)*ln(tan(x)-_R),_R=RootOf((a+b)*_Z^6+3*a*_Z^4+3*a*_Z^2+a))","C"
251,1,85,169,0.262000," ","int(1/(a+b*sin(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{8}+4 a \,\textit{\_Z}^{6}+6 a \,\textit{\_Z}^{4}+4 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{7} a +\textit{\_R}^{7} b +3 \textit{\_R}^{5} a +3 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{8}"," ",0,"1/8*sum((_R^6+3*_R^4+3*_R^2+1)/(_R^7*a+_R^7*b+3*_R^5*a+3*_R^3*a+_R*a)*ln(tan(x)-_R),_R=RootOf((a+b)*_Z^8+4*a*_Z^6+6*a*_Z^4+4*a*_Z^2+a))","C"
252,1,109,245,0.246000," ","int(1/(a-b*sin(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{10}+5 a \,\textit{\_Z}^{8}+10 a \,\textit{\_Z}^{6}-32 b \,\textit{\_Z}^{5}+10 a \,\textit{\_Z}^{4}+5 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{8}+4 \textit{\_R}^{6}+6 \textit{\_R}^{4}+4 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a +4 \textit{\_R}^{7} a +6 \textit{\_R}^{5} a -16 \textit{\_R}^{4} b +4 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{5}"," ",0,"1/5*sum((_R^8+4*_R^6+6*_R^4+4*_R^2+1)/(_R^9*a+4*_R^7*a+6*_R^5*a-16*_R^4*b+4*_R^3*a+_R*a)*ln(tan(1/2*x)-_R),_R=RootOf(_Z^10*a+5*_Z^8*a+10*_Z^6*a-32*_Z^5*b+10*_Z^4*a+5*_Z^2*a+a))","C"
253,1,71,113,1.415000," ","int(1/(a-b*sin(x)^6),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{5} a -\textit{\_R}^{5} b +2 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{6}"," ",0,"1/6*sum((_R^4+2*_R^2+1)/(_R^5*a-_R^5*b+2*_R^3*a+_R*a)*ln(tan(x)-_R),_R=RootOf((a-b)*_Z^6+3*a*_Z^4+3*a*_Z^2+a))","C"
254,1,88,137,0.263000," ","int(1/(a-b*sin(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{8}+4 a \,\textit{\_Z}^{6}+6 a \,\textit{\_Z}^{4}+4 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{7} a -\textit{\_R}^{7} b +3 \textit{\_R}^{5} a +3 \textit{\_R}^{3} a +\textit{\_R} a}\right)}{8}"," ",0,"1/8*sum((_R^6+3*_R^4+3*_R^2+1)/(_R^7*a-_R^7*b+3*_R^5*a+3*_R^3*a+_R*a)*ln(tan(x)-_R),_R=RootOf((a-b)*_Z^8+4*a*_Z^6+6*a*_Z^4+4*a*_Z^2+a))","C"
255,1,133,133,0.220000," ","int(1/(1+sin(x)^5),x)","\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}-2 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-14 \textit{\_Z}^{5}+30 \textit{\_Z}^{4}-14 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{6}-3 \textit{\_R}^{5}+10 \textit{\_R}^{4}-10 \textit{\_R}^{3}+10 \textit{\_R}^{2}-3 \textit{\_R} +2\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{4 \textit{\_R}^{7}-7 \textit{\_R}^{6}+24 \textit{\_R}^{5}-35 \textit{\_R}^{4}+60 \textit{\_R}^{3}-21 \textit{\_R}^{2}+8 \textit{\_R} -1}\right)}{5}-\frac{2}{5 \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"2/5*sum((2*_R^6-3*_R^5+10*_R^4-10*_R^3+10*_R^2-3*_R+2)/(4*_R^7-7*_R^6+24*_R^5-35*_R^4+60*_R^3-21*_R^2+8*_R-1)*ln(tan(1/2*x)-_R),_R=RootOf(_Z^8-2*_Z^7+8*_Z^6-14*_Z^5+30*_Z^4-14*_Z^3+8*_Z^2-2*_Z+1))-2/5/(tan(1/2*x)+1)","C"
256,1,72,73,0.179000," ","int(1/(1+sin(x)^6),x)","\frac{\arctan \left(\sqrt{2}\, \tan \left(x \right)\right) \sqrt{2}}{6}+\frac{\ln \left(\tan^{2}\left(x \right)+\tan \left(x \right)+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(1+2 \tan \left(x \right)\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(\tan^{2}\left(x \right)-\tan \left(x \right)+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \tan \left(x \right)-1\right) \sqrt{3}}{3}\right)}{6}"," ",0,"1/6*arctan(2^(1/2)*tan(x))*2^(1/2)+1/12*ln(tan(x)^2+tan(x)+1)+1/6*3^(1/2)*arctan(1/3*(1+2*tan(x))*3^(1/2))-1/12*ln(tan(x)^2-tan(x)+1)+1/6*3^(1/2)*arctan(1/3*(2*tan(x)-1)*3^(1/2))","A"
257,1,71,152,0.204000," ","int(1/(1+sin(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{8}+4 \textit{\_Z}^{6}+6 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+1\right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{2 \textit{\_R}^{7}+3 \textit{\_R}^{5}+3 \textit{\_R}^{3}+\textit{\_R}}\right)}{8}"," ",0,"1/8*sum((_R^6+3*_R^4+3*_R^2+1)/(2*_R^7+3*_R^5+3*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(2*_Z^8+4*_Z^6+6*_Z^4+4*_Z^2+1))","C"
258,1,133,129,0.214000," ","int(1/(1-sin(x)^5),x)","-\frac{2}{5 \left(\tan \left(\frac{x}{2}\right)-1\right)}+\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+2 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}+14 \textit{\_Z}^{5}+30 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)}{\sum}\frac{\left(2 \textit{\_R}^{6}+3 \textit{\_R}^{5}+10 \textit{\_R}^{4}+10 \textit{\_R}^{3}+10 \textit{\_R}^{2}+3 \textit{\_R} +2\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{4 \textit{\_R}^{7}+7 \textit{\_R}^{6}+24 \textit{\_R}^{5}+35 \textit{\_R}^{4}+60 \textit{\_R}^{3}+21 \textit{\_R}^{2}+8 \textit{\_R} +1}\right)}{5}"," ",0,"-2/5/(tan(1/2*x)-1)+2/5*sum((2*_R^6+3*_R^5+10*_R^4+10*_R^3+10*_R^2+3*_R+2)/(4*_R^7+7*_R^6+24*_R^5+35*_R^4+60*_R^3+21*_R^2+8*_R+1)*ln(tan(1/2*x)-_R),_R=RootOf(_Z^8+2*_Z^7+8*_Z^6+14*_Z^5+30*_Z^4+14*_Z^3+8*_Z^2+2*_Z+1))","C"
259,1,255,49,0.452000," ","int(1/(1-sin(x)^6),x)","\frac{\tan \left(x \right)}{3}+\frac{\sqrt{3}\, \sqrt{2 \sqrt{3}-3}\, \ln \left(\sqrt{3}+3 \left(\tan^{2}\left(x \right)\right)+\sqrt{2 \sqrt{3}-3}\, \sqrt{3}\, \tan \left(x \right)\right)}{36}+\frac{\arctan \left(\frac{6 \tan \left(x \right)+\sqrt{2 \sqrt{3}-3}\, \sqrt{3}}{\sqrt{6 \sqrt{3}+9}}\right) \sqrt{3}}{3 \sqrt{6 \sqrt{3}+9}}+\frac{\arctan \left(\frac{6 \tan \left(x \right)+\sqrt{2 \sqrt{3}-3}\, \sqrt{3}}{\sqrt{6 \sqrt{3}+9}}\right)}{2 \sqrt{6 \sqrt{3}+9}}-\frac{\sqrt{3}\, \sqrt{2 \sqrt{3}-3}\, \ln \left(-\sqrt{2 \sqrt{3}-3}\, \sqrt{3}\, \tan \left(x \right)+3 \left(\tan^{2}\left(x \right)\right)+\sqrt{3}\right)}{36}+\frac{\arctan \left(\frac{-\sqrt{2 \sqrt{3}-3}\, \sqrt{3}+6 \tan \left(x \right)}{\sqrt{6 \sqrt{3}+9}}\right) \sqrt{3}}{3 \sqrt{6 \sqrt{3}+9}}+\frac{\arctan \left(\frac{-\sqrt{2 \sqrt{3}-3}\, \sqrt{3}+6 \tan \left(x \right)}{\sqrt{6 \sqrt{3}+9}}\right)}{2 \sqrt{6 \sqrt{3}+9}}"," ",0,"1/3*tan(x)+1/36*3^(1/2)*(2*3^(1/2)-3)^(1/2)*ln(3^(1/2)+3*tan(x)^2+(2*3^(1/2)-3)^(1/2)*3^(1/2)*tan(x))+1/3/(6*3^(1/2)+9)^(1/2)*arctan((6*tan(x)+(2*3^(1/2)-3)^(1/2)*3^(1/2))/(6*3^(1/2)+9)^(1/2))*3^(1/2)+1/2/(6*3^(1/2)+9)^(1/2)*arctan((6*tan(x)+(2*3^(1/2)-3)^(1/2)*3^(1/2))/(6*3^(1/2)+9)^(1/2))-1/36*3^(1/2)*(2*3^(1/2)-3)^(1/2)*ln(-(2*3^(1/2)-3)^(1/2)*3^(1/2)*tan(x)+3*tan(x)^2+3^(1/2))+1/3/(6*3^(1/2)+9)^(1/2)*arctan((-(2*3^(1/2)-3)^(1/2)*3^(1/2)+6*tan(x))/(6*3^(1/2)+9)^(1/2))*3^(1/2)+1/2/(6*3^(1/2)+9)^(1/2)*arctan((-(2*3^(1/2)-3)^(1/2)*3^(1/2)+6*tan(x))/(6*3^(1/2)+9)^(1/2))","B"
260,1,255,65,0.221000," ","int(1/(1-sin(x)^8),x)","\frac{\tan \left(x \right)}{4}-\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(-\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \tan \left(x \right)+2 \left(\tan^{2}\left(x \right)\right)+\sqrt{2}\right)}{32}+\frac{\arctan \left(\frac{-\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}+4 \tan \left(x \right)}{2 \sqrt{1+\sqrt{2}}}\right) \sqrt{2}}{8 \sqrt{1+\sqrt{2}}}+\frac{\arctan \left(\frac{-\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}+4 \tan \left(x \right)}{2 \sqrt{1+\sqrt{2}}}\right)}{8 \sqrt{1+\sqrt{2}}}+\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\sqrt{2}+2 \left(\tan^{2}\left(x \right)\right)+\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \tan \left(x \right)\right)}{32}+\frac{\arctan \left(\frac{4 \tan \left(x \right)+\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right) \sqrt{2}}{8 \sqrt{1+\sqrt{2}}}+\frac{\arctan \left(\frac{4 \tan \left(x \right)+\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right)}{8 \sqrt{1+\sqrt{2}}}+\frac{\arctan \left(\sqrt{2}\, \tan \left(x \right)\right) \sqrt{2}}{8}"," ",0,"1/4*tan(x)-1/32*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(-(-2+2*2^(1/2))^(1/2)*2^(1/2)*tan(x)+2*tan(x)^2+2^(1/2))+1/8/(1+2^(1/2))^(1/2)*arctan(1/2*(-2^(1/2)*(-2+2*2^(1/2))^(1/2)+4*tan(x))/(1+2^(1/2))^(1/2))*2^(1/2)+1/8/(1+2^(1/2))^(1/2)*arctan(1/2*(-2^(1/2)*(-2+2*2^(1/2))^(1/2)+4*tan(x))/(1+2^(1/2))^(1/2))+1/32*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(2^(1/2)+2*tan(x)^2+(-2+2*2^(1/2))^(1/2)*2^(1/2)*tan(x))+1/8/(1+2^(1/2))^(1/2)*arctan(1/2*(4*tan(x)+2^(1/2)*(-2+2*2^(1/2))^(1/2))/(1+2^(1/2))^(1/2))*2^(1/2)+1/8/(1+2^(1/2))^(1/2)*arctan(1/2*(4*tan(x)+2^(1/2)*(-2+2*2^(1/2))^(1/2))/(1+2^(1/2))^(1/2))+1/8*arctan(2^(1/2)*tan(x))*2^(1/2)","B"
261,1,26,34,0.167000," ","int(cos(x)^9/(a-a*sin(x)^2),x)","\frac{-\frac{\left(\sin^{7}\left(x \right)\right)}{7}+\frac{3 \left(\sin^{5}\left(x \right)\right)}{5}-\left(\sin^{3}\left(x \right)\right)+\sin \left(x \right)}{a}"," ",0,"1/a*(-1/7*sin(x)^7+3/5*sin(x)^5-sin(x)^3+sin(x))","A"
262,1,20,25,0.151000," ","int(cos(x)^7/(a-a*sin(x)^2),x)","\frac{\frac{\left(\sin^{5}\left(x \right)\right)}{5}-\frac{2 \left(\sin^{3}\left(x \right)\right)}{3}+\sin \left(x \right)}{a}"," ",0,"1/a*(1/5*sin(x)^5-2/3*sin(x)^3+sin(x))","A"
263,1,14,16,0.149000," ","int(cos(x)^5/(a-a*sin(x)^2),x)","\frac{-\frac{\left(\sin^{3}\left(x \right)\right)}{3}+\sin \left(x \right)}{a}"," ",0,"1/a*(-1/3*sin(x)^3+sin(x))","A"
264,1,7,6,0.129000," ","int(cos(x)^3/(a-a*sin(x)^2),x)","\frac{\sin \left(x \right)}{a}"," ",0,"sin(x)/a","A"
265,1,8,7,0.104000," ","int(cos(x)/(a-a*sin(x)^2),x)","\frac{\arctanh \left(\sin \left(x \right)\right)}{a}"," ",0,"arctanh(sin(x))/a","A"
266,1,66,29,0.220000," ","int(sec(x)^3/(a-a*sin(x)^2),x)","\frac{1}{16 a \left(-1+\sin \left(x \right)\right)^{2}}-\frac{3}{16 a \left(-1+\sin \left(x \right)\right)}-\frac{3 \ln \left(-1+\sin \left(x \right)\right)}{16 a}-\frac{1}{16 a \left(1+\sin \left(x \right)\right)^{2}}-\frac{3}{16 a \left(1+\sin \left(x \right)\right)}+\frac{3 \ln \left(1+\sin \left(x \right)\right)}{16 a}"," ",0,"1/16/a/(-1+sin(x))^2-3/16/a/(-1+sin(x))-3/16/a*ln(-1+sin(x))-1/16/a/(1+sin(x))^2-3/16/a/(1+sin(x))+3/16/a*ln(1+sin(x))","B"
267,1,40,27,0.152000," ","int(cos(x)^6/(a-a*sin(x)^2),x)","\frac{\tan \left(x \right)}{4 a \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \tan \left(x \right)}{8 a \left(\tan^{2}\left(x \right)+1\right)}+\frac{3 \arctan \left(\tan \left(x \right)\right)}{8 a}"," ",0,"1/4/a*tan(x)/(tan(x)^2+1)^2+3/8/a*tan(x)/(tan(x)^2+1)+3/8/a*arctan(tan(x))","A"
268,1,25,16,0.160000," ","int(cos(x)^4/(a-a*sin(x)^2),x)","\frac{\tan \left(x \right)}{2 a \left(\tan^{2}\left(x \right)+1\right)}+\frac{\arctan \left(\tan \left(x \right)\right)}{2 a}"," ",0,"1/2/a*tan(x)/(tan(x)^2+1)+1/2/a*arctan(tan(x))","A"
269,1,8,5,0.194000," ","int(cos(x)^2/(a-a*sin(x)^2),x)","\frac{\arctan \left(\tan \left(x \right)\right)}{a}"," ",0,"1/a*arctan(tan(x))","C"
270,1,44,18,0.209000," ","int(sec(x)/(a-a*sin(x)^2),x)","-\frac{1}{4 a \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right)}{4 a}-\frac{1}{4 a \left(1+\sin \left(x \right)\right)}+\frac{\ln \left(1+\sin \left(x \right)\right)}{4 a}"," ",0,"-1/4/a/(-1+sin(x))-1/4/a*ln(-1+sin(x))-1/4/a/(1+sin(x))+1/4/a*ln(1+sin(x))","B"
271,1,14,16,0.207000," ","int(sec(x)^2/(a-a*sin(x)^2),x)","\frac{\frac{\left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)}{a}"," ",0,"1/a*(1/3*tan(x)^3+tan(x))","A"
272,1,20,25,0.212000," ","int(sec(x)^4/(a-a*sin(x)^2),x)","\frac{\frac{\left(\tan^{5}\left(x \right)\right)}{5}+\frac{2 \left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)}{a}"," ",0,"1/a*(1/5*tan(x)^5+2/3*tan(x)^3+tan(x))","A"
273,1,20,25,0.158000," ","int(cos(x)^9/(a-a*sin(x)^2)^2,x)","\frac{\frac{\left(\sin^{5}\left(x \right)\right)}{5}-\frac{2 \left(\sin^{3}\left(x \right)\right)}{3}+\sin \left(x \right)}{a^{2}}"," ",0,"1/a^2*(1/5*sin(x)^5-2/3*sin(x)^3+sin(x))","A"
274,1,14,16,0.143000," ","int(cos(x)^7/(a-a*sin(x)^2)^2,x)","\frac{-\frac{\left(\sin^{3}\left(x \right)\right)}{3}+\sin \left(x \right)}{a^{2}}"," ",0,"1/a^2*(-1/3*sin(x)^3+sin(x))","A"
275,1,7,6,0.143000," ","int(cos(x)^5/(a-a*sin(x)^2)^2,x)","\frac{\sin \left(x \right)}{a^{2}}"," ",0,"sin(x)/a^2","A"
276,1,8,7,0.185000," ","int(cos(x)^3/(a-a*sin(x)^2)^2,x)","\frac{\arctanh \left(\sin \left(x \right)\right)}{a^{2}}"," ",0,"arctanh(sin(x))/a^2","A"
277,1,44,18,0.120000," ","int(cos(x)/(a-a*sin(x)^2)^2,x)","-\frac{1}{4 a^{2} \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right)}{4 a^{2}}-\frac{1}{4 a^{2} \left(1+\sin \left(x \right)\right)}+\frac{\ln \left(1+\sin \left(x \right)\right)}{4 a^{2}}"," ",0,"-1/4/a^2/(-1+sin(x))-1/4/a^2*ln(-1+sin(x))-1/4/a^2/(1+sin(x))+1/4/a^2*ln(1+sin(x))","B"
278,1,66,29,0.197000," ","int(sec(x)/(a-a*sin(x)^2)^2,x)","\frac{1}{16 a^{2} \left(-1+\sin \left(x \right)\right)^{2}}-\frac{3}{16 a^{2} \left(-1+\sin \left(x \right)\right)}-\frac{3 \ln \left(-1+\sin \left(x \right)\right)}{16 a^{2}}-\frac{1}{16 a^{2} \left(1+\sin \left(x \right)\right)^{2}}-\frac{3}{16 a^{2} \left(1+\sin \left(x \right)\right)}+\frac{3 \ln \left(1+\sin \left(x \right)\right)}{16 a^{2}}"," ",0,"1/16/a^2/(-1+sin(x))^2-3/16/a^2/(-1+sin(x))-3/16/a^2*ln(-1+sin(x))-1/16/a^2/(1+sin(x))^2-3/16/a^2/(1+sin(x))+3/16/a^2*ln(1+sin(x))","B"
279,1,40,27,0.161000," ","int(cos(x)^8/(a-a*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{4 a^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \tan \left(x \right)}{8 a^{2} \left(\tan^{2}\left(x \right)+1\right)}+\frac{3 \arctan \left(\tan \left(x \right)\right)}{8 a^{2}}"," ",0,"1/4/a^2*tan(x)/(tan(x)^2+1)^2+3/8/a^2*tan(x)/(tan(x)^2+1)+3/8/a^2*arctan(tan(x))","A"
280,1,25,16,0.156000," ","int(cos(x)^6/(a-a*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{2 a^{2} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\arctan \left(\tan \left(x \right)\right)}{2 a^{2}}"," ",0,"1/2/a^2*tan(x)/(tan(x)^2+1)+1/2/a^2*arctan(tan(x))","A"
281,1,8,5,0.193000," ","int(cos(x)^4/(a-a*sin(x)^2)^2,x)","\frac{\arctan \left(\tan \left(x \right)\right)}{a^{2}}"," ",0,"1/a^2*arctan(tan(x))","C"
282,1,7,6,0.204000," ","int(cos(x)^2/(a-a*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{a^{2}}"," ",0,"tan(x)/a^2","A"
283,1,20,25,0.236000," ","int(sec(x)^2/(a-a*sin(x)^2)^2,x)","\frac{\frac{\left(\tan^{5}\left(x \right)\right)}{5}+\frac{2 \left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)}{a^{2}}"," ",0,"1/a^2*(1/5*tan(x)^5+2/3*tan(x)^3+tan(x))","A"
284,1,24,33,0.239000," ","int(sec(x)^4/(a-a*sin(x)^2)^2,x)","\frac{\frac{\left(\tan^{7}\left(x \right)\right)}{7}+\frac{3 \left(\tan^{5}\left(x \right)\right)}{5}+\tan^{3}\left(x \right)+\tan \left(x \right)}{a^{2}}"," ",0,"1/a^2*(1/7*tan(x)^7+3/5*tan(x)^5+tan(x)^3+tan(x))","A"
285,1,112,99,0.537000," ","int(cos(f*x+e)^6*(a+b*sin(f*x+e)^2),x)","\frac{b \left(-\frac{\sin \left(f x +e \right) \left(\cos^{7}\left(f x +e \right)\right)}{8}+\frac{\left(\cos^{5}\left(f x +e \right)+\frac{5 \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{15 \cos \left(f x +e \right)}{8}\right) \sin \left(f x +e \right)}{48}+\frac{5 f x}{128}+\frac{5 e}{128}\right)+a \left(\frac{\left(\cos^{5}\left(f x +e \right)+\frac{5 \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{15 \cos \left(f x +e \right)}{8}\right) \sin \left(f x +e \right)}{6}+\frac{5 f x}{16}+\frac{5 e}{16}\right)}{f}"," ",0,"1/f*(b*(-1/8*sin(f*x+e)*cos(f*x+e)^7+1/48*(cos(f*x+e)^5+5/4*cos(f*x+e)^3+15/8*cos(f*x+e))*sin(f*x+e)+5/128*f*x+5/128*e)+a*(1/6*(cos(f*x+e)^5+5/4*cos(f*x+e)^3+15/8*cos(f*x+e))*sin(f*x+e)+5/16*f*x+5/16*e))","A"
286,1,92,75,0.569000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2),x)","\frac{b \left(-\frac{\sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)}{6}+\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{24}+\frac{f x}{16}+\frac{e}{16}\right)+a \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(b*(-1/6*sin(f*x+e)*cos(f*x+e)^5+1/24*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+1/16*f*x+1/16*e)+a*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e))","A"
287,1,70,51,0.352000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2),x)","\frac{b \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)+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*(b*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)+a*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
288,1,32,26,0.073000," ","int(a+b*sin(f*x+e)^2,x)","a 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)}{f}"," ",0,"a*x+b/f*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)","A"
289,1,30,18,0.477000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2),x)","\frac{\tan \left(f x +e \right) a +b \left(\tan \left(f x +e \right)-f x -e \right)}{f}"," ",0,"1/f*(tan(f*x+e)*a+b*(tan(f*x+e)-f*x-e))","A"
290,1,46,28,0.465000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2),x)","\frac{-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)+\frac{b \left(\sin^{3}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)^{3}}}{f}"," ",0,"1/f*(-a*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)+1/3*b*sin(f*x+e)^3/cos(f*x+e)^3)","A"
291,1,76,46,0.536000," ","int(sec(f*x+e)^6*(a+b*sin(f*x+e)^2),x)","\frac{-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)+b \left(\frac{\sin^{3}\left(f x +e \right)}{5 \cos \left(f x +e \right)^{5}}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right)}{15 \cos \left(f x +e \right)^{3}}\right)}{f}"," ",0,"1/f*(-a*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e)+b*(1/5*sin(f*x+e)^3/cos(f*x+e)^5+2/15*sin(f*x+e)^3/cos(f*x+e)^3))","A"
292,1,104,66,0.504000," ","int(sec(f*x+e)^8*(a+b*sin(f*x+e)^2),x)","\frac{-a \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(f x +e \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(f x +e \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(f x +e \right)\right)}{35}\right) \tan \left(f x +e \right)+b \left(\frac{\sin^{3}\left(f x +e \right)}{7 \cos \left(f x +e \right)^{7}}+\frac{4 \left(\sin^{3}\left(f x +e \right)\right)}{35 \cos \left(f x +e \right)^{5}}+\frac{8 \left(\sin^{3}\left(f x +e \right)\right)}{105 \cos \left(f x +e \right)^{3}}\right)}{f}"," ",0,"1/f*(-a*(-16/35-1/7*sec(f*x+e)^6-6/35*sec(f*x+e)^4-8/35*sec(f*x+e)^2)*tan(f*x+e)+b*(1/7*sin(f*x+e)^3/cos(f*x+e)^7+4/35*sin(f*x+e)^3/cos(f*x+e)^5+8/105*sin(f*x+e)^3/cos(f*x+e)^3))","A"
293,1,167,146,0.508000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)\right) \left(\cos^{5}\left(f x +e \right)\right)}{8}-\frac{\sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)}{16}+\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{64}+\frac{3 f x}{128}+\frac{3 e}{128}\right)+2 a b \left(-\frac{\sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)}{6}+\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{24}+\frac{f x}{16}+\frac{e}{16}\right)+a^{2} \left(\frac{\left(\cos^{3}\left(f x +e \right)+\frac{3 \cos \left(f x +e \right)}{2}\right) \sin \left(f x +e \right)}{4}+\frac{3 f x}{8}+\frac{3 e}{8}\right)}{f}"," ",0,"1/f*(b^2*(-1/8*sin(f*x+e)^3*cos(f*x+e)^5-1/16*sin(f*x+e)*cos(f*x+e)^5+1/64*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/128*f*x+3/128*e)+2*a*b*(-1/6*sin(f*x+e)*cos(f*x+e)^5+1/24*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+1/16*f*x+1/16*e)+a^2*(1/4*(cos(f*x+e)^3+3/2*cos(f*x+e))*sin(f*x+e)+3/8*f*x+3/8*e))","A"
294,1,134,108,0.364000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^2,x)","\frac{b^{2} \left(-\frac{\left(\sin^{3}\left(f x +e \right)\right) \left(\cos^{3}\left(f x +e \right)\right)}{6}-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{8}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{16}+\frac{f x}{16}+\frac{e}{16}\right)+2 a b \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)+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*(-1/6*sin(f*x+e)^3*cos(f*x+e)^3-1/8*sin(f*x+e)*cos(f*x+e)^3+1/16*sin(f*x+e)*cos(f*x+e)+1/16*f*x+1/16*e)+2*a*b*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)+a^2*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
295,1,78,66,0.352000," ","int((a+b*sin(f*x+e)^2)^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)+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)+a^{2} \left(f x +e \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*a*b*(-1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e)+a^2*(f*x+e))","A"
296,1,87,47,0.625000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^2,x)","\frac{a^{2} \tan \left(f x +e \right)+2 a b \left(\tan \left(f x +e \right)-f x -e \right)+b^{2} \left(\frac{\sin^{5}\left(f x +e \right)}{\cos \left(f x +e \right)}+\left(\sin^{3}\left(f x +e \right)+\frac{3 \sin \left(f x +e \right)}{2}\right) \cos \left(f x +e \right)-\frac{3 f x}{2}-\frac{3 e}{2}\right)}{f}"," ",0,"1/f*(a^2*tan(f*x+e)+2*a*b*(tan(f*x+e)-f*x-e)+b^2*(sin(f*x+e)^5/cos(f*x+e)+(sin(f*x+e)^3+3/2*sin(f*x+e))*cos(f*x+e)-3/2*f*x-3/2*e))","A"
297,1,76,43,0.528000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(f x +e \right)\right)}{3}\right) \tan \left(f x +e \right)+\frac{2 a b \left(\sin^{3}\left(f x +e \right)\right)}{3 \cos \left(f x +e \right)^{3}}+b^{2} \left(\frac{\left(\tan^{3}\left(f x +e \right)\right)}{3}-\tan \left(f x +e \right)+f x +e \right)}{f}"," ",0,"1/f*(-a^2*(-2/3-1/3*sec(f*x+e)^2)*tan(f*x+e)+2/3*a*b*sin(f*x+e)^3/cos(f*x+e)^3+b^2*(1/3*tan(f*x+e)^3-tan(f*x+e)+f*x+e))","A"
298,1,101,49,0.602000," ","int(sec(f*x+e)^6*(a+b*sin(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(f x +e \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(f x +e \right)\right)}{15}\right) \tan \left(f x +e \right)+2 a b \left(\frac{\sin^{3}\left(f x +e \right)}{5 \cos \left(f x +e \right)^{5}}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right)}{15 \cos \left(f x +e \right)^{3}}\right)+\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)}{5 \cos \left(f x +e \right)^{5}}}{f}"," ",0,"1/f*(-a^2*(-8/15-1/5*sec(f*x+e)^4-4/15*sec(f*x+e)^2)*tan(f*x+e)+2*a*b*(1/5*sin(f*x+e)^3/cos(f*x+e)^5+2/15*sin(f*x+e)^3/cos(f*x+e)^3)+1/5*b^2*sin(f*x+e)^5/cos(f*x+e)^5)","B"
299,1,149,74,0.605000," ","int(sec(f*x+e)^8*(a+b*sin(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(f x +e \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(f x +e \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(f x +e \right)\right)}{35}\right) \tan \left(f x +e \right)+2 a b \left(\frac{\sin^{3}\left(f x +e \right)}{7 \cos \left(f x +e \right)^{7}}+\frac{4 \left(\sin^{3}\left(f x +e \right)\right)}{35 \cos \left(f x +e \right)^{5}}+\frac{8 \left(\sin^{3}\left(f x +e \right)\right)}{105 \cos \left(f x +e \right)^{3}}\right)+b^{2} \left(\frac{\sin^{5}\left(f x +e \right)}{7 \cos \left(f x +e \right)^{7}}+\frac{2 \left(\sin^{5}\left(f x +e \right)\right)}{35 \cos \left(f x +e \right)^{5}}\right)}{f}"," ",0,"1/f*(-a^2*(-16/35-1/7*sec(f*x+e)^6-6/35*sec(f*x+e)^4-8/35*sec(f*x+e)^2)*tan(f*x+e)+2*a*b*(1/7*sin(f*x+e)^3/cos(f*x+e)^7+4/35*sin(f*x+e)^3/cos(f*x+e)^5+8/105*sin(f*x+e)^3/cos(f*x+e)^3)+b^2*(1/7*sin(f*x+e)^5/cos(f*x+e)^7+2/35*sin(f*x+e)^5/cos(f*x+e)^5))","A"
300,1,195,98,0.610000," ","int(sec(f*x+e)^10*(a+b*sin(f*x+e)^2)^2,x)","\frac{-a^{2} \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(f x +e \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(f x +e \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(f x +e \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(f x +e \right)\right)}{315}\right) \tan \left(f x +e \right)+2 a b \left(\frac{\sin^{3}\left(f x +e \right)}{9 \cos \left(f x +e \right)^{9}}+\frac{2 \left(\sin^{3}\left(f x +e \right)\right)}{21 \cos \left(f x +e \right)^{7}}+\frac{8 \left(\sin^{3}\left(f x +e \right)\right)}{105 \cos \left(f x +e \right)^{5}}+\frac{16 \left(\sin^{3}\left(f x +e \right)\right)}{315 \cos \left(f x +e \right)^{3}}\right)+b^{2} \left(\frac{\sin^{5}\left(f x +e \right)}{9 \cos \left(f x +e \right)^{9}}+\frac{4 \left(\sin^{5}\left(f x +e \right)\right)}{63 \cos \left(f x +e \right)^{7}}+\frac{8 \left(\sin^{5}\left(f x +e \right)\right)}{315 \cos \left(f x +e \right)^{5}}\right)}{f}"," ",0,"1/f*(-a^2*(-128/315-1/9*sec(f*x+e)^8-8/63*sec(f*x+e)^6-16/105*sec(f*x+e)^4-64/315*sec(f*x+e)^2)*tan(f*x+e)+2*a*b*(1/9*sin(f*x+e)^3/cos(f*x+e)^9+2/21*sin(f*x+e)^3/cos(f*x+e)^7+8/105*sin(f*x+e)^3/cos(f*x+e)^5+16/315*sin(f*x+e)^3/cos(f*x+e)^3)+b^2*(1/9*sin(f*x+e)^5/cos(f*x+e)^9+4/63*sin(f*x+e)^5/cos(f*x+e)^7+8/315*sin(f*x+e)^5/cos(f*x+e)^5))","A"
301,1,136,66,0.202000," ","int(cos(x)^7/(a+b*sin(x)^2),x)","-\frac{\sin^{5}\left(x \right)}{5 b}+\frac{a \left(\sin^{3}\left(x \right)\right)}{3 b^{2}}+\frac{\sin^{3}\left(x \right)}{b}-\frac{a^{2} \sin \left(x \right)}{b^{3}}-\frac{3 a \sin \left(x \right)}{b^{2}}-\frac{3 \sin \left(x \right)}{b}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a^{3}}{b^{3} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}+\frac{3 \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-1/5*sin(x)^5/b+1/3/b^2*a*sin(x)^3+sin(x)^3/b-1/b^3*a^2*sin(x)-3/b^2*a*sin(x)-3*sin(x)/b+1/b^3/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a^3+3/b^2/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a^2+3/b/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a+1/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","B"
302,1,202,73,0.239000," ","int(cos(x)^6/(a+b*sin(x)^2),x)","-\frac{\left(\tan^{3}\left(x \right)\right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{7 \left(\tan^{3}\left(x \right)\right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\tan \left(x \right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{9 \tan \left(x \right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) a^{2}}{b^{3}}-\frac{5 \arctan \left(\tan \left(x \right)\right) a}{2 b^{2}}-\frac{15 \arctan \left(\tan \left(x \right)\right)}{8 b}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a^{3}}{b^{3} \sqrt{a \left(a +b \right)}}+\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a^{2}}{b^{2} \sqrt{a \left(a +b \right)}}+\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a}{b \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\sqrt{a \left(a +b \right)}}"," ",0,"-1/2/b^2/(tan(x)^2+1)^2*tan(x)^3*a-7/8/b/(tan(x)^2+1)^2*tan(x)^3-1/2/b^2/(tan(x)^2+1)^2*tan(x)*a-9/8/b/(tan(x)^2+1)^2*tan(x)-1/b^3*arctan(tan(x))*a^2-5/2/b^2*arctan(tan(x))*a-15/8/b*arctan(tan(x))+1/b^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a^3+3/b^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a^2+3/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a+1/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","B"
303,1,85,44,0.195000," ","int(cos(x)^5/(a+b*sin(x)^2),x)","\frac{\sin^{3}\left(x \right)}{3 b}-\frac{a \sin \left(x \right)}{b^{2}}-\frac{2 \sin \left(x \right)}{b}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}+\frac{2 \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"1/3*sin(x)^3/b-1/b^2*a*sin(x)-2*sin(x)/b+1/b^2/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a^2+2/b/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a+1/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
304,1,111,47,0.212000," ","int(cos(x)^4/(a+b*sin(x)^2),x)","-\frac{\tan \left(x \right)}{2 b \left(\tan^{2}\left(x \right)+1\right)}-\frac{3 \arctan \left(\tan \left(x \right)\right)}{2 b}-\frac{\arctan \left(\tan \left(x \right)\right) a}{b^{2}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a^{2}}{b^{2} \sqrt{a \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a}{b \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\sqrt{a \left(a +b \right)}}"," ",0,"-1/2/b*tan(x)/(tan(x)^2+1)-3/2/b*arctan(tan(x))-1/b^2*arctan(tan(x))*a+1/b^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a^2+2/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a+1/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","B"
305,1,45,28,0.240000," ","int(cos(x)^3/(a+b*sin(x)^2),x)","-\frac{\sin \left(x \right)}{b}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-sin(x)/b+1/b/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))*a+1/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
306,1,58,31,0.206000," ","int(cos(x)^2/(a+b*sin(x)^2),x)","-\frac{\arctan \left(\tan \left(x \right)\right)}{b}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a}{b \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\sqrt{a \left(a +b \right)}}"," ",0,"-1/b*arctan(tan(x))+1/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a+1/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
307,1,17,17,0.112000," ","int(cos(x)/(a+b*sin(x)^2),x)","\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"1/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
308,1,55,32,0.207000," ","int(sec(x)/(a+b*sin(x)^2),x)","-\frac{\ln \left(-1+\sin \left(x \right)\right)}{2 a +2 b}+\frac{b \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right) \sqrt{a b}}+\frac{\ln \left(1+\sin \left(x \right)\right)}{2 a +2 b}"," ",0,"-1/(2*a+2*b)*ln(-1+sin(x))+b/(a+b)/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/(2*a+2*b)*ln(1+sin(x))","A"
309,1,38,31,0.236000," ","int(sec(x)^2/(a+b*sin(x)^2),x)","\frac{\tan \left(x \right)}{a +b}+\frac{b \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\left(a +b \right) \sqrt{a \left(a +b \right)}}"," ",0,"tan(x)/(a+b)+b/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
310,1,112,49,0.240000," ","int(sec(x)^3/(a+b*sin(x)^2),x)","-\frac{1}{\left(4 a +4 b \right) \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right) a}{4 \left(a +b \right)^{2}}-\frac{3 \ln \left(-1+\sin \left(x \right)\right) b}{4 \left(a +b \right)^{2}}+\frac{b^{2} \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right)^{2} \sqrt{a b}}-\frac{1}{\left(4 a +4 b \right) \left(1+\sin \left(x \right)\right)}+\frac{\ln \left(1+\sin \left(x \right)\right) a}{4 \left(a +b \right)^{2}}+\frac{3 \ln \left(1+\sin \left(x \right)\right) b}{4 \left(a +b \right)^{2}}"," ",0,"-1/(4*a+4*b)/(-1+sin(x))-1/4/(a+b)^2*ln(-1+sin(x))*a-3/4/(a+b)^2*ln(-1+sin(x))*b+b^2/(a+b)^2/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))-1/(4*a+4*b)/(1+sin(x))+1/4/(a+b)^2*ln(1+sin(x))*a+3/4/(a+b)^2*ln(1+sin(x))*b","B"
311,1,75,49,0.256000," ","int(sec(x)^4/(a+b*sin(x)^2),x)","\frac{\left(\tan^{3}\left(x \right)\right) a}{3 \left(a +b \right)^{2}}+\frac{\left(\tan^{3}\left(x \right)\right) b}{3 \left(a +b \right)^{2}}+\frac{\tan \left(x \right) a}{\left(a +b \right)^{2}}+\frac{2 \tan \left(x \right) b}{\left(a +b \right)^{2}}+\frac{b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\left(a +b \right)^{2} \sqrt{a \left(a +b \right)}}"," ",0,"1/3/(a+b)^2*tan(x)^3*a+1/3/(a+b)^2*tan(x)^3*b+1/(a+b)^2*tan(x)*a+2/(a+b)^2*tan(x)*b+b^2/(a+b)^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
312,1,204,79,0.317000," ","int(sec(x)^5/(a+b*sin(x)^2),x)","\frac{1}{2 \left(8 a +8 b \right) \left(-1+\sin \left(x \right)\right)^{2}}-\frac{3 a}{16 \left(a +b \right)^{2} \left(-1+\sin \left(x \right)\right)}-\frac{7 b}{16 \left(a +b \right)^{2} \left(-1+\sin \left(x \right)\right)}-\frac{3 \ln \left(-1+\sin \left(x \right)\right) a^{2}}{16 \left(a +b \right)^{3}}-\frac{5 \ln \left(-1+\sin \left(x \right)\right) a b}{8 \left(a +b \right)^{3}}-\frac{15 \ln \left(-1+\sin \left(x \right)\right) b^{2}}{16 \left(a +b \right)^{3}}+\frac{b^{3} \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right)^{3} \sqrt{a b}}-\frac{1}{2 \left(8 a +8 b \right) \left(1+\sin \left(x \right)\right)^{2}}-\frac{3 a}{16 \left(a +b \right)^{2} \left(1+\sin \left(x \right)\right)}-\frac{7 b}{16 \left(a +b \right)^{2} \left(1+\sin \left(x \right)\right)}+\frac{3 \ln \left(1+\sin \left(x \right)\right) a^{2}}{16 \left(a +b \right)^{3}}+\frac{5 \ln \left(1+\sin \left(x \right)\right) a b}{8 \left(a +b \right)^{3}}+\frac{15 \ln \left(1+\sin \left(x \right)\right) b^{2}}{16 \left(a +b \right)^{3}}"," ",0,"1/2/(8*a+8*b)/(-1+sin(x))^2-3/16/(a+b)^2/(-1+sin(x))*a-7/16/(a+b)^2/(-1+sin(x))*b-3/16/(a+b)^3*ln(-1+sin(x))*a^2-5/8/(a+b)^3*ln(-1+sin(x))*a*b-15/16/(a+b)^3*ln(-1+sin(x))*b^2+b^3/(a+b)^3/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))-1/2/(8*a+8*b)/(1+sin(x))^2-3/16/(a+b)^2/(1+sin(x))*a-7/16/(a+b)^2/(1+sin(x))*b+3/16/(a+b)^3*ln(1+sin(x))*a^2+5/8/(a+b)^3*ln(1+sin(x))*a*b+15/16/(a+b)^3*ln(1+sin(x))*b^2","B"
313,1,147,75,0.225000," ","int(sec(x)^6/(a+b*sin(x)^2),x)","\frac{\left(\tan^{5}\left(x \right)\right) a^{2}}{5 \left(a +b \right)^{3}}+\frac{2 \left(\tan^{5}\left(x \right)\right) a b}{5 \left(a +b \right)^{3}}+\frac{b^{2} \left(\tan^{5}\left(x \right)\right)}{5 \left(a +b \right)^{3}}+\frac{2 \left(\tan^{3}\left(x \right)\right) a^{2}}{3 \left(a +b \right)^{3}}+\frac{5 a b \left(\tan^{3}\left(x \right)\right)}{3 \left(a +b \right)^{3}}+\frac{\left(\tan^{3}\left(x \right)\right) b^{2}}{\left(a +b \right)^{3}}+\frac{a^{2} \tan \left(x \right)}{\left(a +b \right)^{3}}+\frac{3 a b \tan \left(x \right)}{\left(a +b \right)^{3}}+\frac{3 b^{2} \tan \left(x \right)}{\left(a +b \right)^{3}}+\frac{b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\left(a +b \right)^{3} \sqrt{a \left(a +b \right)}}"," ",0,"1/5/(a+b)^3*tan(x)^5*a^2+2/5/(a+b)^3*tan(x)^5*a*b+1/5/(a+b)^3*b^2*tan(x)^5+2/3/(a+b)^3*tan(x)^3*a^2+5/3/(a+b)^3*a*b*tan(x)^3+1/(a+b)^3*tan(x)^3*b^2+1/(a+b)^3*a^2*tan(x)+3/(a+b)^3*a*b*tan(x)+3/(a+b)^3*b^2*tan(x)+b^3/(a+b)^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
314,1,211,97,0.230000," ","int(cos(x)^6/(a+b*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)}+\frac{5 \arctan \left(\tan \left(x \right)\right)}{2 b^{2}}+\frac{2 \arctan \left(\tan \left(x \right)\right) a}{b^{3}}+\frac{a \tan \left(x \right)}{2 b^{2} \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{\tan \left(x \right)}{b \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{\tan \left(x \right)}{2 a \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}-\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a^{2}}{b^{3} \sqrt{a \left(a +b \right)}}-\frac{7 \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a}{2 b^{2} \sqrt{a \left(a +b \right)}}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{b \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 a \sqrt{a \left(a +b \right)}}"," ",0,"1/2/b^2*tan(x)/(tan(x)^2+1)+5/2/b^2*arctan(tan(x))+2/b^3*arctan(tan(x))*a+1/2/b^2*a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+1/b*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+1/2/a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)-2/b^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a^2-7/2/b^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a-1/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))+1/2/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","B"
315,1,120,60,0.217000," ","int(cos(x)^5/(a+b*sin(x)^2)^2,x)","\frac{\sin \left(x \right)}{b^{2}}+\frac{a \sin \left(x \right)}{2 b^{2} \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{\sin \left(x \right)}{b \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{\sin \left(x \right)}{2 a \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}-\frac{3 a \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 b^{2} \sqrt{a b}}-\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{b \sqrt{a b}}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 a \sqrt{a b}}"," ",0,"sin(x)/b^2+1/2/b^2*a*sin(x)/(a+b*sin(x)^2)+1/b*sin(x)/(a+b*sin(x)^2)+1/2*sin(x)/a/(a+b*sin(x)^2)-3/2/b^2*a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))-1/b/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/2/a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
316,1,132,63,0.212000," ","int(cos(x)^4/(a+b*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{2 b \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right) a}{b^{2} \sqrt{a \left(a +b \right)}}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 b \sqrt{a \left(a +b \right)}}+\frac{\tan \left(x \right)}{2 a \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 a \sqrt{a \left(a +b \right)}}+\frac{x}{b^{2}}"," ",0,"1/2/b*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)-1/b^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))*a-1/2/b/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))+1/2/a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+1/2/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))+x/b^2","B"
317,1,65,47,0.233000," ","int(cos(x)^3/(a+b*sin(x)^2)^2,x)","\frac{\left(a +b \right) \sin \left(x \right)}{2 a b \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}-\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 b \sqrt{a b}}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 a \sqrt{a b}}"," ",0,"1/2*(a+b)*sin(x)/a/b/(a+b*sin(x)^2)-1/2/b/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/2/a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
318,1,51,42,0.217000," ","int(cos(x)^2/(a+b*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{2 a \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 a \sqrt{a \left(a +b \right)}}"," ",0,"1/2/a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+1/2/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
319,1,39,36,0.108000," ","int(cos(x)/(a+b*sin(x)^2)^2,x)","\frac{\sin \left(x \right)}{2 a \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{\arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 a \sqrt{a b}}"," ",0,"1/2*sin(x)/a/(a+b*sin(x)^2)+1/2/a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))","A"
320,1,122,61,0.219000," ","int(sec(x)/(a+b*sin(x)^2)^2,x)","-\frac{\ln \left(-1+\sin \left(x \right)\right)}{2 \left(a +b \right)^{2}}+\frac{b \sin \left(x \right)}{2 \left(a +b \right)^{2} \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{b^{2} \sin \left(x \right)}{2 \left(a +b \right)^{2} a \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{3 b \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 \left(a +b \right)^{2} \sqrt{a b}}+\frac{b^{2} \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 \left(a +b \right)^{2} a \sqrt{a b}}+\frac{\ln \left(1+\sin \left(x \right)\right)}{2 \left(a +b \right)^{2}}"," ",0,"-1/2/(a+b)^2*ln(-1+sin(x))+1/2*b/(a+b)^2*sin(x)/(a+b*sin(x)^2)+1/2*b^2/(a+b)^2/a*sin(x)/(a+b*sin(x)^2)+3/2*b/(a+b)^2/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/2*b^2/(a+b)^2/a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/2/(a+b)^2*ln(1+sin(x))","A"
321,1,112,64,0.254000," ","int(sec(x)^2/(a+b*sin(x)^2)^2,x)","\frac{\tan \left(x \right)}{a^{2}+2 a b +b^{2}}+\frac{b^{2} \tan \left(x \right)}{2 \left(a +b \right)^{2} a \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{2 b \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\left(a +b \right)^{2} \sqrt{a \left(a +b \right)}}+\frac{b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 \left(a +b \right)^{2} a \sqrt{a \left(a +b \right)}}"," ",0,"1/(a^2+2*a*b+b^2)*tan(x)+1/2*b^2/(a+b)^2/a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+2*b/(a+b)^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))+1/2*b^2/(a+b)^2/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","A"
322,1,180,93,0.293000," ","int(sec(x)^3/(a+b*sin(x)^2)^2,x)","-\frac{1}{4 \left(a +b \right)^{2} \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right) a}{4 \left(a +b \right)^{3}}-\frac{5 \ln \left(-1+\sin \left(x \right)\right) b}{4 \left(a +b \right)^{3}}+\frac{b^{2} \sin \left(x \right)}{2 \left(a +b \right)^{3} \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{b^{3} \sin \left(x \right)}{2 \left(a +b \right)^{3} a \left(a +b \left(\sin^{2}\left(x \right)\right)\right)}+\frac{5 b^{2} \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 \left(a +b \right)^{3} \sqrt{a b}}+\frac{b^{3} \arctan \left(\frac{\sin \left(x \right) b}{\sqrt{a b}}\right)}{2 \left(a +b \right)^{3} a \sqrt{a b}}-\frac{1}{4 \left(a +b \right)^{2} \left(1+\sin \left(x \right)\right)}+\frac{\ln \left(1+\sin \left(x \right)\right) a}{4 \left(a +b \right)^{3}}+\frac{5 \ln \left(1+\sin \left(x \right)\right) b}{4 \left(a +b \right)^{3}}"," ",0,"-1/4/(a+b)^2/(-1+sin(x))-1/4/(a+b)^3*ln(-1+sin(x))*a-5/4/(a+b)^3*ln(-1+sin(x))*b+1/2/(a+b)^3*b^2*sin(x)/(a+b*sin(x)^2)+1/2/(a+b)^3*b^3/a*sin(x)/(a+b*sin(x)^2)+5/2/(a+b)^3*b^2/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))+1/2/(a+b)^3*b^3/a/(a*b)^(1/2)*arctan(sin(x)*b/(a*b)^(1/2))-1/4/(a+b)^2/(1+sin(x))+1/4/(a+b)^3*ln(1+sin(x))*a+5/4/(a+b)^3*ln(1+sin(x))*b","A"
323,1,193,82,0.268000," ","int(sec(x)^4/(a+b*sin(x)^2)^2,x)","\frac{\left(\tan^{3}\left(x \right)\right) a}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)}+\frac{\left(\tan^{3}\left(x \right)\right) b}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)}+\frac{\tan \left(x \right) a}{\left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)}+\frac{3 \tan \left(x \right) b}{\left(a^{2}+2 a b +b^{2}\right) \left(a +b \right)}+\frac{b^{3} \tan \left(x \right)}{2 \left(a +b \right)^{3} a \left(\left(\tan^{2}\left(x \right)\right) a +\left(\tan^{2}\left(x \right)\right) b +a \right)}+\frac{3 b^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{\left(a +b \right)^{3} \sqrt{a \left(a +b \right)}}+\frac{b^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(x \right)}{\sqrt{a \left(a +b \right)}}\right)}{2 \left(a +b \right)^{3} a \sqrt{a \left(a +b \right)}}"," ",0,"1/3/(a^2+2*a*b+b^2)/(a+b)*tan(x)^3*a+1/3/(a^2+2*a*b+b^2)/(a+b)*tan(x)^3*b+1/(a^2+2*a*b+b^2)/(a+b)*tan(x)*a+3/(a^2+2*a*b+b^2)/(a+b)*tan(x)*b+1/2*b^3/(a+b)^3/a*tan(x)/(tan(x)^2*a+tan(x)^2*b+a)+3*b^2/(a+b)^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))+1/2*b^3/(a+b)^3/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(x)/(a*(a+b))^(1/2))","B"
324,1,155,101,1.535000," ","int(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\left(\sin^{3}\left(f x +e \right)\right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{4 f}-\frac{a \sin \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f b}+\frac{a^{2} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{8 f \,b^{\frac{3}{2}}}+\frac{\sin \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 f}+\frac{a \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{2 f \sqrt{b}}"," ",0,"-1/4/f*sin(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2)-1/8/f*a/b*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2)+1/8/f/b^(3/2)*a^2*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))+1/2*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2)/f+1/2/f*a*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))/b^(1/2)","A"
325,1,62,60,0.166000," ","int(cos(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 f}+\frac{a \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{2 f \sqrt{b}}"," ",0,"1/2*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2)/f+1/2/f*a*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))/b^(1/2)","A"
326,1,155,70,4.140000," ","int(sec(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{b}\, \ln \left(\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{b}+b \sin \left(f x +e \right)}{\sqrt{b}}\right)}{f}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 f}-\frac{\sqrt{a +b}\, \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 f}"," ",0,"-1/f*b^(1/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))+1/2/f*(a+b)^(1/2)*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))-1/2/f*(a+b)^(1/2)*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))","B"
327,1,291,70,4.431000," ","int(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{a +b}\, b \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{a +b}\, \sin \left(f x +e \right)-a \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{4 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/4*(2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(1/2)*b*sin(f*x+e)*cos(f*x+e)^2+2*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(1/2)*sin(f*x+e)-a*(ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b)*cos(f*x+e)^2)/(a+b)^(3/2)/cos(f*x+e)^2/f","B"
328,1,570,127,4.852000," ","int(sec(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}} b \left(3 a +4 b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+2 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}} \left(3 a +4 b \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{5}{2}} \sin \left(f x +e \right)+a \left(3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3}+10 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b +11 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{2}+4 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{3}-3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3}-10 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b -11 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{2}-4 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{3}\right) \left(\cos^{4}\left(f x +e \right)\right)}{16 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{4} \left(a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/16*(2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2)*b*(3*a+4*b)*sin(f*x+e)*cos(f*x+e)^4+2*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(3/2)*(3*a+4*b)*cos(f*x+e)^2*sin(f*x+e)+4*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(5/2)*sin(f*x+e)+a*(3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3+10*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b+11*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^2+4*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^3-3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3-10*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b-11*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^2-4*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^3)*cos(f*x+e)^4)/(a+b)^(3/2)/cos(f*x+e)^4/(a^2+2*a*b+b^2)/f","B"
329,1,432,242,1.638000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{-3 b^{3} \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right)+4 a \,b^{2} \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-a^{2} b +2 a \,b^{2}+3 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +6 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{15 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/15*(-3*b^3*sin(f*x+e)*cos(f*x+e)^6+4*a*b^2*sin(f*x+e)*cos(f*x+e)^4+(-a^2*b+2*a*b^2+3*b^3)*cos(f*x+e)^2*sin(f*x+e)+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+6*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-7*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+3*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
330,1,265,185,1.641000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{-b^{2} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -a b \left(\sin^{3}\left(f x +e \right)\right)+b^{2} \left(\sin^{3}\left(f x +e \right)\right)+a b \sin \left(f x +e \right)}{3 b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(-b^2*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b-a*b*sin(f*x+e)^3+b^2*sin(f*x+e)^3+a*b*sin(f*x+e))/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
331,1,71,68,0.699000," ","int((a+b*sin(f*x+e)^2)^(1/2),x)","\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
332,1,294,163,2.303000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right) \sin \left(f x +e \right)+a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*sin(f*x+e)*cos(f*x+e)^2+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a+b)*sin(f*x+e)+a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
333,1,368,218,2.585000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(2 a +b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a \left(2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(2*a+b)*sin(f*x+e)*cos(f*x+e)^4-2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*(a+b)*cos(f*x+e)^2*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*(2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)/(sin(f*x+e)-1)/(1+sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
334,1,277,137,1.972000," ","int(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)}{6 f}+\frac{7 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) a}{24 f}+\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) b}{12 f}-\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sin \left(f x +e \right) a^{2}}{16 b f}+\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sin \left(f x +e \right) a}{3 f}+\frac{b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sin \left(f x +e \right)}{12 f}+\frac{a^{3} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right)}{16 b^{\frac{3}{2}} f}+\frac{3 a^{2} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right)}{8 \sqrt{b}\, f}"," ",0,"-1/6*b/f*(a+b-b*cos(f*x+e)^2)^(1/2)*sin(f*x+e)*cos(f*x+e)^4+7/24/f*(a+b-b*cos(f*x+e)^2)^(1/2)*cos(f*x+e)^2*sin(f*x+e)*a+1/12/f*(a+b-b*cos(f*x+e)^2)^(1/2)*cos(f*x+e)^2*sin(f*x+e)*b-1/16/b/f*(a+b-b*cos(f*x+e)^2)^(1/2)*sin(f*x+e)*a^2+1/3/f*(a+b-b*cos(f*x+e)^2)^(1/2)*sin(f*x+e)*a+1/12*b/f*(a+b-b*cos(f*x+e)^2)^(1/2)*sin(f*x+e)+1/16/b^(3/2)/f*a^3*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))+3/8/b^(1/2)/f*a^2*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))","B"
335,1,90,88,0.219000," ","int(cos(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{4 f}+\frac{3 a \sin \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f}+\frac{3 a^{2} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{8 f \sqrt{b}}"," ",0,"1/4*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2)/f+3/8*a*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2)/f+3/8/f*a^2*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))/b^(1/2)","A"
336,1,451,103,3.708000," ","int(sec(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{b^{\frac{3}{2}} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right)}{f}-\frac{b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sin \left(f x +e \right)}{2 f}-\frac{3 a \sqrt{b}\, \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right)}{2 f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}}{2 \sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b}{\sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}}{2 \sqrt{a +b}\, f}-\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}}{2 \sqrt{a +b}\, f}-\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b}{\sqrt{a +b}\, f}-\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}}{2 \sqrt{a +b}\, f}"," ",0,"-1/f*b^(3/2)*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))-1/2*b/f*(a+b-b*cos(f*x+e)^2)^(1/2)*sin(f*x+e)-3/2/f*a*b^(1/2)*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))+1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+1/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b+1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2-1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2-1/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b-1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2","B"
337,1,402,109,3.870000," ","int(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sin \left(f x +e \right) \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{5}{2}}-\left(-4 b^{\frac{3}{2}} \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) \left(a +b \right)^{\frac{3}{2}}-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{3}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3}-3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{2}-2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)}{4 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/4*(2*sin(f*x+e)*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(5/2)-(-4*b^(3/2)*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*(a+b)^(3/2)-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^2+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^3+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3-3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^2-2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^3)*cos(f*x+e)^2)/(a+b)^(3/2)/cos(f*x+e)^2/f","B"
338,1,406,106,3.192000," ","int(sec(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{5}{2}} \left(3 a -2 b \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{7}{2}} \sin \left(f x +e \right)-3 a^{2} \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}-2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}\right) \left(\cos^{4}\left(f x +e \right)\right)}{16 \left(a +b \right)^{\frac{5}{2}} \cos \left(f x +e \right)^{4} f}"," ",0,"1/16*(2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(5/2)*(3*a-2*b)*sin(f*x+e)*cos(f*x+e)^2+4*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(7/2)*sin(f*x+e)-3*a^2*(ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2-2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2)*cos(f*x+e)^4)/(a+b)^(5/2)/cos(f*x+e)^4/f","B"
339,1,693,175,4.209000," ","int(sec(f*x+e)^7*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{7}{2}} \left(15 a^{2}+8 a b -4 b^{2}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{7}{2}} \left(5 a^{2}+3 a b -2 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+16 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{7}{2}} \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)+3 a^{2} \left(5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{4}+21 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3} b +33 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{2}+23 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{3}+6 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{4}-5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{4}-21 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3} b -33 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{2}-23 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{3}-6 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{4}\right) \left(\cos^{6}\left(f x +e \right)\right)}{96 \left(a +b \right)^{\frac{9}{2}} \cos \left(f x +e \right)^{6} f}"," ",0,"1/96*(2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(7/2)*(15*a^2+8*a*b-4*b^2)*sin(f*x+e)*cos(f*x+e)^4+4*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(7/2)*(5*a^2+3*a*b-2*b^2)*cos(f*x+e)^2*sin(f*x+e)+16*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(7/2)*(a^2+2*a*b+b^2)*sin(f*x+e)+3*a^2*(5*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4+21*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b+33*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^2+23*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^3+6*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^4-5*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4-21*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b-33*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^2-23*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^3-6*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^4)*cos(f*x+e)^6)/(a+b)^(9/2)/cos(f*x+e)^6/f","B"
340,1,590,295,1.694000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{5 b^{4} \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right)+\left(-13 a \,b^{3}-7 b^{4}\right) \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(9 a^{2} b^{2}+a \,b^{3}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(-a^{3} b +8 a^{2} b^{2}+11 a \,b^{3}+2 b^{4}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}+11 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}-10 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +10 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}}{35 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/35*(5*b^4*sin(f*x+e)*cos(f*x+e)^8+(-13*a*b^3-7*b^4)*cos(f*x+e)^6*sin(f*x+e)+(9*a^2*b^2+a*b^3)*cos(f*x+e)^4*sin(f*x+e)+(-a^3*b+8*a^2*b^2+11*a*b^3+2*b^4)*cos(f*x+e)^2*sin(f*x+e)+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^4+11*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^4-10*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+10*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3)/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
341,1,429,237,1.799000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-3 b^{3} \left(\sin^{7}\left(f x +e \right)\right)-9 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+4 b^{3} \left(\sin^{5}\left(f x +e \right)\right)+3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+2 a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-6 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)+10 a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)-b^{3} \left(\sin^{3}\left(f x +e \right)\right)+6 a^{2} b \sin \left(f x +e \right)-a \,b^{2} \sin \left(f x +e \right)}{15 b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/15*(-3*b^3*sin(f*x+e)^7-9*a*b^2*sin(f*x+e)^5+4*b^3*sin(f*x+e)^5+3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+2*a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+7*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-6*a^2*b*sin(f*x+e)^3+10*a*b^2*sin(f*x+e)^3-b^3*sin(f*x+e)^3+6*a^2*b*sin(f*x+e)-a*b^2*sin(f*x+e))/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
342,1,266,180,1.497000," ","int((a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}-\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b}{3}+\frac{4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}+\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b}{3}+\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)}{3}+\frac{a b \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{b^{2} \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{a b \sin \left(f x +e \right)}{3}}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-1/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2-1/3*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b+4/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+1/3*b^2*sin(f*x+e)^5+1/3*a*b*sin(f*x+e)^3-1/3*b^2*sin(f*x+e)^3-1/3*a*b*sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
343,1,466,170,2.401000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(a +b \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}+a b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a b}{\sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(a+b)*sin(f*x+e)*cos(f*x+e)^2+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2+a*b*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*b)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
344,1,375,214,2.688000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(a -b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 a^{2}-a b -3 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\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) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(a-b)*sin(f*x+e)*cos(f*x+e)^4-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*a^2-a*b-3*b^2)*cos(f*x+e)^2*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a-EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/(1+sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
345,1,98,67,1.491000," ","int(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sin \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 b f}+\frac{a \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{2 f \,b^{\frac{3}{2}}}+\frac{\ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{f \sqrt{b}}"," ",0,"-1/2*sin(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2)/b/f+1/2/f*a/b^(3/2)*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))+1/f*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))/b^(1/2)","A"
346,1,34,32,0.133000," ","int(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{f \sqrt{b}}"," ",0,"1/f*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))/b^(1/2)","A"
347,1,113,36,3.100000," ","int(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 \sqrt{a +b}\, f}-\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 \sqrt{a +b}\, f}"," ",0,"1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))-1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))","B"
348,1,360,79,3.290000," ","int(sec(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sin \left(f x +e \right) \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}}-\left(-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}-3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b -2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b +2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)}{4 \left(a +b \right)^{\frac{5}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/4*(2*sin(f*x+e)*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2)-(-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2-3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b-2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2)*cos(f*x+e)^2)/(a+b)^(5/2)/cos(f*x+e)^2/f","B"
349,1,316,194,1.542000," ","int(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+5 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b +3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +a b \left(\sin^{3}\left(f x +e \right)\right)-b^{2} \left(\sin^{3}\left(f x +e \right)\right)-a b \sin \left(f x +e \right)}{3 b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(b^2*sin(f*x+e)^5+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+5*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b+3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+a*b*sin(f*x+e)^3-b^2*sin(f*x+e)^3-a*b*sin(f*x+e))/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
350,1,111,148,1.140000," ","int(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \right)}{b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a)/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
351,1,60,68,0.359000," ","int(1/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)-a -b}{a}}\, \mathrm{am}^{-1}\left(f x +e \bigg| \frac{i \sqrt{b}}{\sqrt{a}}\right)}{f \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}"," ",0,"1/f/(a+b-b*cos(f*x+e)^2)^(1/2)*(-(b*cos(f*x+e)^2-a-b)/a)^(1/2)*InverseJacobiAM(f*x+e,I/a^(1/2)*b^(1/2))","C"
352,1,278,172,2.815000," ","int(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b +a \sin \left(f x +e \right)+b \sin \left(f x +e \right)\right)}{\left(a +b \right) \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))+b*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))-sin(f*x+e)*cos(f*x+e)^2*b+a*sin(f*x+e)+b*sin(f*x+e))/(a+b)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
353,1,405,234,3.033000," ","int(sec(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(a +2 b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 a^{2}+5 a b +3 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+5 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-4 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(a +b \right)^{2} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(a+2*b)*sin(f*x+e)*cos(f*x+e)^4-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*a^2+5*a*b+3*b^2)*cos(f*x+e)^2*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+5*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b+3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-4*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b)*cos(f*x+e)^2)/(1+sin(f*x+e))/(sin(f*x+e)-1)/(a+b)^2/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
354,1,90,67,1.480000," ","int(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right)}{f b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\right)}{f \,b^{\frac{3}{2}}}+\frac{\sin \left(f x +e \right)}{a f \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}"," ",0,"1/f*sin(f*x+e)/b/(a+b*sin(f*x+e)^2)^(1/2)-1/f/b^(3/2)*ln(sin(f*x+e)*b^(1/2)+(a+b*sin(f*x+e)^2)^(1/2))+sin(f*x+e)/a/f/(a+b*sin(f*x+e)^2)^(1/2)","A"
355,1,28,27,0.158000," ","int(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right)}{a f \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}"," ",0,"sin(f*x+e)/a/f/(a+b*sin(f*x+e)^2)^(1/2)","A"
356,1,397,70,4.630000," ","int(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{2 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, \sqrt{a +b}\, b \sin \left(f x +e \right)+a b \left(-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)\right) \left(\cos^{2}\left(f x +e \right)\right)+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b}{2 \sqrt{a +b}\, a \left(-a b \left(\cos^{2}\left(f x +e \right)\right)-b^{2} \left(\cos^{2}\left(f x +e \right)\right)+a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/2/(a+b)^(1/2)/a/(-a*b*cos(f*x+e)^2-b^2*cos(f*x+e)^2+a^2+2*a*b+b^2)*(2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*(a+b)^(1/2)*b*sin(f*x+e)+a*b*(-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a)))*cos(f*x+e)^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b)/f","B"
357,1,3217,118,11.571000," ","int(sec(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"1/4/(a+b)^(1/2)/a/b^5/cos(f*x+e)^2/(a^4*b^2*cos(f*x+e)^4+4*a^3*b^3*cos(f*x+e)^4+6*a^2*b^4*cos(f*x+e)^4+4*a*b^5*cos(f*x+e)^4+b^6*cos(f*x+e)^4-2*a^5*b*cos(f*x+e)^2-10*a^4*b^2*cos(f*x+e)^2-20*a^3*b^3*cos(f*x+e)^2-20*a^2*b^4*cos(f*x+e)^2-10*a*b^5*cos(f*x+e)^2-2*b^6*cos(f*x+e)^2+a^6+6*a^5*b+15*a^4*b^2+20*a^3*b^3+15*a^2*b^4+6*a*b^5+b^6)*(-2*a*(8*(a+b)^(1/2)*b^(19/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))-8*(a+b)^(1/2)*b^(19/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))+16*(a+b)^(1/2)*b^(17/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a-16*(a+b)^(1/2)*b^(17/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a+8*(a+b)^(1/2)*b^(15/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a^2-8*(a+b)^(1/2)*b^(15/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4*b^6+7*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^7+15*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^8+13*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^9+4*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^10-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4*b^6-7*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^7-15*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^8-13*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^9-4*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^10)*cos(f*x+e)^4+a*(8*(a+b)^(1/2)*b^(19/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))-8*(a+b)^(1/2)*b^(19/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))+8*(a+b)^(1/2)*b^(17/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a-8*(a+b)^(1/2)*b^(17/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^7+6*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^8+9*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^9+4*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^10-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^7-6*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^8-9*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^9-4*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^10)*cos(f*x+e)^6+a*(8*(a+b)^(1/2)*b^(19/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))-8*(a+b)^(1/2)*b^(19/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))+24*(a+b)^(1/2)*b^(17/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a-24*(a+b)^(1/2)*b^(17/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a+24*(a+b)^(1/2)*b^(15/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a^2-24*(a+b)^(1/2)*b^(15/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a^2+8*(a+b)^(1/2)*b^(13/2)*ln(((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(3/2)+sin(f*x+e)*b^2)/b^(3/2))*a^3-8*(a+b)^(1/2)*b^(13/2)*ln(((a+b-b*cos(f*x+e)^2)^(1/2)*b^(1/2)+b*sin(f*x+e))/b^(1/2))*a^3+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^5*b^5+8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4*b^6+22*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^7+28*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^8+17*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^9+4*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^10-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^5*b^5-8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4*b^6-22*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^7-28*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^8-17*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^9-4*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^10)*cos(f*x+e)^2+2*sin(f*x+e)*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(1/2)*a*b^5*(a^3+3*a^2*b+3*a*b^2+b^3)-2*cos(f*x+e)^4*sin(f*x+e)*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^7*(a*b*cos(f*x+e)^2+b^2*cos(f*x+e)^2+a^2+2*a*b+b^2)+2*sin(f*x+e)*cos(f*x+e)^6*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^8-2*sin(f*x+e)*cos(f*x+e)^2*(a+b)^(1/2)*b^6*(2*(a+b-b*cos(f*x+e)^2)^(3/2)*a^3+4*(a+b-b*cos(f*x+e)^2)^(3/2)*a^2*b+2*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b^2-2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a^2*b-4*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a*b^2-2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*b^3-(a+b-b*cos(f*x+e)^2)^(1/2)*a^4-3*(a+b-b*cos(f*x+e)^2)^(1/2)*a^3*b-3*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2*b^2-(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^3))/f","B"
358,1,415,254,1.809000," ","int(cos(f*x+e)^6/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{a \,b^{2} \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-4 a^{2} b -7 a \,b^{2}-3 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+17 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +9 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-13 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -3 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{3 a \,b^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(a*b^2*sin(f*x+e)*cos(f*x+e)^4+(-4*a^2*b-7*a*b^2-3*b^3)*cos(f*x+e)^2*sin(f*x+e)+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+17*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+9*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-13*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-3*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/a/b^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
359,1,274,190,1.419000," ","int(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\left(-a b -b^{2}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b}{a \,b^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-((-a*b-b^2)*sin(f*x+e)*cos(f*x+e)^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b)/a/b^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
360,1,145,176,1.277000," ","int(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+b \left(\sin^{3}\left(f x +e \right)\right)-b \sin \left(f x +e \right)}{a b \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-(a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))+b*sin(f*x+e)^3-b*sin(f*x+e))/a/b/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
361,1,103,116,1.430000," ","int(1/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b}{a \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"((cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))+sin(f*x+e)*cos(f*x+e)^2*b)/a/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
362,1,468,226,2.751000," ","int(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(a -b \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(a +b \right) \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}+a b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a b}{\left(a +b \right)^{2} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\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{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(a-b)*sin(f*x+e)*cos(f*x+e)^2+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*(a+b)*sin(f*x+e)+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2+a*b*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*b)/(a+b)^2/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/a/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
363,1,383,116,4.003000," ","int(cos(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{3 \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) a^{4} b^{4}+6 \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) a^{3} b^{5}+3 \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) a^{2} b^{6}+3 \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) a^{2} b^{6} \left(\cos^{4}\left(f x +e \right)\right)-6 \ln \left(\sin \left(f x +e \right) \sqrt{b}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\right) a^{2} b^{5} \left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{\frac{11}{2}} \left(2 a^{2}+a b -b^{2}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-\sin \left(f x +e \right) \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{\frac{9}{2}} \left(3 a^{3}+4 a^{2} b -a \,b^{2}-2 b^{3}\right)}{3 b^{\frac{13}{2}} a^{2} \left(b^{2} \left(\cos^{4}\left(f x +e \right)\right)-2 a b \left(\cos^{2}\left(f x +e \right)\right)-2 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/3/b^(13/2)/a^2/(b^2*cos(f*x+e)^4-2*a*b*cos(f*x+e)^2-2*b^2*cos(f*x+e)^2+a^2+2*a*b+b^2)*(3*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*a^4*b^4+6*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*a^3*b^5+3*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*a^2*b^6+3*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*a^2*b^6*cos(f*x+e)^4-6*ln(sin(f*x+e)*b^(1/2)+(a+b-b*cos(f*x+e)^2)^(1/2))*a^2*b^5*(a+b)*cos(f*x+e)^2+2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(11/2)*(2*a^2+a*b-b^2)*sin(f*x+e)*cos(f*x+e)^2-sin(f*x+e)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^(9/2)*(3*a^3+4*a^2*b-a*b^2-2*b^3))/f","B"
364,1,120,65,3.887000," ","int(cos(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sin \left(f x +e \right) \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, \left(a \left(\cos^{2}\left(f x +e \right)\right)-2 b \left(\cos^{2}\left(f x +e \right)\right)+2 a +2 b \right)}{3 a^{2} \left(b^{2} \left(\cos^{4}\left(f x +e \right)\right)-2 a b \left(\cos^{2}\left(f x +e \right)\right)-2 b^{2} \left(\cos^{2}\left(f x +e \right)\right)+a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/3/a^2/(b^2*cos(f*x+e)^4-2*a*b*cos(f*x+e)^2-2*b^2*cos(f*x+e)^2+a^2+2*a*b+b^2)*sin(f*x+e)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*(a*cos(f*x+e)^2-2*b*cos(f*x+e)^2+2*a+2*b)/f","A"
365,1,56,57,0.151000," ","int(cos(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\frac{\sin \left(f x +e \right)}{3 a \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \sin \left(f x +e \right)}{3 a^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}}{f}"," ",0,"1/f*(1/3*sin(f*x+e)/a/(a+b*sin(f*x+e)^2)^(3/2)+2/3/a^2*sin(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2))","A"
366,1,899,112,5.683000," ","int(sec(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{-3 a^{4} b^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+3 a^{4} b^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)-3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{4}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{4}-6 a^{3} b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+6 a^{3} b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+3 a^{2} b^{4} \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)\right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{4} \left(5 a +2 b \right)+4 \sin \left(f x +e \right) \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{3} \left(3 a^{2}+4 a b +b^{2}\right)-6 a^{2} b^{3} \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{6 b^{2} \sqrt{a +b}\, a^{2} \left(a^{2} b^{2} \left(\cos^{4}\left(f x +e \right)\right)+2 a \,b^{3} \left(\cos^{4}\left(f x +e \right)\right)+b^{4} \left(\cos^{4}\left(f x +e \right)\right)-2 a^{3} b \left(\cos^{2}\left(f x +e \right)\right)-6 a^{2} b^{2} \left(\cos^{2}\left(f x +e \right)\right)-6 a \,b^{3} \left(\cos^{2}\left(f x +e \right)\right)-2 b^{4} \left(\cos^{2}\left(f x +e \right)\right)+a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) f}"," ",0,"1/6/b^2/(a+b)^(1/2)/a^2/(a^2*b^2*cos(f*x+e)^4+2*a*b^3*cos(f*x+e)^4+b^4*cos(f*x+e)^4-2*a^3*b*cos(f*x+e)^2-6*a^2*b^2*cos(f*x+e)^2-6*a*b^3*cos(f*x+e)^2-2*b^4*cos(f*x+e)^2+a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*(-3*a^4*b^2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+3*a^4*b^2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))-3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^4+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^4-6*a^3*b^3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+6*a^3*b^3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+3*a^2*b^4*(ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a)))*cos(f*x+e)^4-2*sin(f*x+e)*cos(f*x+e)^2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^4*(5*a+2*b)+4*sin(f*x+e)*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^3*(3*a^2+4*a*b+b^2)-6*a^2*b^3*(ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b)*cos(f*x+e)^2)/f","B"
367,1,712,265,1.898000," ","int(cos(f*x+e)^6/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\left(5 a^{2} b^{2}+3 a \,b^{3}-2 b^{4}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-4 a^{3} b -6 a^{2} b^{2}+2 b^{4}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a b \left(8 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+7 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-3 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}+15 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +6 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}-11 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b -\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}}{3 a^{2} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} b^{3} \cos \left(f x +e \right) f}"," ",0,"1/3*((5*a^2*b^2+3*a*b^3-2*b^4)*sin(f*x+e)*cos(f*x+e)^4+(-4*a^3*b-6*a^2*b^2+2*b^4)*cos(f*x+e)^2*sin(f*x+e)-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*b*(8*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+7*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b-EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-3*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^2)*cos(f*x+e)^2+8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^4+15*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+6*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3-8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^4-11*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3)/a^2/(a+b*sin(f*x+e)^2)^(3/2)/b^3/cos(f*x+e)/f","B"
368,1,485,245,1.828000," ","int(cos(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\left(2 a \,b^{2}-2 b^{3}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-a^{2} b +a \,b^{2}+2 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a b \left(2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{3 a^{2} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} b^{2} \cos \left(f x +e \right) f}"," ",0,"1/3*((2*a*b^2-2*b^3)*sin(f*x+e)*cos(f*x+e)^4+(-a^2*b+a*b^2+2*b^3)*cos(f*x+e)^2*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*b*(2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a-EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/a^2/(a+b*sin(f*x+e)^2)^(3/2)/b^2/cos(f*x+e)/f","A"
369,1,552,239,1.850000," ","int(cos(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)-a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)-2 b^{3} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-2 a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)+2 b^{3} \left(\sin^{3}\left(f x +e \right)\right)+2 a^{2} b \sin \left(f x +e \right)+3 a \,b^{2} \sin \left(f x +e \right)}{3 a^{2} \left(a +b \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} b \cos \left(f x +e \right) f}"," ",0,"1/3*((cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2-a*b^2*sin(f*x+e)^5-2*b^3*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3-a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*a^2*b*sin(f*x+e)^3-2*a*b^2*sin(f*x+e)^3+2*b^3*sin(f*x+e)^3+2*a^2*b*sin(f*x+e)+3*a*b^2*sin(f*x+e))/a^2/(a+b)/(a+b*sin(f*x+e)^2)^(3/2)/b/cos(f*x+e)/f","B"
370,1,547,245,1.960000," ","int(1/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)+4 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+2 b^{3} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +5 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)-2 b^{3} \left(\sin^{3}\left(f x +e \right)\right)-5 a^{2} b \sin \left(f x +e \right)-3 a \,b^{2} \sin \left(f x +e \right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} a^{2} \left(a +b \right)^{2} \cos \left(f x +e \right) f}"," ",0,"-1/3*((cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2+4*a*b^2*sin(f*x+e)^5+2*b^3*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+5*a^2*b*sin(f*x+e)^3-a*b^2*sin(f*x+e)^3-2*b^3*sin(f*x+e)^3-5*a^2*b*sin(f*x+e)-3*a*b^2*sin(f*x+e))/(a+b*sin(f*x+e)^2)^(3/2)/a^2/(a+b)^2/cos(f*x+e)/f","B"
371,1,1082,308,3.247000," ","int(sec(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2} \left(3 a^{2}-7 a b -2 b^{2}\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(3 a^{3}-a^{2} b -5 a \,b^{2}-b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2} \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a b \left(3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-3 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+3 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}+5 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}-3 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{4}+4 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} b +9 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b^{2}+2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{3}}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} a^{2} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right)^{3} \cos \left(f x +e \right) f}"," ",0,"1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^2*(3*a^2-7*a*b-2*b^2)*sin(f*x+e)*cos(f*x+e)^4-2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(3*a^3-a^2*b-5*a*b^2-b^3)*cos(f*x+e)^2*sin(f*x+e)+3*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*b*(3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b-EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-3*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^2)*cos(f*x+e)^2+3*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^4+5*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3-3*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^4+4*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3*b+9*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b^2+2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^3)/(a+b*sin(f*x+e)^2)^(3/2)/a^2/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)^3/cos(f*x+e)/f","B"
372,0,0,103,2.560000," ","int((d*cos(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x)","\int \left(d \cos \left(f x +e \right)\right)^{m} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((d*cos(f*x+e))^m*(a+b*sin(f*x+e)^2)^p,x)","F"
373,0,0,208,2.932000," ","int(cos(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^5*(a+b*sin(f*x+e)^2)^p,x)","F"
374,0,0,122,7.105000," ","int(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","F"
375,0,0,65,2.600000," ","int(cos(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","\int \cos \left(f x +e \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","F"
376,0,0,72,1.938000," ","int(sec(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","\int \sec \left(f x +e \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(a+b*sin(f*x+e)^2)^p,x)","F"
377,0,0,72,1.965000," ","int(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*sin(f*x+e)^2)^p,x)","F"
378,0,0,82,4.612000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","F"
379,0,0,82,6.166000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","F"
380,0,0,82,1.355000," ","int((a+b*sin(f*x+e)^2)^p,x)","\int \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e)^2)^p,x)","F"
381,0,0,82,1.773000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*sin(f*x+e)^2)^p,x)","F"
382,0,0,82,1.236000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(a+b*sin(f*x+e)^2)^p,x)","F"
383,1,278,167,0.919000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c)^3),x)","\frac{\sin^{2}\left(d x +c \right)}{2 b d}+\frac{\ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 b d}"," ",0,"1/2*sin(d*x+c)^2/b/d+1/3/d/b/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/6/d/b/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/3/d/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+1/3/d/b^2*a/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/6/d/b^2*a/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/3/d/b^2*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-2/3*ln(a+b*sin(d*x+c)^3)/b/d","A"
384,1,141,128,0.843000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c)^3),x)","\frac{\ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 b d}"," ",0,"1/3/d/b/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/6/d/b/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/3/d/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-1/3*ln(a+b*sin(d*x+c)^3)/b/d","A"
385,1,120,107,0.467000," ","int(cos(d*x+c)/(a+b*sin(d*x+c)^3),x)","\frac{\ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d b \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3/d/b/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/6/d/b/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/3/d/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))","A"
386,1,374,235,0.959000," ","int(sec(d*x+c)/(a+b*sin(d*x+c)^3),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{b \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a -b \right) \left(a +b \right) \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{b \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 d \left(a -b \right) \left(a +b \right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)-1/3/d*b/(a-b)/(a+b)/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))+1/6/d*b/(a-b)/(a+b)/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/3/d*b/(a-b)/(a+b)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-1/3/d/(a-b)/(a+b)*a/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))+1/6/d/(a-b)/(a+b)*a/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/3/d/(a-b)/(a+b)*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-1/3/d*b/(a-b)/(a+b)*ln(a+b*sin(d*x+c)^3)+1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
387,1,668,326,0.973000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c)^3),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{d \left(a +b \right)^{2}}+\frac{2 b \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b^{3} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b^{3} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 b \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b^{3} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b^{2} a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{b^{2} a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{b^{2} a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{b \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{2 b^{3} \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}-\frac{b \ln \left(1+\sin \left(d x +c \right)\right)}{\left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*a-1/d/(a+b)^2*ln(sin(d*x+c)-1)*b+2/3/d*b/(a-b)^2/(a+b)^2/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))*a^2+1/3/d*b^3/(a-b)^2/(a+b)^2/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/3/d*b/(a-b)^2/(a+b)^2/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))*a^2-1/6/d*b^3/(a-b)^2/(a+b)^2/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/3/d*b/(a-b)^2/(a+b)^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))*a^2+1/3/d*b^3/(a-b)^2/(a+b)^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+1/d*b^2/(a-b)^2/(a+b)^2*a/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/2/d*b^2/(a-b)^2/(a+b)^2*a/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/d*b^2/(a-b)^2/(a+b)^2*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+1/3/d*b/(a-b)^2/(a+b)^2*ln(a+b*sin(d*x+c)^3)*a^2+2/3/d*b^3/(a-b)^2/(a+b)^2*ln(a+b*sin(d*x+c)^3)-1/d/(4*a-4*b)/(1+sin(d*x+c))+1/4*a*ln(1+sin(d*x+c))/(a-b)^2/d-b*ln(1+sin(d*x+c))/(a-b)^2/d","B"
388,1,123,527,1.008000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c)^3),x)","-\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4} b -2 \textit{\_R}^{3} a -6 \textit{\_R}^{2} b -2 \textit{\_R} a +b \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}}{3 d b}"," ",0,"-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)+1/3/d/b*sum((_R^4*b-2*_R^3*a-6*_R^2*b-2*_R*a+b)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
389,1,83,332,0.890000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c)^3),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}-2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}}{3 d}"," ",0,"1/3/d*sum((_R^4-2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
390,1,83,168,0.569000," ","int(1/(a+b*sin(d*x+c)^3),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}}{3 d}"," ",0,"1/3/d*sum((_R^4+2*_R^2+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
391,1,164,214,0.956000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c)^3),x)","-\frac{2}{d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4} b -2 \textit{\_R}^{3} a +6 \textit{\_R}^{2} b -2 \textit{\_R} a +b \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a -b \right) \left(a +b \right)}"," ",0,"-2/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)-2/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)-1/3/d*b/(a-b)/(a+b)*sum((_R^4*b-2*_R^3*a+6*_R^2*b-2*_R*a+b)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
392,1,346,852,1.133000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c)^3),x)","-\frac{2}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(2 a +2 b \right)}-\frac{1}{d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5 b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(2 a -2 b \right)}+\frac{1}{d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{b^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\left(2 a^{2}+b^{2}\right) \textit{\_R}^{4}-6 \textit{\_R}^{3} a b +2 \left(4 a^{2}+5 b^{2}\right) \textit{\_R}^{2}-6 a \textit{\_R} b +2 a^{2}+b^{2}\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2}}"," ",0,"-2/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(2*a+2*b)-1/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-5/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-2/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(2*a-2*b)+1/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)^2-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a+5/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b+1/3/d*b^2/(a-b)^2/(a+b)^2*sum(((2*a^2+b^2)*_R^4-6*_R^3*a*b+2*(4*a^2+5*b^2)*_R^2-6*a*_R*b+2*a^2+b^2)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","C"
393,1,490,235,0.928000," ","int(cos(d*x+c)^7/(a+b*sin(d*x+c)^3)^2,x)","-\frac{\sin \left(d x +c \right)}{b^{2} d}-\frac{\sin^{2}\left(d x +c \right)}{d b \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{\sin \left(d x +c \right) a}{3 d \,b^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{\sin \left(d x +c \right)}{3 a d \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{1}{d b \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{4 a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \,b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \,b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{4 a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \,b^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-sin(d*x+c)/b^2/d-1/d/b/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2-1/3/d/b^2/(a+b*sin(d*x+c)^3)*sin(d*x+c)*a+1/3*sin(d*x+c)/a/d/(a+b*sin(d*x+c)^3)+1/d/b/(a+b*sin(d*x+c)^3)+4/9/d/b^3*a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))+2/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-2/9/d/b^3*a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+4/9/d/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+2/9/d/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-2/3/d/b^2/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))+1/3/d/b^2/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/3/d/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))","B"
394,1,327,185,0.977000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c)^3)^2,x)","-\frac{\sin^{2}\left(d x +c \right)}{3 d b \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{\sin \left(d x +c \right)}{3 a d \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{2}{3 d b \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"-1/3/d/b/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2+1/3*sin(d*x+c)/a/d/(a+b*sin(d*x+c)^3)+2/3/d/b/(a+b*sin(d*x+c)^3)+2/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/9/d/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-2/9/d/b^2/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))+1/9/d/b^2/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/9/d/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))","A"
395,1,179,142,0.929000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c)^3)^2,x)","\frac{\sin \left(d x +c \right)}{3 a d \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{1}{3 d b \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}"," ",0,"1/3*sin(d*x+c)/a/d/(a+b*sin(d*x+c)^3)+2/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/9/d/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+1/3/d/b/(a+b*sin(d*x+c)^3)","A"
396,1,157,135,0.528000," ","int(cos(d*x+c)/(a+b*sin(d*x+c)^3)^2,x)","\frac{\sin \left(d x +c \right)}{3 a d \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{2 \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d b a \left(\frac{a}{b}\right)^{\frac{2}{3}}}"," ",0,"1/3*sin(d*x+c)/a/d/(a+b*sin(d*x+c)^3)+2/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/9/d/b/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/9/d/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))","A"
397,1,934,479,0.961000," ","int(sec(d*x+c)/(a+b*sin(d*x+c)^3)^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{b \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{2} \sin \left(d x +c \right) a}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{b^{4} \sin \left(d x +c \right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right) a}+\frac{b \,a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{3}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{8 b a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 b^{3} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{4 b a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b^{3} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{8 b a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{2 b^{3} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{4 a^{2} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 b^{2} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 a^{2} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{b^{2} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{4 a^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 b^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{2 b a \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}"," ",0,"-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)+1/3/d*b/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2*a^2-1/3/d*b^3/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2-1/3/d*b^2/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)*sin(d*x+c)*a+1/3/d*b^4/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)/a*sin(d*x+c)+1/3/d*b/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)*a^2-1/3/d*b^3/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c)^3)-8/9/d*b/(a-b)^2/(a+b)^2*a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))+2/9/d*b^3/(a-b)^2/(a+b)^2/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))+4/9/d*b/(a-b)^2/(a+b)^2*a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/9/d*b^3/(a-b)^2/(a+b)^2/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-8/9/d*b/(a-b)^2/(a+b)^2*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+2/9/d*b^3/(a-b)^2/(a+b)^2/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-4/9/d/(a-b)^2/(a+b)^2*a^2/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))-2/9/d*b^2/(a-b)^2/(a+b)^2/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))+2/9/d/(a-b)^2/(a+b)^2*a^2/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/9/d*b^2/(a-b)^2/(a+b)^2/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+4/9/d/(a-b)^2/(a+b)^2*a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+2/9/d*b^2/(a-b)^2/(a+b)^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-2/3/d*b/(a-b)^2/(a+b)^2*a*ln(a+b*sin(d*x+c)^3)+1/2*ln(1+sin(d*x+c))/(a-b)^2/d","A"
398,1,1309,631,1.051000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c)^3)^2,x)","\frac{22 b^{3} a \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 b^{5} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{10 b^{2} a^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{16 b \,a^{3} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{1}{4 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{1}{4 \left(a -b \right)^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{16 b \,a^{3} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{22 b^{3} a \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 b^{5} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{2 b^{4} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}-\frac{7 \ln \left(1+\sin \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{3}}-\frac{7 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{3}}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{3} d}+\frac{10 b^{2} a^{2} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 b^{2} a^{3} \sin \left(d x +c \right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{2 b^{5}}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}+\frac{b^{5} \left(\sin^{2}\left(d x +c \right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b \,a^{4}}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{3} a^{2}}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{4} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 b \,a^{3} \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3}}+\frac{10 b^{3} a \ln \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3}}-\frac{8 b \,a^{3} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{11 b^{3} a \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{b^{5} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{b^{3} \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{4} a \sin \left(d x +c \right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right)}-\frac{b^{6} \sin \left(d x +c \right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \left(\sin^{3}\left(d x +c \right)\right)\right) a}-\frac{5 b^{2} a^{2} \ln \left(\sin^{2}\left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}+\frac{2 b^{4} \ln \left(\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{3}}}"," ",0,"22/9/d*b^3/(a-b)^3/(a+b)^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-2/9/d*b^5/(a-b)^3/(a+b)^3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-10/3/d*b^2/(a-b)^3/(a+b)^3*a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))+16/9/d*b/(a-b)^3/(a+b)^3*a^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-1/4/d/(a+b)^2/(sin(d*x+c)-1)-1/4/(a-b)^2/d/(1+sin(d*x+c))+2/3/d*b^2/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*a^3*sin(d*x+c)+16/9/d*b/(a-b)^3/(a+b)^3*a^3/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))+22/9/d*b^3/(a-b)^3/(a+b)^3*a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-2/9/d*b^5/(a-b)^3/(a+b)^3/a/(a/b)^(2/3)*ln(sin(d*x+c)+(a/b)^(1/3))-8/9/d*b/(a-b)^3/(a+b)^3*a^3/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-11/9/d*b^3/(a-b)^3/(a+b)^3*a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+1/9/d*b^5/(a-b)^3/(a+b)^3/a/(a/b)^(2/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))-1/d*b^3/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2*a^2-1/3/d*b^4/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*a*sin(d*x+c)-1/3/d*b^6/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)/a*sin(d*x+c)-2/3/d*b^4/(a-b)^3/(a+b)^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(d*x+c)-1))-5/3/d*b^2/(a-b)^3/(a+b)^3*a^2/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/3/d*b^5/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)-7/4/d/(a-b)^3*ln(1+sin(d*x+c))*b-1/4/d/(a+b)^3*ln(sin(d*x+c)-1)*a-7/4/d/(a+b)^3*ln(sin(d*x+c)-1)*b+1/4*a*ln(1+sin(d*x+c))/(a-b)^3/d+10/3/d*b^2/(a-b)^3/(a+b)^3*a^2/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))+1/d*b^5/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*sin(d*x+c)^2-1/3/d*b/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*a^4-1/3/d*b^3/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c)^3)*a^2+2/3/d*b^4/(a-b)^3/(a+b)^3/(a/b)^(1/3)*ln(sin(d*x+c)+(a/b)^(1/3))-1/3/d*b^4/(a-b)^3/(a+b)^3/(a/b)^(1/3)*ln(sin(d*x+c)^2-(a/b)^(1/3)*sin(d*x+c)+(a/b)^(2/3))+2/3/d*b/(a-b)^3/(a+b)^3*a^3*ln(a+b*sin(d*x+c)^3)+10/3/d*b^3/(a-b)^3/(a+b)^3*a*ln(a+b*sin(d*x+c)^3)","B"
399,1,550,25,0.965000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x)","-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) b}+\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) b}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{2}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) b}+\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4} b +\textit{\_R}^{3} a +\textit{\_R} a +b \right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{9 d a b}"," ",0,"-2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^5+2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/b*tan(1/2*d*x+1/2*c)^4+8/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^3+4/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/b*tan(1/2*d*x+1/2*c)^2+2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)+2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/b+2/9/d/a/b*sum((_R^4*b+_R^3*a+_R*a+b)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","B"
400,1,236,25,0.944000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x)","-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{2 \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\textit{\_R}^{4}+1\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{9 d a}"," ",0,"-2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^5+2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)+2/9/d/a*sum((_R^4+1)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","B"
401,1,658,16,0.650000," ","int(1/(a+b*sin(d*x+c)^3)^2,x)","\frac{2 b^{2} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a \left(a^{2}-b^{2}\right)}-\frac{2 b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) \left(a^{2}-b^{2}\right)}+\frac{8 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a \left(a^{2}-b^{2}\right)}+\frac{8 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) \left(a^{2}-b^{2}\right)}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a \left(a^{2}-b^{2}\right)}+\frac{2 b}{3 d \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) \left(a^{2}-b^{2}\right)}+\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\left(3 a^{2}-2 b^{2}\right) \textit{\_R}^{4}-2 \textit{\_R}^{3} a b +6 \textit{\_R}^{2} a^{2}-2 a \textit{\_R} b +3 a^{2}-2 b^{2}\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}}{9 d a \left(a^{2}-b^{2}\right)}"," ",0,"2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^5-2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)^4+8/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+8/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)+2/3/d/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*b/(a^2-b^2)+1/9/d/a/(a^2-b^2)*sum(((3*a^2-2*b^2)*_R^4-2*_R^3*a*b+6*_R^2*a^2-2*a*_R*b+3*a^2-2*b^2)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","B"
402,1,1276,25,0.956000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c)^3)^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{2 b^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}-\frac{2 b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{8 b^{3} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{8 b^{2} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{16 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}-\frac{4 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{20 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{4 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}-\frac{2 b \,a^{2}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{4 b^{3}}{3 d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{b \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(b \left(11 a^{2}-2 b^{2}\right) \textit{\_R}^{4}+2 a \left(-5 a^{2}-4 b^{2}\right) \textit{\_R}^{3}+54 \textit{\_R}^{2} a^{2} b +2 a \left(-5 a^{2}-4 b^{2}\right) \textit{\_R} +11 a^{2} b -2 b^{3}\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{9 d \left(a -b \right)^{2} \left(a +b \right)^{2} a}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)-4/3/d*b^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)^5-2/3/d*b^4/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^5-2/3/d*b/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^4*a^2+8/3/d*b^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^4-8/3/d*b^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)^3-16/3/d*b^4/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^3-4/3/d*b/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^2*a^2-20/3/d*b^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^2+4/3/d*b^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)+2/3/d*b^4/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)-2/3/d*b/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a^2-4/3/d*b^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)-1/9/d*b/(a-b)^2/(a+b)^2/a*sum((b*(11*a^2-2*b^2)*_R^4+2*a*(-5*a^2-4*b^2)*_R^3+54*_R^2*a^2*b+2*a*(-5*a^2-4*b^2)*_R+11*a^2*b-2*b^3)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","B"
403,1,1549,25,1.183000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c)^3)^2,x)","-\frac{1}{3 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4 b}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{4 b}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{2} a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{14 b^{4} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{2 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}-\frac{6 b^{5} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{16 b^{4} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{8 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{12 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{12 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{2 b^{2} a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{14 b^{4} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right) a}+\frac{4 b^{3} a^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{2 b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +8 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +a \right)}+\frac{b^{2} \left(\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+8 b \,\textit{\_Z}^{3}+3 a \,\textit{\_Z}^{2}+a \right)}{\sum}\frac{\left(\left(19 a^{4}+28 a^{2} b^{2}-2 b^{4}\right) \textit{\_R}^{4}+18 a b \left(-4 a^{2}-b^{2}\right) \textit{\_R}^{3}+6 a^{2} \left(11 a^{2}+34 b^{2}\right) \textit{\_R}^{2}+18 a b \left(-4 a^{2}-b^{2}\right) \textit{\_R} +19 a^{4}+28 a^{2} b^{2}-2 b^{4}\right) \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{5} a +2 \textit{\_R}^{3} a +4 \textit{\_R}^{2} b +\textit{\_R} a}\right)}{9 d \left(a -b \right)^{3} \left(a +b \right)^{3} a}"," ",0,"-1/3/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*a-4/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*b-1/3/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^2-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*a+4/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*b+2/3/d*b^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a^3*tan(1/2*d*x+1/2*c)^5+14/3/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)^5+2/3/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^5-6/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^4+16/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)^3+8/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)^3+12/d*b^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^2*a^2+12/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*tan(1/2*d*x+1/2*c)^2-2/3/d*b^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a^3*tan(1/2*d*x+1/2*c)-14/3/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a*tan(1/2*d*x+1/2*c)-2/3/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)/a*tan(1/2*d*x+1/2*c)+4/d*b^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)*a^2+2/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^6*a+3*tan(1/2*d*x+1/2*c)^4*a+8*b*tan(1/2*d*x+1/2*c)^3+3*tan(1/2*d*x+1/2*c)^2*a+a)+1/9/d*b^2/(a-b)^3/(a+b)^3/a*sum(((19*a^4+28*a^2*b^2-2*b^4)*_R^4+18*a*b*(-4*a^2-b^2)*_R^3+6*a^2*(11*a^2+34*b^2)*_R^2+18*a*b*(-4*a^2-b^2)*_R+19*a^4+28*a^2*b^2-2*b^4)/(_R^5*a+2*_R^3*a+4*_R^2*b+_R*a)*ln(tan(1/2*d*x+1/2*c)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+8*_Z^3*b+3*_Z^2*a+a))","B"
404,1,350,101,0.631000," ","int(cos(d*x+c)^7/(a-b*sin(d*x+c)^4),x)","\frac{\sin^{3}\left(d x +c \right)}{3 b d}-\frac{3 \sin \left(d x +c \right)}{b d}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d a}+\frac{a \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{a \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \,b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{3 \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"1/3*sin(d*x+c)^3/b/d-3*sin(d*x+c)/b/d+3/2/d/b*(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))+3/4/d/b*(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/4/d*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/2/d/b^2/(a/b)^(1/4)*a*arctan(sin(d*x+c)/(a/b)^(1/4))+3/2/d/b/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/4/d/b^2/(a/b)^(1/4)*a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))-3/4/d/b/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
405,1,252,85,0.612000," ","int(cos(d*x+c)^5/(a-b*sin(d*x+c)^4),x)","-\frac{\sin \left(d x +c \right)}{b d}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d a}+\frac{\arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"-sin(d*x+c)/b/d+1/2/d/b*(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))+1/4/d/b*(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/4/d*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/d/b/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/2/d/b/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
406,1,160,67,0.610000," ","int(cos(d*x+c)^3/(a-b*sin(d*x+c)^4),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d a}+\frac{\arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d b \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"1/4/d*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/2/d*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d/b/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/4/d/b/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
407,1,81,51,0.227000," ","int(cos(d*x+c)/(a-b*sin(d*x+c)^4),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d a}"," ",0,"1/4/d*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/2/d*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))","A"
408,1,229,89,0.613000," ","int(sec(d*x+c)/(a-b*sin(d*x+c)^4),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a -2 b \right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}-\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right) a}-\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right) a}+\frac{\arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right) \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"-1/d/(2*a-2*b)*ln(sin(d*x+c)-1)+1/d/(2*a-2*b)*ln(1+sin(d*x+c))-1/4/d*b/(a-b)*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))-1/2/d*b/(a-b)*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d/(a-b)/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/4/d/(a-b)/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
409,1,415,141,0.704000," ","int(sec(d*x+c)^3/(a-b*sin(d*x+c)^4),x)","-\frac{1}{d \left(4 a -4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a -b \right)^{2}}+\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a -b \right)^{2}}-\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}-\frac{5 b \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}+\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{2}}+\frac{b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{2} a}+\frac{b \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{2}}+\frac{b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{2} a}-\frac{b \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{d \left(a -b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{b \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"-1/d/(4*a-4*b)/(sin(d*x+c)-1)-1/4/d/(a-b)^2*ln(sin(d*x+c)-1)*a+5/4/d/(a-b)^2*ln(sin(d*x+c)-1)*b-1/d/(4*a-4*b)/(1+sin(d*x+c))+1/4*a*ln(1+sin(d*x+c))/(a-b)^2/d-5/4*b*ln(1+sin(d*x+c))/(a-b)^2/d+1/2/d*b/(a-b)^2*(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d*b^2/(a-b)^2*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))+1/4/d*b/(a-b)^2*(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/4/d*b^2/(a-b)^2*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))-1/d*b/(a-b)^2/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))+1/2/d*b/(a-b)^2/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
410,1,660,211,0.707000," ","int(sec(d*x+c)^5/(a-b*sin(d*x+c)^4),x)","\frac{1}{2 d \left(8 a -8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3 a}{16 d \left(a -b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{11 b}{16 d \left(a -b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a -b \right)^{3}}+\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a b}{8 d \left(a -b \right)^{3}}-\frac{35 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a -b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{11 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a b}{8 d \left(a -b \right)^{3}}+\frac{35 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}-\frac{3 b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{3}}-\frac{b^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{3} a}-\frac{3 b^{2} \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{3}}-\frac{b^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{3} a}+\frac{b a \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{3 b^{2} \arctan \left(\frac{\sin \left(d x +c \right)}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 d \left(a -b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{b a \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{3 b^{2} \ln \left(\frac{\sin \left(d x +c \right)+\left(\frac{a}{b}\right)^{\frac{1}{4}}}{\sin \left(d x +c \right)-\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 d \left(a -b \right)^{3} \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"1/2/d/(8*a-8*b)/(sin(d*x+c)-1)^2-3/16/d/(a-b)^2/(sin(d*x+c)-1)*a+11/16/d/(a-b)^2/(sin(d*x+c)-1)*b-3/16/d/(a-b)^3*ln(sin(d*x+c)-1)*a^2+3/8/d/(a-b)^3*ln(sin(d*x+c)-1)*a*b-35/16/d/(a-b)^3*ln(sin(d*x+c)-1)*b^2-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-3/16/d/(a-b)^2/(1+sin(d*x+c))*a+11/16/d/(a-b)^2/(1+sin(d*x+c))*b+3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-3/8/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+35/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2-3/2/d*b^2/(a-b)^3*(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/2/d*b^3/(a-b)^3*(a/b)^(1/4)/a*arctan(sin(d*x+c)/(a/b)^(1/4))-3/4/d*b^2/(a-b)^3*(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))-1/4/d*b^3/(a-b)^3*(a/b)^(1/4)/a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))+1/2/d*b/(a-b)^3/(a/b)^(1/4)*a*arctan(sin(d*x+c)/(a/b)^(1/4))+3/2/d*b^2/(a-b)^3/(a/b)^(1/4)*arctan(sin(d*x+c)/(a/b)^(1/4))-1/4/d*b/(a-b)^3/(a/b)^(1/4)*a*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))-3/4/d*b^2/(a-b)^3/(a/b)^(1/4)*ln((sin(d*x+c)+(a/b)^(1/4))/(sin(d*x+c)-(a/b)^(1/4)))","B"
411,1,880,200,0.667000," ","int(cos(d*x+c)^10/(a-b*sin(d*x+c)^4),x)","-\frac{\left(\tan^{5}\left(d x +c \right)\right) a}{2 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{41 \left(\tan^{5}\left(d x +c \right)\right)}{16 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) a}{d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{35 \left(\tan^{3}\left(d x +c \right)\right)}{6 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{\tan \left(d x +c \right) a}{2 d \,b^{2} \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{55 \tan \left(d x +c \right)}{16 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{3}}-\frac{9 \arctan \left(\tan \left(d x +c \right)\right) a}{2 d \,b^{2}}-\frac{105 \arctan \left(\tan \left(d x +c \right)\right)}{16 d b}+\frac{2 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{d \,b^{2} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{3}}{2 d \,b^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{5 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{5 a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{2 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{d \,b^{2} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{3}}{2 d \,b^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{5 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{5 a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{2 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{2 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/2/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)^5*a-41/16/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)^5-1/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)^3*a-35/6/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)^3-1/2/d/b^2/(tan(d*x+c)^2+1)^3*tan(d*x+c)*a-55/16/d/b/(tan(d*x+c)^2+1)^3*tan(d*x+c)-9/2/d/b^2*arctan(tan(d*x+c))*a-105/16/d/b*arctan(tan(d*x+c))+2/d/b^2/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+1/2/d/b^2/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^3+5/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2-5/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+2/d/b^2/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2-1/2/d/b^2/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^3-5/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+5/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-2/d/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-2/d/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
412,1,750,144,0.678000," ","int(cos(d*x+c)^8/(a-b*sin(d*x+c)^4),x)","-\frac{11 \left(\tan^{3}\left(d x +c \right)\right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{13 \tan \left(d x +c \right)}{8 d b \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{35 \arctan \left(\tan \left(d x +c \right)\right)}{8 d b}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a}{d \,b^{2}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{2 d \,b^{2} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d b \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{2 d \,b^{2} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d b \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-11/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3-13/8/d/b/(tan(d*x+c)^2+1)^2*tan(d*x+c)-35/8/d/b*arctan(tan(d*x+c))-1/d/b^2*arctan(tan(d*x+c))*a+1/2/d/b^2/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+1/d/b*a/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+3/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2-1/d*a/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/b^2/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+1/d/b*a/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-3/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+1/d*a/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-3/2/d/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-3/2/d/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
413,1,483,111,0.655000," ","int(cos(d*x+c)^6/(a-b*sin(d*x+c)^4),x)","-\frac{\tan \left(d x +c \right)}{2 d b \left(\tan^{2}\left(d x +c \right)+1\right)}-\frac{5 \arctan \left(\tan \left(d x +c \right)\right)}{2 d b}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d b \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{2 d b \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d b \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/2/d/b*tan(d*x+c)/(tan(d*x+c)^2+1)-5/2/d/b*arctan(tan(d*x+c))+1/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+1/d/b*a/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2+1/d/b*a/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/d/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/d/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
414,1,449,91,0.616000," ","int(cos(d*x+c)^4/(a-b*sin(d*x+c)^4),x)","-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d b}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d b \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"-1/d/b*arctan(tan(d*x+c))+1/2/d/b*a/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d/b*a/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
415,1,226,85,0.579000," ","int(cos(d*x+c)^2/(a-b*sin(d*x+c)^4),x)","\frac{a \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{a \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*a/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*b/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
416,1,393,102,0.702000," ","int(sec(d*x+c)^2/(a-b*sin(d*x+c)^4),x)","\frac{\tan \left(d x +c \right)}{\left(a -b \right) d}+\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d \left(a -b \right) \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{\arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) b^{2}}{2 d \sqrt{a b}\, \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d \left(a -b \right) \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"tan(d*x+c)/(a-b)/d+1/2/d*b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a+1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*b^2-1/d*b/(a-b)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-1/2/d*b/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a-1/2/d/(a*b)^(1/2)/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*b^2-1/d*b/(a-b)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
417,1,581,123,0.762000," ","int(sec(d*x+c)^4/(a-b*sin(d*x+c)^4),x)","\frac{\left(\tan^{3}\left(d x +c \right)\right) a}{3 d \left(a -b \right)^{2}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{3 d \left(a -b \right)^{2}}+\frac{\tan \left(d x +c \right) a}{d \left(a -b \right)^{2}}-\frac{3 \tan \left(d x +c \right) b}{d \left(a -b \right)^{2}}+\frac{b \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a}{2 d \left(a -b \right)^{2} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{2} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{3 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a}{2 d \left(a -b \right)^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a}{2 d \left(a -b \right)^{2} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{2} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{3 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a}{2 d \left(a -b \right)^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}+\frac{b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{2} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/3/d/(a-b)^2*tan(d*x+c)^3*a-1/3/d/(a-b)^2*tan(d*x+c)^3*b+1/d/(a-b)^2*tan(d*x+c)*a-3/d/(a-b)^2*tan(d*x+c)*b+1/2/d*b/(a-b)^2/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a+3/2/d*b^2/(a-b)^2/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-3/2/d*b^2/(a-b)^2/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a-1/2/d*b^3/(a-b)^2/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*b/(a-b)^2/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a+3/2/d*b^2/(a-b)^2/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))+3/2/d*b^2/(a-b)^2/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a+1/2/d*b^3/(a-b)^2/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
418,1,839,160,0.765000," ","int(sec(d*x+c)^6/(a-b*sin(d*x+c)^4),x)","\frac{\left(\tan^{5}\left(d x +c \right)\right) a^{2}}{5 d \left(a -b \right)^{3}}-\frac{2 \left(\tan^{5}\left(d x +c \right)\right) a b}{5 d \left(a -b \right)^{3}}+\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{2}}{5 d \left(a -b \right)^{3}}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{2}}{3 d \left(a -b \right)^{3}}-\frac{2 \left(\tan^{3}\left(d x +c \right)\right) b a}{d \left(a -b \right)^{3}}+\frac{4 \left(\tan^{3}\left(d x +c \right)\right) b^{2}}{3 d \left(a -b \right)^{3}}+\frac{a^{2} \tan \left(d x +c \right)}{d \left(a -b \right)^{3}}-\frac{3 a b \tan \left(d x +c \right)}{d \left(a -b \right)^{3}}+\frac{6 b^{2} \tan \left(d x +c \right)}{d \left(a -b \right)^{3}}-\frac{2 b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a}{d \left(a -b \right)^{3} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{2 b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{d \left(a -b \right)^{3} \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{2} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a^{2}}{2 d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{3 b^{3} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right) a}{d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}+\frac{b^{4} \arctanh \left(\frac{\left(-a +b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}-a \right) \left(a -b \right)}}-\frac{2 b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a}{d \left(a -b \right)^{3} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{2 b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{d \left(a -b \right)^{3} \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{2} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a^{2}}{2 d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{3 b^{3} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right) a}{d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}-\frac{b^{4} \arctan \left(\frac{\left(a -b \right) \tan \left(d x +c \right)}{\sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}\right)}{2 d \left(a -b \right)^{3} \sqrt{a b}\, \sqrt{\left(\sqrt{a b}+a \right) \left(a -b \right)}}"," ",0,"1/5/d/(a-b)^3*tan(d*x+c)^5*a^2-2/5/d/(a-b)^3*tan(d*x+c)^5*a*b+1/5/d/(a-b)^3*tan(d*x+c)^5*b^2+2/3/d/(a-b)^3*tan(d*x+c)^3*a^2-2/d/(a-b)^3*tan(d*x+c)^3*b*a+4/3/d/(a-b)^3*tan(d*x+c)^3*b^2+1/d/(a-b)^3*a^2*tan(d*x+c)-3/d/(a-b)^3*a*b*tan(d*x+c)+6/d/(a-b)^3*b^2*tan(d*x+c)-2/d*b^2/(a-b)^3/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a-2/d*b^3/(a-b)^3/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))+1/2/d*b^2/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a^2+3/d*b^3/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))*a+1/2/d*b^4/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)-a)*(a-b))^(1/2)*arctanh((-a+b)*tan(d*x+c)/(((a*b)^(1/2)-a)*(a-b))^(1/2))-2/d*b^2/(a-b)^3/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a-2/d*b^3/(a-b)^3/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))-1/2/d*b^2/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a^2-3/d*b^3/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))*a-1/2/d*b^4/(a-b)^3/(a*b)^(1/2)/(((a*b)^(1/2)+a)*(a-b))^(1/2)*arctan((a-b)*tan(d*x+c)/(((a*b)^(1/2)+a)*(a-b))^(1/2))","B"
419,0,0,25,4.550000," ","int(cos(f*x+e)^m*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\cos^{m}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^m*(a+b*sin(f*x+e)^4)^p,x)","F"
420,0,0,191,5.240000," ","int(cos(f*x+e)^5*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^5*(a+b*sin(f*x+e)^4)^p,x)","F"
421,0,0,134,10.180000," ","int(cos(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x)","F"
422,0,0,65,4.067000," ","int(cos(f*x+e)*(a+b*sin(f*x+e)^4)^p,x)","\int \cos \left(f x +e \right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(a+b*sin(f*x+e)^4)^p,x)","F"
423,0,0,148,2.944000," ","int(sec(f*x+e)*(a+b*sin(f*x+e)^4)^p,x)","\int \sec \left(f x +e \right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(a+b*sin(f*x+e)^4)^p,x)","F"
424,0,0,223,2.916000," ","int(sec(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*sin(f*x+e)^4)^p,x)","F"
425,0,0,25,8.284000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x)","F"
426,0,0,25,9.685000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x)","F"
427,0,0,16,2.142000," ","int((a+b*sin(f*x+e)^4)^p,x)","\int \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e)^4)^p,x)","F"
428,0,0,25,2.365000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*sin(f*x+e)^4)^p,x)","F"
429,0,0,25,1.836000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{4}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(a+b*sin(f*x+e)^4)^p,x)","F"
430,0,0,25,2.606000," ","int(cos(f*x+e)^m*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\cos^{m}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^m*(a+b*sin(f*x+e)^n)^p,x)","F"
431,0,0,228,1.690000," ","int(cos(f*x+e)^5*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^5*(a+b*sin(f*x+e)^n)^p,x)","F"
432,0,0,150,1.722000," ","int(cos(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x)","F"
433,0,0,71,1.030000," ","int(cos(f*x+e)*(a+b*sin(f*x+e)^n)^p,x)","\int \cos \left(f x +e \right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)*(a+b*sin(f*x+e)^n)^p,x)","F"
434,0,0,23,0.848000," ","int(sec(f*x+e)*(a+b*sin(f*x+e)^n)^p,x)","\int \sec \left(f x +e \right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)*(a+b*sin(f*x+e)^n)^p,x)","F"
435,0,0,25,0.864000," ","int(sec(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^3*(a+b*sin(f*x+e)^n)^p,x)","F"
436,0,0,25,1.587000," ","int(cos(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x)","F"
437,0,0,25,1.310000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x)","F"
438,0,0,16,0.621000," ","int((a+b*sin(f*x+e)^n)^p,x)","\int \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e)^n)^p,x)","F"
439,0,0,25,0.818000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^2*(a+b*sin(f*x+e)^n)^p,x)","F"
440,0,0,25,0.885000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +b \left(\sin^{n}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int(sec(f*x+e)^4*(a+b*sin(f*x+e)^n)^p,x)","F"
441,1,170,120,0.528000," ","int(tan(d*x+c)^7/(a+b*sin(d*x+c)^2),x)","-\frac{a^{3} \ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d \left(a +b \right)^{4}}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{\left(a +b \right)^{4} d}-\frac{3 a}{4 d \left(a +b \right)^{2} \cos \left(d x +c \right)^{4}}-\frac{b}{2 d \left(a +b \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{2}}{2 d \left(a +b \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{3 a b}{2 d \left(a +b \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{b^{2}}{2 d \left(a +b \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{1}{6 d \left(a +b \right) \cos \left(d x +c \right)^{6}}"," ",0,"-1/2/d*a^3/(a+b)^4*ln(b*cos(d*x+c)^2-a-b)+a^3*ln(cos(d*x+c))/(a+b)^4/d-3/4/d/(a+b)^2/cos(d*x+c)^4*a-1/2/d/(a+b)^2/cos(d*x+c)^4*b+3/2/d/(a+b)^3/cos(d*x+c)^2*a^2+3/2/d/(a+b)^3/cos(d*x+c)^2*a*b+1/2/d/(a+b)^3/cos(d*x+c)^2*b^2+1/6/d/(a+b)/cos(d*x+c)^6","A"
442,1,109,88,0.459000," ","int(tan(d*x+c)^5/(a+b*sin(d*x+c)^2),x)","\frac{a^{2} \ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d \left(a +b \right)^{3}}-\frac{a}{d \left(a +b \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{b}{2 d \left(a +b \right)^{2} \cos \left(d x +c \right)^{2}}+\frac{1}{4 d \left(a +b \right) \cos \left(d x +c \right)^{4}}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{\left(a +b \right)^{3} d}"," ",0,"1/2/d*a^2/(a+b)^3*ln(b*cos(d*x+c)^2-a-b)-1/d/(a+b)^2/cos(d*x+c)^2*a-1/2/d/(a+b)^2/cos(d*x+c)^2*b+1/4/d/(a+b)/cos(d*x+c)^4-a^2*ln(cos(d*x+c))/(a+b)^3/d","A"
443,1,66,60,0.492000," ","int(tan(d*x+c)^3/(a+b*sin(d*x+c)^2),x)","-\frac{a \ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d \left(a +b \right)^{2}}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{\left(a +b \right)^{2} d}+\frac{1}{2 d \left(a +b \right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/2/d*a/(a+b)^2*ln(b*cos(d*x+c)^2-a-b)+a*ln(cos(d*x+c))/(a+b)^2/d+1/2/d/(a+b)/cos(d*x+c)^2","A"
444,1,47,41,0.437000," ","int(tan(d*x+c)/(a+b*sin(d*x+c)^2),x)","\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d \left(a +b \right)}-\frac{\ln \left(\cos \left(d x +c \right)\right)}{\left(a +b \right) d}"," ",0,"1/2/d/(a+b)*ln(b*cos(d*x+c)^2-a-b)-ln(cos(d*x+c))/(a+b)/d","A"
445,1,37,36,0.303000," ","int(cot(d*x+c)/(a+b*sin(d*x+c)^2),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)}{2 d a}"," ",0,"ln(sin(d*x+c))/a/d-1/2*ln(a+b*sin(d*x+c)^2)/d/a","A"
446,1,161,59,0.662000," ","int(cot(d*x+c)^3/(a+b*sin(d*x+c)^2),x)","\frac{1}{4 d a \left(\cos \left(d x +c \right)-1\right)}-\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d a}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{2 d \,a^{2}}+\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d a}+\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b}{2 d \,a^{2}}-\frac{1}{4 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d a}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{2 d \,a^{2}}"," ",0,"1/4/d/a/(cos(d*x+c)-1)-1/2/d/a*ln(cos(d*x+c)-1)-1/2/d/a^2*ln(cos(d*x+c)-1)*b+1/2/d/a*ln(b*cos(d*x+c)^2-a-b)+1/2/d/a^2*ln(b*cos(d*x+c)^2-a-b)*b-1/4/a/d/(1+cos(d*x+c))-1/2/d/a*ln(1+cos(d*x+c))-1/2/d/a^2*ln(1+cos(d*x+c))*b","B"
447,1,302,83,0.636000," ","int(cot(d*x+c)^5/(a+b*sin(d*x+c)^2),x)","-\frac{1}{16 d a \left(\cos \left(d x +c \right)-1\right)^{2}}-\frac{7}{16 d a \left(\cos \left(d x +c \right)-1\right)}-\frac{b}{4 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d a}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{d \,a^{2}}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) b^{2}}{2 d \,a^{3}}-\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d a}-\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b}{d \,a^{2}}-\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b^{2}}{2 d \,a^{3}}-\frac{1}{16 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{7}{16 a d \left(1+\cos \left(d x +c \right)\right)}+\frac{b}{4 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d a}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b}{d \,a^{2}}+\frac{\ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{2 d \,a^{3}}"," ",0,"-1/16/d/a/(cos(d*x+c)-1)^2-7/16/d/a/(cos(d*x+c)-1)-1/4/d/a^2/(cos(d*x+c)-1)*b+1/2/d/a*ln(cos(d*x+c)-1)+1/d/a^2*ln(cos(d*x+c)-1)*b+1/2/d/a^3*ln(cos(d*x+c)-1)*b^2-1/2/d/a*ln(b*cos(d*x+c)^2-a-b)-1/d/a^2*ln(b*cos(d*x+c)^2-a-b)*b-1/2/d/a^3*ln(b*cos(d*x+c)^2-a-b)*b^2-1/16/a/d/(1+cos(d*x+c))^2+7/16/a/d/(1+cos(d*x+c))+1/4/d/a^2/(1+cos(d*x+c))*b+1/2/d/a*ln(1+cos(d*x+c))+1/d/a^2*ln(1+cos(d*x+c))*b+1/2/d/a^3*ln(1+cos(d*x+c))*b^2","B"
448,1,489,113,0.643000," ","int(cot(d*x+c)^7/(a+b*sin(d*x+c)^2),x)","\frac{1}{48 d a \left(\cos \left(d x +c \right)-1\right)^{3}}+\frac{5}{32 d a \left(\cos \left(d x +c \right)-1\right)^{2}}+\frac{b}{16 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)^{2}}+\frac{19}{32 d a \left(\cos \left(d x +c \right)-1\right)}+\frac{11 b}{16 d \,a^{2} \left(\cos \left(d x +c \right)-1\right)}+\frac{b^{2}}{4 d \,a^{3} \left(\cos \left(d x +c \right)-1\right)}-\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{2 d a}-\frac{3 \ln \left(\cos \left(d x +c \right)-1\right) b}{2 d \,a^{2}}-\frac{3 \ln \left(\cos \left(d x +c \right)-1\right) b^{2}}{2 d \,a^{3}}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b^{3}}{2 d \,a^{4}}+\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right)}{2 d a}+\frac{3 \ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b}{2 d \,a^{2}}+\frac{3 \ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b^{2}}{2 d \,a^{3}}+\frac{\ln \left(b \left(\cos^{2}\left(d x +c \right)\right)-a -b \right) b^{3}}{2 d \,a^{4}}-\frac{1}{48 d a \left(1+\cos \left(d x +c \right)\right)^{3}}+\frac{5}{32 a d \left(1+\cos \left(d x +c \right)\right)^{2}}+\frac{b}{16 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)^{2}}-\frac{19}{32 a d \left(1+\cos \left(d x +c \right)\right)}-\frac{11 b}{16 d \,a^{2} \left(1+\cos \left(d x +c \right)\right)}-\frac{b^{2}}{4 d \,a^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{2 d a}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right) b}{2 d \,a^{2}}-\frac{3 \ln \left(1+\cos \left(d x +c \right)\right) b^{2}}{2 d \,a^{3}}-\frac{\ln \left(1+\cos \left(d x +c \right)\right) b^{3}}{2 d \,a^{4}}"," ",0,"1/48/d/a/(cos(d*x+c)-1)^3+5/32/d/a/(cos(d*x+c)-1)^2+1/16/d/a^2/(cos(d*x+c)-1)^2*b+19/32/d/a/(cos(d*x+c)-1)+11/16/d/a^2/(cos(d*x+c)-1)*b+1/4/d/a^3/(cos(d*x+c)-1)*b^2-1/2/d/a*ln(cos(d*x+c)-1)-3/2/d/a^2*ln(cos(d*x+c)-1)*b-3/2/d/a^3*ln(cos(d*x+c)-1)*b^2-1/2/d/a^4*ln(cos(d*x+c)-1)*b^3+1/2/d/a*ln(b*cos(d*x+c)^2-a-b)+3/2/d/a^2*ln(b*cos(d*x+c)^2-a-b)*b+3/2/d/a^3*ln(b*cos(d*x+c)^2-a-b)*b^2+1/2/d/a^4*ln(b*cos(d*x+c)^2-a-b)*b^3-1/48/d/a/(1+cos(d*x+c))^3+5/32/a/d/(1+cos(d*x+c))^2+1/16/d/a^2/(1+cos(d*x+c))^2*b-19/32/a/d/(1+cos(d*x+c))-11/16/d/a^2/(1+cos(d*x+c))*b-1/4/d/a^3/(1+cos(d*x+c))*b^2-1/2/d/a*ln(1+cos(d*x+c))-3/2/d/a^2*ln(1+cos(d*x+c))*b-3/2/d/a^3*ln(1+cos(d*x+c))*b^2-1/2/d/a^4*ln(1+cos(d*x+c))*b^3","B"
449,1,252,106,0.552000," ","int(tan(d*x+c)^8/(a+b*sin(d*x+c)^2),x)","\frac{\left(\tan^{7}\left(d x +c \right)\right) a^{3}}{7 d \left(a +b \right)^{4}}+\frac{3 \left(\tan^{7}\left(d x +c \right)\right) a^{2} b}{7 d \left(a +b \right)^{4}}+\frac{3 \left(\tan^{7}\left(d x +c \right)\right) a \,b^{2}}{7 d \left(a +b \right)^{4}}+\frac{\left(\tan^{7}\left(d x +c \right)\right) b^{3}}{7 d \left(a +b \right)^{4}}-\frac{a^{3} \left(\tan^{5}\left(d x +c \right)\right)}{5 d \left(a +b \right)^{4}}-\frac{2 a^{2} \left(\tan^{5}\left(d x +c \right)\right) b}{5 d \left(a +b \right)^{4}}-\frac{\left(\tan^{5}\left(d x +c \right)\right) a \,b^{2}}{5 d \left(a +b \right)^{4}}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{3}}{3 d \left(a +b \right)^{4}}+\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2} b}{3 d \left(a +b \right)^{4}}-\frac{a^{3} \tan \left(d x +c \right)}{\left(a +b \right)^{4} d}+\frac{a^{4} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a +b \right)^{4} \sqrt{a \left(a +b \right)}}"," ",0,"1/7/d/(a+b)^4*tan(d*x+c)^7*a^3+3/7/d/(a+b)^4*tan(d*x+c)^7*a^2*b+3/7/d/(a+b)^4*tan(d*x+c)^7*a*b^2+1/7/d/(a+b)^4*tan(d*x+c)^7*b^3-1/5/d/(a+b)^4*a^3*tan(d*x+c)^5-2/5/d/(a+b)^4*a^2*tan(d*x+c)^5*b-1/5/d/(a+b)^4*tan(d*x+c)^5*a*b^2+1/3/d/(a+b)^4*tan(d*x+c)^3*a^3+1/3/d/(a+b)^4*tan(d*x+c)^3*a^2*b-a^3*tan(d*x+c)/(a+b)^4/d+1/d*a^4/(a+b)^4/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","B"
450,1,161,85,0.542000," ","int(tan(d*x+c)^6/(a+b*sin(d*x+c)^2),x)","\frac{\left(\tan^{5}\left(d x +c \right)\right) a^{2}}{5 d \left(a +b \right)^{3}}+\frac{2 \left(\tan^{5}\left(d x +c \right)\right) a b}{5 d \left(a +b \right)^{3}}+\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{2}}{5 d \left(a +b \right)^{3}}-\frac{a^{2} \left(\tan^{3}\left(d x +c \right)\right)}{3 \left(a +b \right)^{3} d}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b a}{3 d \left(a +b \right)^{3}}+\frac{a^{2} \tan \left(d x +c \right)}{\left(a +b \right)^{3} d}-\frac{a^{3} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a +b \right)^{3} \sqrt{a \left(a +b \right)}}"," ",0,"1/5/d/(a+b)^3*tan(d*x+c)^5*a^2+2/5/d/(a+b)^3*tan(d*x+c)^5*a*b+1/5/d/(a+b)^3*tan(d*x+c)^5*b^2-1/3*a^2*tan(d*x+c)^3/(a+b)^3/d-1/3/d/(a+b)^3*tan(d*x+c)^3*b*a+a^2*tan(d*x+c)/(a+b)^3/d-1/d*a^3/(a+b)^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
451,1,94,64,0.490000," ","int(tan(d*x+c)^4/(a+b*sin(d*x+c)^2),x)","\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 \left(a +b \right)^{2} d}+\frac{\left(\tan^{3}\left(d x +c \right)\right) b}{3 d \left(a +b \right)^{2}}-\frac{a \tan \left(d x +c \right)}{\left(a +b \right)^{2} d}+\frac{a^{2} \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a +b \right)^{2} \sqrt{a \left(a +b \right)}}"," ",0,"1/3*a*tan(d*x+c)^3/(a+b)^2/d+1/3/d/(a+b)^2*tan(d*x+c)^3*b-a*tan(d*x+c)/(a+b)^2/d+1/d*a^2/(a+b)^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
452,1,53,45,0.408000," ","int(tan(d*x+c)^2/(a+b*sin(d*x+c)^2),x)","\frac{\tan \left(d x +c \right)}{\left(a +b \right) d}-\frac{a \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \left(a +b \right) \sqrt{a \left(a +b \right)}}"," ",0,"tan(d*x+c)/(a+b)/d-1/d*a/(a+b)/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))","A"
453,1,82,44,0.470000," ","int(cot(d*x+c)^2/(a+b*sin(d*x+c)^2),x)","-\frac{1}{d a \tan \left(d x +c \right)}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \sqrt{a \left(a +b \right)}}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \sqrt{a \left(a +b \right)}}"," ",0,"-1/d/a/tan(d*x+c)-1/d/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-1/d/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b","A"
454,1,147,61,0.551000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c)^2),x)","\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \sqrt{a \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{d \,a^{2} \sqrt{a \left(a +b \right)}}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}+\frac{1}{d a \tan \left(d x +c \right)}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)}"," ",0,"1/d/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+2/d/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b+1/d/a^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2-1/3/d/a/tan(d*x+c)^3+1/d/a/tan(d*x+c)+1/d/a^2/tan(d*x+c)*b","B"
455,1,239,84,0.666000," ","int(cot(d*x+c)^6/(a+b*sin(d*x+c)^2),x)","-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \sqrt{a \left(a +b \right)}}-\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \sqrt{a \left(a +b \right)}}-\frac{3 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{d \,a^{2} \sqrt{a \left(a +b \right)}}-\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{3}}{d \,a^{3} \sqrt{a \left(a +b \right)}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{2 b}{d \,a^{2} \tan \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \tan \left(d x +c \right)}-\frac{1}{5 d a \tan \left(d x +c \right)^{5}}+\frac{1}{3 d a \tan \left(d x +c \right)^{3}}+\frac{b}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}"," ",0,"-1/d/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))-3/d/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b-3/d/a^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2-1/d/a^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^3-1/d/a/tan(d*x+c)-2/d/a^2/tan(d*x+c)*b-1/d/a^3/tan(d*x+c)*b^2-1/5/d/a/tan(d*x+c)^5+1/3/d/a/tan(d*x+c)^3+1/3/d/a^2/tan(d*x+c)^3*b","B"
456,1,342,103,0.681000," ","int(cot(d*x+c)^8/(a+b*sin(d*x+c)^2),x)","\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right)}{d \sqrt{a \left(a +b \right)}}+\frac{4 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b}{d a \sqrt{a \left(a +b \right)}}+\frac{6 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{2}}{d \,a^{2} \sqrt{a \left(a +b \right)}}+\frac{4 \arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{3}}{d \,a^{3} \sqrt{a \left(a +b \right)}}+\frac{\arctan \left(\frac{\left(a +b \right) \tan \left(d x +c \right)}{\sqrt{a \left(a +b \right)}}\right) b^{4}}{d \,a^{4} \sqrt{a \left(a +b \right)}}+\frac{1}{d a \tan \left(d x +c \right)}+\frac{3 b}{d \,a^{2} \tan \left(d x +c \right)}+\frac{3 b^{2}}{d \,a^{3} \tan \left(d x +c \right)}+\frac{b^{3}}{d \,a^{4} \tan \left(d x +c \right)}+\frac{1}{5 d a \tan \left(d x +c \right)^{5}}+\frac{b}{5 d \,a^{2} \tan \left(d x +c \right)^{5}}-\frac{1}{7 d a \tan \left(d x +c \right)^{7}}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}-\frac{2 b}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{b^{2}}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}"," ",0,"1/d/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))+4/d/a/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b+6/d/a^2/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^2+4/d/a^3/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^3+1/d/a^4/(a*(a+b))^(1/2)*arctan((a+b)*tan(d*x+c)/(a*(a+b))^(1/2))*b^4+1/d/a/tan(d*x+c)+3/d/a^2/tan(d*x+c)*b+3/d/a^3/tan(d*x+c)*b^2+1/d/a^4/tan(d*x+c)*b^3+1/5/d/a/tan(d*x+c)^5+1/5/d/a^2/tan(d*x+c)^5*b-1/7/d/a/tan(d*x+c)^7-1/3/d/a/tan(d*x+c)^3-2/3/d/a^2/tan(d*x+c)^3*b-1/3/d/a^3/tan(d*x+c)^3*b^2","B"
457,1,48,56,2.511000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x)","-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(3 \left(\cos^{4}\left(f x +e \right)\right)+6 \left(\cos^{2}\left(f x +e \right)\right)-1\right)}{3 \cos \left(f x +e \right)^{4} f}"," ",0,"-1/3/cos(f*x+e)^4*(a*cos(f*x+e)^2)^(1/2)*(3*cos(f*x+e)^4+6*cos(f*x+e)^2-1)/f","A"
458,1,35,34,2.102000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x)","\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(\cos^{2}\left(f x +e \right)+1\right)}{\cos \left(f x +e \right)^{2} f}"," ",0,"1/cos(f*x+e)^2*(a*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2+1)/f","A"
459,1,21,17,0.169000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e),x)","-\frac{\sqrt{a -a \left(\sin^{2}\left(f x +e \right)\right)}}{f}"," ",0,"-1/f*(a-a*sin(f*x+e)^2)^(1/2)","A"
460,1,55,42,1.635000," ","int(cot(f*x+e)*(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a}\, \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)}{f}+\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}}{f}"," ",0,"-1/f*a^(1/2)*ln(2/sin(f*x+e)*(a^(1/2)*(a*cos(f*x+e)^2)^(1/2)+a))+(a*cos(f*x+e)^2)^(1/2)/f","A"
461,1,83,71,1.850000," ","int(cot(f*x+e)^3*(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}}{f}+\frac{3 \sqrt{a}\, \ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)}{2 f}-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}}{2 f \sin \left(f x +e \right)^{2}}"," ",0,"-(a*cos(f*x+e)^2)^(1/2)/f+3/2/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a*cos(f*x+e)^2)^(1/2))/sin(f*x+e))-1/2/f/sin(f*x+e)^2*(a*cos(f*x+e)^2)^(1/2)","A"
462,1,120,104,1.667000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^6,x)","\frac{a \left(16 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+18 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \sin \left(f x +e \right)+\left(-15 \ln \left(1+\sin \left(f x +e \right)\right)+15 \ln \left(\sin \left(f x +e \right)-1\right)\right) \left(\cos^{4}\left(f x +e \right)\right)\right)}{16 \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{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/16*a*(16*cos(f*x+e)^4*sin(f*x+e)+18*cos(f*x+e)^2*sin(f*x+e)-4*sin(f*x+e)+(-15*ln(1+sin(f*x+e))+15*ln(sin(f*x+e)-1))*cos(f*x+e)^4)/(1+sin(f*x+e))/(sin(f*x+e)-1)/cos(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
463,1,84,79,1.848000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x)","-\frac{a \left(-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 \sin \left(f x +e \right)+\left(-3 \ln \left(\sin \left(f x +e \right)-1\right)+3 \ln \left(1+\sin \left(f x +e \right)\right)\right) \left(\cos^{2}\left(f x +e \right)\right)\right)}{4 \cos \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/4*a*(-4*cos(f*x+e)^2*sin(f*x+e)-2*sin(f*x+e)+(-3*ln(sin(f*x+e)-1)+3*ln(1+sin(f*x+e)))*cos(f*x+e)^2)/cos(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
464,1,54,53,1.441000," ","int((a-a*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x)","-\frac{a \cos \left(f x +e \right) \left(2 \sin \left(f x +e \right)+\ln \left(\sin \left(f x +e \right)-1\right)-\ln \left(1+\sin \left(f x +e \right)\right)\right)}{2 \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/2*a*cos(f*x+e)*(2*sin(f*x+e)+ln(sin(f*x+e)-1)-ln(1+sin(f*x+e)))/(a*cos(f*x+e)^2)^(1/2)/f","A"
465,1,43,53,0.930000," ","int(cot(f*x+e)^2*(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\cos \left(f x +e \right) a \left(1+\sin^{2}\left(f x +e \right)\right)}{\sin \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-cos(f*x+e)*a*(1+sin(f*x+e)^2)/sin(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
466,1,55,83,0.900000," ","int(cot(f*x+e)^4*(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{\cos \left(f x +e \right) a \left(3 \left(\sin^{4}\left(f x +e \right)\right)+6 \left(\sin^{2}\left(f x +e \right)\right)-1\right)}{3 \sin \left(f x +e \right)^{3} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*cos(f*x+e)*a*(3*sin(f*x+e)^4+6*sin(f*x+e)^2-1)/sin(f*x+e)^3/(a*cos(f*x+e)^2)^(1/2)/f","A"
467,1,65,114,1.097000," ","int(cot(f*x+e)^6*(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\cos \left(f x +e \right) a \left(5 \left(\sin^{6}\left(f x +e \right)\right)+15 \left(\sin^{4}\left(f x +e \right)\right)-5 \left(\sin^{2}\left(f x +e \right)\right)+1\right)}{5 \sin \left(f x +e \right)^{5} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/5*cos(f*x+e)*a*(5*sin(f*x+e)^6+15*sin(f*x+e)^4-5*sin(f*x+e)^2+1)/sin(f*x+e)^5/(a*cos(f*x+e)^2)^(1/2)/f","A"
468,1,51,55,2.107000," ","int(tan(f*x+e)^5/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(15 \left(\cos^{4}\left(f x +e \right)\right)-10 \left(\cos^{2}\left(f x +e \right)\right)+3\right)}{15 a \cos \left(f x +e \right)^{6} f}"," ",0,"1/15/a/cos(f*x+e)^6*(a*cos(f*x+e)^2)^(1/2)*(15*cos(f*x+e)^4-10*cos(f*x+e)^2+3)/f","A"
469,1,41,36,2.139000," ","int(tan(f*x+e)^3/(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(3 \left(\cos^{2}\left(f x +e \right)\right)-1\right)}{3 a \cos \left(f x +e \right)^{4} f}"," ",0,"-1/3/a/cos(f*x+e)^4*(a*cos(f*x+e)^2)^(1/2)*(3*cos(f*x+e)^2-1)/f","A"
470,1,20,16,0.137000," ","int(tan(f*x+e)/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{1}{f \sqrt{a -a \left(\sin^{2}\left(f x +e \right)\right)}}"," ",0,"1/f/(a-a*sin(f*x+e)^2)^(1/2)","A"
471,1,40,25,1.067000," ","int(cot(f*x+e)/(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)}{\sqrt{a}\, f}"," ",0,"-1/a^(1/2)*ln((2*a+2*a^(1/2)*(a*cos(f*x+e)^2)^(1/2))/sin(f*x+e))/f","A"
472,1,69,54,1.715000," ","int(cot(f*x+e)^3/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)}{2 \sqrt{a}\, f}-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}}{2 f a \sin \left(f x +e \right)^{2}}"," ",0,"1/2/a^(1/2)*ln((2*a+2*a^(1/2)*(a*cos(f*x+e)^2)^(1/2))/sin(f*x+e))/f-1/2/f/a/sin(f*x+e)^2*(a*cos(f*x+e)^2)^(1/2)","A"
473,1,103,79,1.603000," ","int(tan(f*x+e)^4/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \sin \left(f x +e \right)+\left(3 \ln \left(\sin \left(f x +e \right)-1\right)-3 \ln \left(1+\sin \left(f x +e \right)\right)\right) \left(\cos^{4}\left(f x +e \right)\right)}{16 \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{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/16*(10*cos(f*x+e)^2*sin(f*x+e)-4*sin(f*x+e)+(3*ln(sin(f*x+e)-1)-3*ln(1+sin(f*x+e)))*cos(f*x+e)^4)/(1+sin(f*x+e))/(sin(f*x+e)-1)/cos(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
474,1,65,54,1.497000," ","int(tan(f*x+e)^2/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{\frac{\sin \left(f x +e \right)}{2}+\frac{\left(\ln \left(\sin \left(f x +e \right)-1\right)-\ln \left(1+\sin \left(f x +e \right)\right)\right) \left(\cos^{2}\left(f x +e \right)\right)}{4}}{\cos \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(1/2*sin(f*x+e)+1/4*(ln(sin(f*x+e)-1)-ln(1+sin(f*x+e)))*cos(f*x+e)^2)/cos(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
475,1,32,23,0.368000," ","int(cot(f*x+e)^2/(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\cos \left(f x +e \right)}{\sin \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-cos(f*x+e)/sin(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
476,1,44,54,0.930000," ","int(cot(f*x+e)^4/(a-a*sin(f*x+e)^2)^(1/2),x)","\frac{\cos \left(f x +e \right) \left(3 \left(\sin^{2}\left(f x +e \right)\right)-1\right)}{3 \sin \left(f x +e \right)^{3} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*cos(f*x+e)*(3*sin(f*x+e)^2-1)/sin(f*x+e)^3/(a*cos(f*x+e)^2)^(1/2)/f","A"
477,1,54,86,0.966000," ","int(cot(f*x+e)^6/(a-a*sin(f*x+e)^2)^(1/2),x)","-\frac{\cos \left(f x +e \right) \left(15 \left(\sin^{4}\left(f x +e \right)\right)-10 \left(\sin^{2}\left(f x +e \right)\right)+3\right)}{15 \sin \left(f x +e \right)^{5} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/15*cos(f*x+e)*(15*sin(f*x+e)^4-10*sin(f*x+e)^2+3)/sin(f*x+e)^5/(a*cos(f*x+e)^2)^(1/2)/f","A"
478,1,51,56,2.132000," ","int(tan(f*x+e)^5/(a-a*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(35 \left(\cos^{4}\left(f x +e \right)\right)-42 \left(\cos^{2}\left(f x +e \right)\right)+15\right)}{105 a^{2} \cos \left(f x +e \right)^{8} f}"," ",0,"1/105/a^2/cos(f*x+e)^8*(a*cos(f*x+e)^2)^(1/2)*(35*cos(f*x+e)^4-42*cos(f*x+e)^2+15)/f","A"
479,1,41,36,2.170000," ","int(tan(f*x+e)^3/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, \left(5 \left(\cos^{2}\left(f x +e \right)\right)-3\right)}{15 a^{2} \cos \left(f x +e \right)^{6} f}"," ",0,"-1/15/a^2/cos(f*x+e)^6*(a*cos(f*x+e)^2)^(1/2)*(5*cos(f*x+e)^2-3)/f","A"
480,1,21,17,0.108000," ","int(tan(f*x+e)/(a-a*sin(f*x+e)^2)^(3/2),x)","\frac{1}{3 f \left(a -a \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/3/f/(a-a*sin(f*x+e)^2)^(3/2)","A"
481,1,75,45,2.962000," ","int(cot(f*x+e)/(a-a*sin(f*x+e)^2)^(3/2),x)","\frac{-\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{2} \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{3}{2}}}{a^{\frac{7}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/a^(7/2)/cos(f*x+e)^2*(-ln(2/sin(f*x+e)*(a^(1/2)*(a*cos(f*x+e)^2)^(1/2)+a))*a^2*cos(f*x+e)^2+(a*cos(f*x+e)^2)^(1/2)*a^(3/2))/f","A"
482,1,69,54,1.605000," ","int(cot(f*x+e)^3/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}}{2 f \,a^{2} \sin \left(f x +e \right)^{2}}-\frac{\ln \left(\frac{2 \sqrt{a}\, \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)}{2 f \,a^{\frac{3}{2}}}"," ",0,"-1/2/f/a^2/sin(f*x+e)^2*(a*cos(f*x+e)^2)^(1/2)-1/2/f/a^(3/2)*ln((2*a+2*a^(1/2)*(a*cos(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
483,1,104,94,1.399000," ","int(tan(f*x+e)^2/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{-2 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \sin \left(f x +e \right)+\left(\ln \left(\sin \left(f x +e \right)-1\right)-\ln \left(1+\sin \left(f x +e \right)\right)\right) \left(\cos^{4}\left(f x +e \right)\right)}{16 a \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{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/16/a*(-2*cos(f*x+e)^2*sin(f*x+e)+4*sin(f*x+e)+(ln(sin(f*x+e)-1)-ln(1+sin(f*x+e)))*cos(f*x+e)^4)/(1+sin(f*x+e))/(sin(f*x+e)-1)/cos(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
484,1,65,59,1.365000," ","int(cot(f*x+e)^2/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\cos \left(f x +e \right) \left(2+\sin \left(f x +e \right) \left(\ln \left(\sin \left(f x +e \right)-1\right)-\ln \left(1+\sin \left(f x +e \right)\right)\right)\right)}{2 a \sin \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/2/a*cos(f*x+e)*(2+sin(f*x+e)*(ln(sin(f*x+e)-1)-ln(1+sin(f*x+e))))/sin(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
485,1,35,34,0.626000," ","int(cot(f*x+e)^4/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\cos \left(f x +e \right)}{3 a \sin \left(f x +e \right)^{3} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3/a*cos(f*x+e)/sin(f*x+e)^3/(a*cos(f*x+e)^2)^(1/2)/f","A"
486,1,67,69,1.328000," ","int(cot(f*x+e)^6/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\cos \left(f x +e \right) \left(5 \left(\cos^{2}\left(f x +e \right)\right)-2\right)}{15 \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} a \sin \left(f x +e \right) \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/15*cos(f*x+e)*(5*cos(f*x+e)^2-2)/(cos(f*x+e)+1)^2/(-1+cos(f*x+e))^2/a/sin(f*x+e)/(a*cos(f*x+e)^2)^(1/2)/f","A"
487,1,57,103,1.124000," ","int(cot(f*x+e)^8/(a-a*sin(f*x+e)^2)^(3/2),x)","-\frac{\cos \left(f x +e \right) \left(35 \left(\cos^{4}\left(f x +e \right)\right)-28 \left(\cos^{2}\left(f x +e \right)\right)+8\right)}{105 a \sin \left(f x +e \right)^{7} \sqrt{a \left(\cos^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/105/a*cos(f*x+e)*(35*cos(f*x+e)^4-28*cos(f*x+e)^2+8)/sin(f*x+e)^7/(a*cos(f*x+e)^2)^(1/2)/f","A"
488,1,721,157,5.289000," ","int((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^5,x)","\frac{\left(-16 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}} a^{2}-48 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}} a b -30 b^{2} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}}+8 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{4}+40 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3} b +71 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{2}+54 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{3}+15 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{4}+8 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{4}+40 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3} b +71 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{2}+54 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{3}+15 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{4}\right) \left(\cos^{4}\left(f x +e \right)\right)-2 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}} \left(8 a +7 b \right) \left(\cos^{2}\left(f x +e \right)\right)+4 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}} a +4 b \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(a +b \right)^{\frac{3}{2}}}{16 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{4} \left(a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/16*((-16*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2)*a^2-48*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2)*a*b-30*b^2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2)+8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4+40*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b+71*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^2+54*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^3+15*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^4+8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4+40*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b+71*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^2+54*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^3+15*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^4)*cos(f*x+e)^4-2*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(3/2)*(8*a+7*b)*cos(f*x+e)^2+4*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(3/2)*a+4*b*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(3/2))/(a+b)^(3/2)/cos(f*x+e)^4/(a^2+2*a*b+b^2)/f","B"
489,1,403,102,4.796000," ","int((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^3,x)","\frac{-\left(-4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{a +b}\, a -6 b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{a +b}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}+5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b +3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}+5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b +3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{a +b}}{4 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/4*(-(-4*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(1/2)*a-6*b*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(1/2)+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+5*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+5*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b+3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2)*cos(f*x+e)^2+2*(a+b-b*cos(f*x+e)^2)^(3/2)*(a+b)^(1/2))/(a+b)^(3/2)/cos(f*x+e)^2/f","B"
490,1,134,50,4.139000," ","int((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e),x)","\frac{\sqrt{a +b}\, \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 f}+\frac{\sqrt{a +b}\, \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 f}-\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{f}"," ",0,"1/2/f*(a+b)^(1/2)*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+1/2/f*(a+b)^(1/2)*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))-1/f*(a+b-b*cos(f*x+e)^2)^(1/2)","B"
491,1,61,46,1.459000," ","int(cot(f*x+e)*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}+\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f}"," ",0,"-1/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))+(a+b*sin(f*x+e)^2)^(1/2)/f","A"
492,1,130,94,1.541000," ","int(cot(f*x+e)^3*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f}+\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b}{2 f \sqrt{a}}-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 f \sin \left(f x +e \right)^{2}}"," ",0,"-(a+b*sin(f*x+e)^2)^(1/2)/f+1/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-1/2/f/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b-1/2/f/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)","A"
493,1,230,145,1.866000," ","int(cot(f*x+e)^5*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f}-\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}+\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b}{f \sqrt{a}}-\frac{b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f a \sin \left(f x +e \right)^{2}}+\frac{b^{2} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{8 f \,a^{\frac{3}{2}}}+\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f \sin \left(f x +e \right)^{2}}-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{4 f \sin \left(f x +e \right)^{4}}"," ",0,"(a+b*sin(f*x+e)^2)^(1/2)/f-1/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))+1/f/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b-1/8/f*b/a/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)+1/8/f*b^2/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))+1/f/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-1/4/f/sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2)","A"
494,1,380,212,2.998000," ","int((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^4,x)","-\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(4 a +5 b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 a^{2}+5 a b +3 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(4*a+5*b)*sin(f*x+e)*cos(f*x+e)^4-2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*a^2+5*a*b+3*b^2)*cos(f*x+e)^2*sin(f*x+e)+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)/(sin(f*x+e)-1)/(1+sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
495,1,294,159,2.532000," ","int((a+b*sin(f*x+e)^2)^(1/2)*tan(f*x+e)^2,x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right) \sin \left(f x +e \right)+a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-2 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*sin(f*x+e)*cos(f*x+e)^2+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a+b)*sin(f*x+e)+a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-2*a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
496,1,71,68,0.908000," ","int((a+b*sin(f*x+e)^2)^(1/2),x)","\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
497,1,156,162,1.397000," ","int(cot(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \right)+b \left(\cos^{4}\left(f x +e \right)\right)+\left(-a -b \right) \left(\cos^{2}\left(f x +e \right)\right)}{\sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(sin(f*x+e)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a)+b*cos(f*x+e)^4+(-a-b)*cos(f*x+e)^2)/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
498,1,351,210,1.634000," ","int(cot(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+4 b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+4 a b \left(\sin^{6}\left(f x +e \right)\right)-b^{2} \left(\sin^{6}\left(f x +e \right)\right)+4 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-6 a b \left(\sin^{4}\left(f x +e \right)\right)+b^{2} \left(\sin^{4}\left(f x +e \right)\right)-5 a^{2} \left(\sin^{2}\left(f x +e \right)\right)+2 a b \left(\sin^{2}\left(f x +e \right)\right)+a^{2}}{3 a \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+4*b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-7*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+4*a*b*sin(f*x+e)^6-b^2*sin(f*x+e)^6+4*a^2*sin(f*x+e)^4-6*a*b*sin(f*x+e)^4+b^2*sin(f*x+e)^4-5*a^2*sin(f*x+e)^2+2*a*b*sin(f*x+e)^2+a^2)/a/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
499,1,711,196,4.035000," ","int((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^5,x)","\frac{16 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(\cos^{6}\left(f x +e \right)\right)+\left(-64 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a -160 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b +24 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{4}+168 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3} b +369 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{2}+330 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{3}+105 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{4}+24 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{4}+168 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3} b +369 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{2}+330 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{3}+105 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{4}\right) \left(\cos^{4}\left(f x +e \right)\right)-6 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(8 a +13 b \right) \left(\cos^{2}\left(f x +e \right)\right)+12 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a +12 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b}{48 \left(a +b \right)^{\frac{5}{2}} \cos \left(f x +e \right)^{4} f}"," ",0,"1/48*(16*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b*cos(f*x+e)^6+(-64*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a-160*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b+24*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4+168*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b+369*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^2+330*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^3+105*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^4+24*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4+168*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b+369*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^2+330*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^3+105*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^4)*cos(f*x+e)^4-6*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*(8*a+13*b)*cos(f*x+e)^2+12*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a+12*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b)/(a+b)^(5/2)/cos(f*x+e)^4/f","B"
500,1,567,128,3.886000," ","int((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^3,x)","\frac{-4 \left(a +b \right)^{\frac{3}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(\cos^{4}\left(f x +e \right)\right)-\left(-16 \left(a +b \right)^{\frac{3}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a -28 \left(a +b \right)^{\frac{3}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b +6 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3}+27 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+36 a \,b^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+15 b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+6 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3}+27 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+36 a \,b^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+15 b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)\right) \left(\cos^{2}\left(f x +e \right)\right)+6 \left(a +b \right)^{\frac{3}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a +6 \left(a +b \right)^{\frac{3}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b}{12 \left(a +b \right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/12*(-4*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b*cos(f*x+e)^4-(-16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a-28*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b+6*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3+27*a^2*b*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+36*a*b^2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+15*b^3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+6*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3+27*a^2*b*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+36*a*b^2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+15*b^3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a)))*cos(f*x+e)^2+6*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a+6*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b)/(a+b)^(3/2)/cos(f*x+e)^2/f","B"
501,1,423,72,3.211000," ","int((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e),x)","\frac{\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(\cos^{2}\left(f x +e \right)\right)}{3 f}-\frac{4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a}{3 f}-\frac{4 b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{3 f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}}{2 \sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b}{\sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}}{2 \sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}}{2 \sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b}{\sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}}{2 \sqrt{a +b}\, f}"," ",0,"1/3/f*(a+b-b*cos(f*x+e)^2)^(1/2)*b*cos(f*x+e)^2-4/3/f*(a+b-b*cos(f*x+e)^2)^(1/2)*a-4/3/f*b*(a+b-b*cos(f*x+e)^2)^(1/2)+1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+1/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b+1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2+1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+1/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b+1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2","B"
502,1,91,66,1.517000," ","int(cot(f*x+e)*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{b \left(\sin^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}+\frac{4 a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}-\frac{a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}"," ",0,"1/3/f*b*sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)+4/3*a*(a+b*sin(f*x+e)^2)^(1/2)/f-1/f*a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
503,1,179,120,1.821000," ","int(cot(f*x+e)^3*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{b \left(\sin^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}-\frac{4 a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}+\frac{b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f}+\frac{a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}-\frac{3 \sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b}{2 f}-\frac{a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 f \sin \left(f x +e \right)^{2}}"," ",0,"-1/3/f*b*sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-4/3*a*(a+b*sin(f*x+e)^2)^(1/2)/f+1/f*b*(a+b*sin(f*x+e)^2)^(1/2)+1/f*a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-3/2/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b-1/2/f*a/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)","A"
504,1,280,184,1.849000," ","int(cot(f*x+e)^5*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{b \left(\sin^{2}\left(f x +e \right)\right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}+\frac{4 a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{3 f}-\frac{2 b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f}-\frac{a^{\frac{3}{2}} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f}+\frac{3 \sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b}{f}-\frac{3 \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b^{2}}{8 f \sqrt{a}}+\frac{a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f \sin \left(f x +e \right)^{2}}-\frac{5 b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f \sin \left(f x +e \right)^{2}}-\frac{a \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{4 f \sin \left(f x +e \right)^{4}}"," ",0,"1/3/f*b*sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)+4/3*a*(a+b*sin(f*x+e)^2)^(1/2)/f-2/f*b*(a+b*sin(f*x+e)^2)^(1/2)-1/f*a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))+3/f*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b-3/8/f/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b^2+1/f*a/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-5/8/f*b/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-1/4/f*a/sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2)","A"
505,1,419,251,2.839000," ","int((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^4,x)","-\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2} \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(3 a +7 b \right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(4 a^{2}+13 a b +9 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(5 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +8 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -16 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\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) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^2*sin(f*x+e)*cos(f*x+e)^6+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(3*a+7*b)*cos(f*x+e)^4*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(4*a^2+13*a*b+9*b^2)*cos(f*x+e)^2*sin(f*x+e)+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(5*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+8*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-16*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/(1+sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
506,1,515,202,2.650000," ","int((a+b*sin(f*x+e)^2)^(3/2)*tan(f*x+e)^2,x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2} \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)+4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}+4 a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}-7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a b}{3 \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^2*sin(f*x+e)*cos(f*x+e)^4-2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(a+b)*cos(f*x+e)^2*sin(f*x+e)+3*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)+4*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)+4*a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)-7*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a^2-8*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*b)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
507,1,266,180,1.387000," ","int((a+b*sin(f*x+e)^2)^(3/2),x)","\frac{-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}-\frac{a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b}{3}+\frac{4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}+\frac{2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b}{3}+\frac{b^{2} \left(\sin^{5}\left(f x +e \right)\right)}{3}+\frac{a b \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{b^{2} \left(\sin^{3}\left(f x +e \right)\right)}{3}-\frac{a b \sin \left(f x +e \right)}{3}}{\cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-1/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2-1/3*a*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b+4/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2/3*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b+1/3*b^2*sin(f*x+e)^5+1/3*a*b*sin(f*x+e)^3-1/3*b^2*sin(f*x+e)^3-1/3*a*b*sin(f*x+e))/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
508,1,204,203,1.651000," ","int(cot(f*x+e)^2*(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right)+b^{2} \left(\cos^{6}\left(f x +e \right)\right)+\left(2 a b -2 b^{2}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-3 a^{2}-2 a b +b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"1/3*(sin(f*x+e)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)+b^2*cos(f*x+e)^6+(2*a*b-2*b^2)*cos(f*x+e)^4+(-3*a^2-2*a*b+b^2)*cos(f*x+e)^2)/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
509,1,419,252,1.735000," ","int(cot(f*x+e)^4*(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{-b^{2} \left(\sin^{8}\left(f x +e \right)\right)+5 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+2 b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-3 b^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) \left(\sin^{3}\left(f x +e \right)\right)-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+3 a b \left(\sin^{6}\left(f x +e \right)\right)-3 b^{2} \left(\sin^{6}\left(f x +e \right)\right)+4 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-8 a b \left(\sin^{4}\left(f x +e \right)\right)+4 b^{2} \left(\sin^{4}\left(f x +e \right)\right)-5 a^{2} \left(\sin^{2}\left(f x +e \right)\right)+5 a b \left(\sin^{2}\left(f x +e \right)\right)+a^{2}}{3 \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(-b^2*sin(f*x+e)^8+5*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+2*b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-3*b^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*sin(f*x+e)^3-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+3*a*b*sin(f*x+e)^6-3*b^2*sin(f*x+e)^6+4*a^2*sin(f*x+e)^4-8*a*b*sin(f*x+e)^4+4*b^2*sin(f*x+e)^4-5*a^2*sin(f*x+e)^2+5*a*b*sin(f*x+e)^2+a^2)/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
510,1,644,118,3.429000," ","int(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\left(8 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{4}+24 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3} b +27 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{2}+14 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{3}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{4}+8 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{4}+24 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3} b +27 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{2}+14 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{3}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{4}\right) \left(\cos^{4}\left(f x +e \right)\right)-2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{5}{2}} \left(8 a +5 b \right) \left(\cos^{2}\left(f x +e \right)\right)+4 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a +4 \left(a +b \right)^{\frac{5}{2}} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b}{16 \left(a +b \right)^{\frac{5}{2}} \cos \left(f x +e \right)^{4} \left(a^{2}+2 a b +b^{2}\right) f}"," ",0,"1/16*((8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4+24*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b+27*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^2+14*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^3+3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^4+8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4+24*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b+27*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^2+14*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^3+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^4)*cos(f*x+e)^4-2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(5/2)*(8*a+5*b)*cos(f*x+e)^2+4*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a+4*(a+b)^(5/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b)/(a+b)^(5/2)/cos(f*x+e)^4/(a^2+2*a*b+b^2)/f","B"
511,1,353,69,3.028000," ","int(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{-\left(2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right)^{\frac{3}{2}}}{4 \left(a +b \right)^{\frac{5}{2}} \cos \left(f x +e \right)^{2} f}"," ",0,"1/4*(-(2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2)*cos(f*x+e)^2+2*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(3/2))/(a+b)^(5/2)/cos(f*x+e)^2/f","B"
512,1,113,30,2.908000," ","int(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 \sqrt{a +b}\, f}+\frac{\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 \sqrt{a +b}\, f}"," ",0,"1/2/(a+b)^(1/2)/f*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+1/2/(a+b)^(1/2)/f*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))","B"
513,1,42,27,0.982000," ","int(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{\sqrt{a}\, f}"," ",0,"-1/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))/f","A"
514,1,114,63,1.706000," ","int(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{\sqrt{a}\, f}-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{2 f a \sin \left(f x +e \right)^{2}}+\frac{b \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{2 f \,a^{\frac{3}{2}}}"," ",0,"1/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))/f-1/2/f/a/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)+1/2/f*b/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
515,1,219,110,1.970000," ","int(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{\sqrt{a}\, f}+\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f a \sin \left(f x +e \right)^{2}}-\frac{b \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{3}{2}}}-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{4 f a \sin \left(f x +e \right)^{4}}+\frac{3 b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f \,a^{2} \sin \left(f x +e \right)^{2}}-\frac{3 b^{2} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{8 f \,a^{\frac{5}{2}}}"," ",0,"-1/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))/f+1/f/a/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-1/f*b/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-1/4/f/a/sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2)+3/8/f/a^2*b/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-3/8/f/a^(5/2)*b^2*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
516,1,377,224,2.831000," ","int(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(2 a +b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(4 a^{2}+7 a b +3 b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -4 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(a +b \right)^{2} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(2*a+b)*sin(f*x+e)*cos(f*x+e)^4-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(4*a^2+7*a*b+3*b^2)*cos(f*x+e)^2*sin(f*x+e)+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-4*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(1+sin(f*x+e))/(sin(f*x+e)-1)/(a+b)^2/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
517,1,222,102,2.760000," ","int(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a +b \right) \sin \left(f x +e \right)-a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)}{\left(a +b \right) \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*sin(f*x+e)*cos(f*x+e)^2+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a+b)*sin(f*x+e)-a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))/(a+b)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","B"
518,1,60,68,0.366000," ","int(1/(a+b*sin(f*x+e)^2)^(1/2),x)","\frac{\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)-a -b}{a}}\, \mathrm{am}^{-1}\left(f x +e \bigg| \frac{i \sqrt{b}}{\sqrt{a}}\right)}{f \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}"," ",0,"1/f/(a+b-b*cos(f*x+e)^2)^(1/2)*(-(b*cos(f*x+e)^2-a-b)/a)^(1/2)*InverseJacobiAM(f*x+e,I/a^(1/2)*b^(1/2))","C"
519,1,120,99,1.578000," ","int(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \sin \left(f x +e \right) \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}{a \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-((cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*sin(f*x+e)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)/a/sin(f*x+e)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
520,1,351,218,1.964000," ","int(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2),x)","-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+4 a b \left(\sin^{6}\left(f x +e \right)\right)+2 b^{2} \left(\sin^{6}\left(f x +e \right)\right)+4 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-3 a b \left(\sin^{4}\left(f x +e \right)\right)-2 b^{2} \left(\sin^{4}\left(f x +e \right)\right)-5 a^{2} \left(\sin^{2}\left(f x +e \right)\right)-a b \left(\sin^{2}\left(f x +e \right)\right)+a^{2}}{3 a^{2} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*((cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+4*a*b*sin(f*x+e)^6+2*b^2*sin(f*x+e)^6+4*a^2*sin(f*x+e)^4-3*a*b*sin(f*x+e)^4-2*b^2*sin(f*x+e)^4-5*a^2*sin(f*x+e)^2-a*b*sin(f*x+e)^2+a^2)/a^2/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
521,1,3763,155,13.202000," ","int(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(3/2),x)","\text{output too large to display}"," ",0,"-1/16/(a^4*b^2*cos(f*x+e)^4+4*a^3*b^3*cos(f*x+e)^4+6*a^2*b^4*cos(f*x+e)^4+4*a*b^5*cos(f*x+e)^4+b^6*cos(f*x+e)^4-2*a^5*b*cos(f*x+e)^2-10*a^4*b^2*cos(f*x+e)^2-20*a^3*b^3*cos(f*x+e)^2-20*a^2*b^4*cos(f*x+e)^2-10*a*b^5*cos(f*x+e)^2-2*b^6*cos(f*x+e)^2+a^6+6*a^5*b+15*a^4*b^2+20*a^3*b^3+15*a^2*b^4+6*a*b^5+b^6)/cos(f*x+e)^4/(a+b)^(3/2)*(-4*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a^3-4*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*b^3+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^6*cos(f*x+e)^8+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^6*cos(f*x+e)^8-2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^6*cos(f*x+e)^6-2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^6*cos(f*x+e)^6-8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^6*cos(f*x+e)^4+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^6*cos(f*x+e)^4-8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^6*cos(f*x+e)^4+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^6*cos(f*x+e)^4-2*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b^4*cos(f*x+e)^8-2*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*b^3*cos(f*x+e)^6+4*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b^4*cos(f*x+e)^6+8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a^3*cos(f*x+e)^4-12*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a^2*b-12*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b^2-8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^8-8*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^8+9*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^8+10*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^8-8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^8-8*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^8+9*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^8-2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^6-38*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^6+10*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^8+16*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^5*b*cos(f*x+e)^6+32*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^6-8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^4*cos(f*x+e)^4+16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^4*cos(f*x+e)^4-2*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b^4*cos(f*x+e)^4+16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a^3*cos(f*x+e)^2+6*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*b^3*cos(f*x+e)^2-22*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^6+16*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^5*b*cos(f*x+e)^6+12*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^4-24*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^5*b*cos(f*x+e)^4-15*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^4+20*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^4+30*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^4+30*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^4+12*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^4+32*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^6-2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^6-38*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^4*cos(f*x+e)^6-22*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^5*cos(f*x+e)^6-24*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^5*b*cos(f*x+e)^4-15*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4*b^2*cos(f*x+e)^4+20*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b^3*cos(f*x+e)^4+16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b^2*cos(f*x+e)^6+16*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^3*b*cos(f*x+e)^6-64*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2*b^2*cos(f*x+e)^6-80*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b^3*cos(f*x+e)^6-32*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^3*b*cos(f*x+e)^6+36*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^3*cos(f*x+e)^6-8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a*b^2*cos(f*x+e)^4-32*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a^2*b*cos(f*x+e)^4-32*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b^2*cos(f*x+e)^4+24*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^3*b*cos(f*x+e)^4+72*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2*b^2*cos(f*x+e)^4+40*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b^3*cos(f*x+e)^4+16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^3*b*cos(f*x+e)^4-18*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2*b^2*cos(f*x+e)^4-20*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^3*cos(f*x+e)^4+38*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a^2*b*cos(f*x+e)^2+28*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b^2*cos(f*x+e)^2-8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2*b^2*cos(f*x+e)^8+40*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b^3*cos(f*x+e)^8+16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2*b^2*cos(f*x+e)^8-16*(a+b)^(3/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^3*cos(f*x+e)^8+8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a^2*b*cos(f*x+e)^6+8*(a+b)^(3/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a*b^2*cos(f*x+e)^6)/f","B"
522,1,2194,102,10.461000," ","int(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\frac{2 b^{3} \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{\sqrt{a +b}}+\frac{2 a^{3} \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{\sqrt{a +b}}+\frac{6 b \,a^{2} \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{\sqrt{a +b}}+\frac{6 b^{2} a \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}}}{\sqrt{a +b}}-\left(\cos^{6}\left(f x +e \right)\right) \left(2 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a -6 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b -4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{a +b}\, a +2 b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{a +b}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{2}\right) b^{2}+2 \left(\cos^{4}\left(f x +e \right)\right) \left(\sqrt{a +b}\, \left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} a +\sqrt{a +b}\, \left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} b +\sqrt{a +b}\, \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} b +2 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{2}-4 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a b -6 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{2}-4 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}-2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a b +2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3}+3 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)-b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3}+3 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)-b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)\right) b +\left(\cos^{2}\left(f x +e \right)\right) \left(2 \sqrt{a +b}\, \left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} a^{2}-2 \sqrt{a +b}\, \left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} b^{2}-4 \sqrt{a +b}\, \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} a b -4 \sqrt{a +b}\, \left(a +b -b \left(\cos^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} b^{2}-2 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{3}+2 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{2} b +10 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a \,b^{2}+6 \sqrt{a +b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{3}+4 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{3}+6 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2} b -2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, b^{3}-2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{4}-5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{3} b -3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a \,b^{3}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b^{4}-2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{4}-5 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{3} b -3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a \,b^{3}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b^{4}\right)}{4 \left(a^{3} b^{2} \left(\cos^{4}\left(f x +e \right)\right)+3 a^{2} b^{3} \left(\cos^{4}\left(f x +e \right)\right)+3 a \,b^{4} \left(\cos^{4}\left(f x +e \right)\right)+b^{5} \left(\cos^{4}\left(f x +e \right)\right)-2 a^{4} b \left(\cos^{2}\left(f x +e \right)\right)-8 a^{3} b^{2} \left(\cos^{2}\left(f x +e \right)\right)-12 a^{2} b^{3} \left(\cos^{2}\left(f x +e \right)\right)-8 a \,b^{4} \left(\cos^{2}\left(f x +e \right)\right)-2 b^{5} \left(\cos^{2}\left(f x +e \right)\right)+a^{5}+5 a^{4} b +10 a^{3} b^{2}+10 a^{2} b^{3}+5 a \,b^{4}+b^{5}\right) \cos \left(f x +e \right)^{2} \sqrt{a +b}\, f}"," ",0,"1/4/(a^3*b^2*cos(f*x+e)^4+3*a^2*b^3*cos(f*x+e)^4+3*a*b^4*cos(f*x+e)^4+b^5*cos(f*x+e)^4-2*a^4*b*cos(f*x+e)^2-8*a^3*b^2*cos(f*x+e)^2-12*a^2*b^3*cos(f*x+e)^2-8*a*b^4*cos(f*x+e)^2-2*b^5*cos(f*x+e)^2+a^5+5*a^4*b+10*a^3*b^2+10*a^2*b^3+5*a*b^4+b^5)/cos(f*x+e)^2/(a+b)^(1/2)*(2*b^3/(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(3/2)+2/(a+b)^(1/2)*a^3*(a+b-b*cos(f*x+e)^2)^(3/2)+6*b/(a+b)^(1/2)*a^2*(a+b-b*cos(f*x+e)^2)^(3/2)+6*b^2/(a+b)^(1/2)*a*(a+b-b*cos(f*x+e)^2)^(3/2)-cos(f*x+e)^6*(2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a-6*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b-4*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(1/2)*a+2*b*(a+b-b*cos(f*x+e)^2)^(1/2)*(a+b)^(1/2)+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^2+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^2)*b^2+2*cos(f*x+e)^4*((a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a+(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*b+(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*b+2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2-4*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b-6*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^2-4*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2-2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b+2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b^2+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3+3*a^2*b*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))-b^3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3+3*a^2*b*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))-b^3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a)))*b+cos(f*x+e)^2*(2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a^2-2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*b^2-4*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*a*b-4*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(3/2)*b^2-2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^3+2*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2*b+10*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b^2+6*(a+b)^(1/2)*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^3+4*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^3+6*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2*b-2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)*b^3-2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^4-5*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^3*b-3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^2+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a*b^3+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b^4-2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^4-5*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^3*b-3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a*b^3+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b^4))/f","B"
523,1,1317,55,8.491000," ","int(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} b^{2}-\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{3}-2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a \,b^{2}-\left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} a^{2}+\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{3}-2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{3}+a^{2} b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}-\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a \,b^{2}-4 a^{2} b \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}\, a \,b^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}\, a^{3}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}\, a \,b^{2}+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}\, a^{3}+2 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}+2 a^{2} b \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}+b^{2} \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}\, a +\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}\, a -2 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a +\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a -\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b \right) \left(\cos^{4}\left(f x +e \right)\right)-b \left(2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}\, a^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) \sqrt{a +b}\, a b +2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}\, a^{2}+2 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) \sqrt{a +b}\, a b +\left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} a +\left(-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}\right)^{\frac{3}{2}} b -4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{2}-4 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a b +2 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{2}-2 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)}{2 a \left(a^{2} b^{2} \left(\cos^{4}\left(f x +e \right)\right)+2 a \,b^{3} \left(\cos^{4}\left(f x +e \right)\right)+b^{4} \left(\cos^{4}\left(f x +e \right)\right)-2 a^{3} b \left(\cos^{2}\left(f x +e \right)\right)-6 a^{2} b^{2} \left(\cos^{2}\left(f x +e \right)\right)-6 a \,b^{3} \left(\cos^{2}\left(f x +e \right)\right)-2 b^{4} \left(\cos^{2}\left(f x +e \right)\right)+a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) f}"," ",0,"1/2/a/(a^2*b^2*cos(f*x+e)^4+2*a*b^3*cos(f*x+e)^4+b^4*cos(f*x+e)^4-2*a^3*b*cos(f*x+e)^2-6*a^2*b^2*cos(f*x+e)^2-6*a*b^3*cos(f*x+e)^2-2*b^4*cos(f*x+e)^2+a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*b^2-(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^3-2*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b^2-(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a^2+(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^3-2*(a+b-b*cos(f*x+e)^2)^(1/2)*a^3+a^2*b*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)-(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a*b^2-4*a^2*b*(a+b-b*cos(f*x+e)^2)^(1/2)+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)*a*b^2+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)*a^3+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)*a*b^2+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)*a^3+2*a^2*b*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)+2*a^2*b*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)+b^2*(ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)*a+ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)*a-2*(a+b-b*cos(f*x+e)^2)^(1/2)*a+(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a-(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b)*cos(f*x+e)^4-b*(2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)*a^2+2*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*(a+b)^(1/2)*a*b+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)*a^2+2*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*(a+b)^(1/2)*a*b+(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*a+(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(3/2)*b-4*(a+b-b*cos(f*x+e)^2)^(1/2)*a^2-4*(a+b-b*cos(f*x+e)^2)^(1/2)*a*b+2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^2-2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*b^2)*cos(f*x+e)^2)/f","B"
524,1,64,49,1.580000," ","int(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{1}{a f \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{3}{2}}}"," ",0,"1/a/f/(a+b*sin(f*x+e)^2)^(1/2)-1/f/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
525,1,159,94,1.779000," ","int(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{1}{a f \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}+\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{3}{2}}}-\frac{1}{2 f a \sin \left(f x +e \right)^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{3 b}{2 f \,a^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}+\frac{3 b \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{2 f \,a^{\frac{5}{2}}}"," ",0,"-1/a/f/(a+b*sin(f*x+e)^2)^(1/2)+1/f/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-1/2/f/a/sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2)-3/2/f/a^2*b/(a+b*sin(f*x+e)^2)^(1/2)+3/2/f/a^(5/2)*b*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
526,1,288,147,2.008000," ","int(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{1}{a f \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{3}{2}}}+\frac{1}{f a \sin \left(f x +e \right)^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}+\frac{3 b}{f \,a^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{3 b \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{5}{2}}}-\frac{1}{4 f a \sin \left(f x +e \right)^{4} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}+\frac{5 b}{8 f \,a^{2} \sin \left(f x +e \right)^{2} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}+\frac{15 b^{2}}{8 f \,a^{3} \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}-\frac{15 b^{2} \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{8 f \,a^{\frac{7}{2}}}"," ",0,"1/a/f/(a+b*sin(f*x+e)^2)^(1/2)-1/f/a^(3/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))+1/f/a/sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2)+3/f/a^2*b/(a+b*sin(f*x+e)^2)^(1/2)-3/f/a^(5/2)*b*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-1/4/f/a/sin(f*x+e)^4/(a+b*sin(f*x+e)^2)^(1/2)+5/8/f/a^2*b/sin(f*x+e)^2/(a+b*sin(f*x+e)^2)^(1/2)+15/8/f/a^3*b^2/(a+b*sin(f*x+e)^2)^(1/2)-15/8/f/a^(7/2)*b^2*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))","A"
527,1,368,266,3.105000," ","int(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(7 a -b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-4 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(7*a-b)*sin(f*x+e)*cos(f*x+e)^4-4*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*(a+b)*cos(f*x+e)^2*sin(f*x+e)+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2)/(1+sin(f*x+e))/(sin(f*x+e)-1)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
528,1,283,210,2.634000," ","int(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-a \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b -a \sin \left(f x +e \right)-b \sin \left(f x +e \right)\right)}{\left(a +b \right)^{2} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))-a*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-b*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))+2*sin(f*x+e)*cos(f*x+e)^2*b-a*sin(f*x+e)-b*sin(f*x+e))/(a+b)^2/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
529,1,103,116,1.823000," ","int(1/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)+\sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) b}{a \left(a +b \right) \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"((cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*a*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))+sin(f*x+e)*cos(f*x+e)^2*b)/a/(a+b)/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
530,1,141,195,1.611000," ","int(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(3/2),x)","\frac{\sin \left(f x +e \right) \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a \left(\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)-2 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right)\right)+2 b \left(\cos^{4}\left(f x +e \right)\right)+\left(-a -2 b \right) \left(\cos^{2}\left(f x +e \right)\right)}{\sin \left(f x +e \right) a^{2} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"(sin(f*x+e)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*(EllipticF(sin(f*x+e),(-1/a*b)^(1/2))-2*EllipticE(sin(f*x+e),(-1/a*b)^(1/2)))+2*b*cos(f*x+e)^4+(-a-2*b)*cos(f*x+e)^2)/sin(f*x+e)/a^2/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
531,1,353,273,1.910000," ","int(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(3/2),x)","-\frac{4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)+4 b \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \left(\sin^{3}\left(f x +e \right)\right)-7 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} \left(\sin^{3}\left(f x +e \right)\right)-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \left(\sin^{3}\left(f x +e \right)\right)+7 a b \left(\sin^{6}\left(f x +e \right)\right)+8 b^{2} \left(\sin^{6}\left(f x +e \right)\right)+4 a^{2} \left(\sin^{4}\left(f x +e \right)\right)-3 a b \left(\sin^{4}\left(f x +e \right)\right)-8 b^{2} \left(\sin^{4}\left(f x +e \right)\right)-5 a^{2} \left(\sin^{2}\left(f x +e \right)\right)-4 a b \left(\sin^{2}\left(f x +e \right)\right)+a^{2}}{3 a^{3} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}\, f}"," ",0,"-1/3*(4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3+4*b*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*sin(f*x+e)^3-7*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*sin(f*x+e)^3-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b*sin(f*x+e)^3+7*a*b*sin(f*x+e)^6+8*b^2*sin(f*x+e)^6+4*a^2*sin(f*x+e)^4-3*a*b*sin(f*x+e)^4-8*b^2*sin(f*x+e)^4-5*a^2*sin(f*x+e)^2-4*a*b*sin(f*x+e)^2+a^2)/a^3/sin(f*x+e)^3/cos(f*x+e)/(a+b*sin(f*x+e)^2)^(1/2)/f","A"
532,1,2139,194,8.430000," ","int(tan(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{b^{4} a^{2} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{2 f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{5} a \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{7 b^{3} a \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right) \left(1+\sin \left(f x +e \right)\right)}-\frac{7 b^{3} a \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right) \left(\sin \left(f x +e \right)-1\right)}-\frac{b^{5} a \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{4} a^{2} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{2 f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{4} a^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{a +b}}-\frac{b^{5} a \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{a +b}}+\frac{7 b^{4} a \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right)^{\frac{3}{2}}}+\frac{7 b^{4} a \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right)^{\frac{3}{2}}}+\frac{b^{4} a^{2} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{a +b}}-\frac{b^{5} a \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{f \left(b +\sqrt{-a b}\right)^{4} \left(-b +\sqrt{-a b}\right)^{4} \sqrt{a +b}}+\frac{b^{2} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right) \left(\sin \left(f x +e \right)-1\right)^{2}}+\frac{b^{2} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right) \left(1+\sin \left(f x +e \right)\right)^{2}}-\frac{3 b^{3} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{2} \left(\sin \left(f x +e \right)-1\right)}-\frac{b^{4} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right) \left(1+\sin \left(f x +e \right)\right)}+\frac{3 b^{3} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{2} \left(1+\sin \left(f x +e \right)\right)}-\frac{b^{2} a \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{b^{2} \sqrt{-a b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{b^{2} a \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}+\frac{b^{2} \sqrt{-a b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{4} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right) \left(\sin \left(f x +e \right)-1\right)}-\frac{b^{5} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right)^{\frac{3}{2}}}-\frac{b^{5} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{16 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \left(a +b \right)^{\frac{3}{2}}}+\frac{3 b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{5}{2}}}-\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{3}{2}}}+\frac{3 b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{5}{2}}}-\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{16 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-1/f*b^5*a/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/2/f*b^4*a^2/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/2/f*b^4*a^2/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/f*b^5*a/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+7/16/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3*a/(a+b)/(1+sin(f*x+e))*(a+b-b*cos(f*x+e)^2)^(1/2)-7/16/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3*a/(a+b)/(sin(f*x+e)-1)*(a+b-b*cos(f*x+e)^2)^(1/2)+1/2/f*b^4*a^2/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))-1/f*b^5*a/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))+7/16/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3*a/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))+7/16/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3*a/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))+1/2/f*b^4*a^2/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))-1/f*b^5*a/(b+(-a*b)^(1/2))^4/(-b+(-a*b)^(1/2))^4/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))+1/16/f*b^2/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)/(sin(f*x+e)-1)^2*(a+b-b*cos(f*x+e)^2)^(1/2)+1/16/f*b^2/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)/(1+sin(f*x+e))^2*(a+b-b*cos(f*x+e)^2)^(1/2)-3/16/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^2/(sin(f*x+e)-1)*(a+b-b*cos(f*x+e)^2)^(1/2)-1/16/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)/(1+sin(f*x+e))*(a+b-b*cos(f*x+e)^2)^(1/2)+3/16/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^2/(1+sin(f*x+e))*(a+b-b*cos(f*x+e)^2)^(1/2)-1/12/f*b^2*a/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f*b^2*(-a*b)^(1/2)/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f*b^2*a/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/12/f*b^2*(-a*b)^(1/2)/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/16/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)/(sin(f*x+e)-1)*(a+b-b*cos(f*x+e)^2)^(1/2)-1/16/f*b^5/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))-1/16/f*b^5/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))+3/16/f*b^4/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(5/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))-1/16/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))+3/16/f*b^4/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(5/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))-1/16/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))","B"
533,1,1256,133,6.279000," ","int(tan(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{a +b}}-\frac{b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{a +b}}-\frac{b^{3} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}\, a}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{4} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{b^{2} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{4 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right) \left(\sin \left(f x +e \right)-1\right)}+\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)}{4 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{3}{2}}}-\frac{b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}+\frac{b \sqrt{-a b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} a \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{a +b}}-\frac{b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{a +b}}+\frac{b^{2} \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}}{4 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right) \left(1+\sin \left(f x +e \right)\right)}+\frac{b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)}{4 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(a +b \right)^{\frac{3}{2}}}-\frac{b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{b \sqrt{-a b}\, \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \left(b +\sqrt{-a b}\right)^{2} \left(-b +\sqrt{-a b}\right)^{2} a \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{b^{3} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}\, a}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{b^{4} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{2 f \left(b +\sqrt{-a b}\right)^{3} \left(-b +\sqrt{-a b}\right)^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}"," ",0,"1/2/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))*a-1/2/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))-1/2/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)*a+1/2/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/4/f*b^2/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)/(sin(f*x+e)-1)*(a+b-b*cos(f*x+e)^2)^(1/2)+1/4/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+2*b*sin(f*x+e)+2*a)/(sin(f*x+e)-1))-1/12/f*b/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/12/f*b*(-a*b)^(1/2)/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/a/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/2/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))*a-1/2/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(a+b)^(1/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))+1/4/f*b^2/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)/(1+sin(f*x+e))*(a+b-b*cos(f*x+e)^2)^(1/2)+1/4/f*b^3/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(a+b)^(3/2)*ln((2*(a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-2*b*sin(f*x+e)+2*a)/(1+sin(f*x+e)))-1/12/f*b/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f*b*(-a*b)^(1/2)/(b+(-a*b)^(1/2))^2/(-b+(-a*b)^(1/2))^2/a/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+1/2/f*b^3/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)*a-1/2/f*b^4/(b+(-a*b)^(1/2))^3/(-b+(-a*b)^(1/2))^3/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)","B"
534,1,898,79,5.352000," ","int(tan(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{-8 a^{3} b^{3} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, \sqrt{a +b}-8 a^{2} b^{4} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, \sqrt{a +b}+3 a^{4} b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+3 a^{4} b^{3} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a^{2} b^{5}+3 \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a^{2} b^{5}+6 a^{3} b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+6 a^{3} b^{4} \ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)+3 a^{2} b^{5} \left(\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right)+\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right)\right) \left(\cos^{4}\left(f x +e \right)\right)+6 \left(\cos^{2}\left(f x +e \right)\right) a^{2} b^{4} \left(\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, \sqrt{a +b}-\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) a -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}-2 b \sin \left(f x +e \right)+2 a}{1+\sin \left(f x +e \right)}\right) b -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) a -\ln \left(\frac{2 \sqrt{a +b}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 b \sin \left(f x +e \right)+2 a}{\sin \left(f x +e \right)-1}\right) b \right)}{6 b^{3} \sqrt{a +b}\, a^{2} \left(a^{2} b^{2} \left(\cos^{4}\left(f x +e \right)\right)+2 a \,b^{3} \left(\cos^{4}\left(f x +e \right)\right)+b^{4} \left(\cos^{4}\left(f x +e \right)\right)-2 a^{3} b \left(\cos^{2}\left(f x +e \right)\right)-6 a^{2} b^{2} \left(\cos^{2}\left(f x +e \right)\right)-6 a \,b^{3} \left(\cos^{2}\left(f x +e \right)\right)-2 b^{4} \left(\cos^{2}\left(f x +e \right)\right)+a^{4}+4 a^{3} b +6 a^{2} b^{2}+4 a \,b^{3}+b^{4}\right) f}"," ",0,"1/6/b^3/(a+b)^(1/2)/a^2/(a^2*b^2*cos(f*x+e)^4+2*a*b^3*cos(f*x+e)^4+b^4*cos(f*x+e)^4-2*a^3*b*cos(f*x+e)^2-6*a^2*b^2*cos(f*x+e)^2-6*a*b^3*cos(f*x+e)^2-2*b^4*cos(f*x+e)^2+a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4)*(-8*a^3*b^3*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*(a+b)^(1/2)-8*a^2*b^4*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*(a+b)^(1/2)+3*a^4*b^3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+3*a^4*b^3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+3*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a^2*b^5+3*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a^2*b^5+6*a^3*b^4*ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+6*a^3*b^4*ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))+3*a^2*b^5*(ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))+ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a)))*cos(f*x+e)^4+6*cos(f*x+e)^2*a^2*b^4*((-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*(a+b)^(1/2)-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*a-ln(2/(1+sin(f*x+e))*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)-b*sin(f*x+e)+a))*b-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*a-ln(2/(sin(f*x+e)-1)*((a+b)^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+b*sin(f*x+e)+a))*b))/f","B"
535,1,271,71,3.426000," ","int(cot(f*x+e)/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{7 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} b \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{7 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{5}{2}}}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} b \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}"," ",0,"7/12/f/a^2/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f/a^2/b/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-7/12/f/a^2/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/f/a^(5/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-1/12/f/a^2/b/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)","B"
536,1,1038,123,4.280000," ","int(cot(f*x+e)^3/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{3 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{11}{2}} b^{2}-6 a^{6} b^{2} \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)+3 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{7}{2}} b^{4}+8 a^{\frac{11}{2}} b^{2} \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}+20 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{9}{2}} b^{3}+6 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{9}{2}} b^{3}+12 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{7}{2}} b^{4}-27 a^{5} b^{3} \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)-36 a^{4} b^{4} \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right)-15 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{3} b^{5}+3 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{3} b^{4} \left(2 a +5 b \right) \left(\cos^{6}\left(f x +e \right)\right)+3 \left(\cos^{4}\left(f x +e \right)\right) b^{3} \left(2 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{9}{2}}+\sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{7}{2}} b +4 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{7}{2}} b -4 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{5}-16 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{4} b -15 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{3} b^{2}\right)-\left(\cos^{2}\left(f x +e \right)\right) b^{2} \left(8 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{11}{2}}+6 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{9}{2}} b +26 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{9}{2}} b +6 \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}\, a^{\frac{7}{2}} b^{2}+24 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a \,b^{2}+b^{3}}{b^{2}}}\, a^{\frac{7}{2}} b^{2}-6 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{6}-39 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{5} b -78 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{4} b^{2}-45 \ln \left(\frac{2 \sqrt{a}\, \sqrt{a +b -b \left(\cos^{2}\left(f x +e \right)\right)}+2 a}{\sin \left(f x +e \right)}\right) a^{3} b^{3}\right)}{6 a^{\frac{13}{2}} b^{2} \left(b^{2} \left(\cos^{6}\left(f x +e \right)\right)-2 a b \left(\cos^{4}\left(f x +e \right)\right)-3 b^{2} \left(\cos^{4}\left(f x +e \right)\right)+a^{2} \left(\cos^{2}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) a b +3 b^{2} \left(\cos^{2}\left(f x +e \right)\right)-a^{2}-2 a b -b^{2}\right) f}"," ",0,"1/6/a^(13/2)/b^2/(b^2*cos(f*x+e)^6-2*a*b*cos(f*x+e)^4-3*b^2*cos(f*x+e)^4+a^2*cos(f*x+e)^2+4*cos(f*x+e)^2*a*b+3*b^2*cos(f*x+e)^2-a^2-2*a*b-b^2)*(3*(a+b-b*cos(f*x+e)^2)^(1/2)*a^(11/2)*b^2-6*a^6*b^2*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))+3*(a+b-b*cos(f*x+e)^2)^(1/2)*a^(7/2)*b^4+8*a^(11/2)*b^2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)+20*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(9/2)*b^3+6*(a+b-b*cos(f*x+e)^2)^(1/2)*a^(9/2)*b^3+12*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(7/2)*b^4-27*a^5*b^3*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))-36*a^4*b^4*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))-15*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^3*b^5+3*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^3*b^4*(2*a+5*b)*cos(f*x+e)^6+3*cos(f*x+e)^4*b^3*(2*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(9/2)+(a+b-b*cos(f*x+e)^2)^(1/2)*a^(7/2)*b+4*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(7/2)*b-4*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^5-16*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^4*b-15*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^3*b^2)-cos(f*x+e)^2*b^2*(8*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(11/2)+6*(a+b-b*cos(f*x+e)^2)^(1/2)*a^(9/2)*b+26*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(9/2)*b+6*(a+b-b*cos(f*x+e)^2)^(1/2)*a^(7/2)*b^2+24*(-b*cos(f*x+e)^2+(a*b^2+b^3)/b^2)^(1/2)*a^(7/2)*b^2-6*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^6-39*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^5*b-78*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^4*b^2-45*ln(2/sin(f*x+e)*(a^(1/2)*(a+b-b*cos(f*x+e)^2)^(1/2)+a))*a^3*b^3))/f","B"
537,1,901,184,5.599000," ","int(cot(f*x+e)^5/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{7 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{13 b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{6 f \,a^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}+\frac{19 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}\, b^{2}}{12 f \,a^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} b \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{6 f \,a^{3} \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{4} \left(\sin \left(f x +e \right)-\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} b \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{\sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{6 f \,a^{3} \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{4} \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)^{2}}-\frac{7 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{12 f \,a^{2} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{13 b \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}}{6 f \,a^{3} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{19 \sqrt{-b \left(\cos^{2}\left(f x +e \right)\right)+\frac{a b +b^{2}}{b}}\, b^{2}}{12 f \,a^{4} \sqrt{-a b}\, \left(\sin \left(f x +e \right)+\frac{\sqrt{-a b}}{b}\right)}-\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right)}{f \,a^{\frac{5}{2}}}-\frac{5 \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b}{f \,a^{\frac{7}{2}}}-\frac{35 \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{\sin \left(f x +e \right)}\right) b^{2}}{8 f \,a^{\frac{9}{2}}}+\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{f \,a^{3} \sin \left(f x +e \right)^{2}}+\frac{11 b \sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{8 f \,a^{4} \sin \left(f x +e \right)^{2}}-\frac{\sqrt{a +b \left(\sin^{2}\left(f x +e \right)\right)}}{4 f \,a^{3} \sin \left(f x +e \right)^{4}}"," ",0,"7/12/f/a^2/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+13/6/f/a^3/(-a*b)^(1/2)*b/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)+19/12/f/a^4/(-a*b)^(1/2)/(sin(f*x+e)-(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)*b^2-1/12/f/a^2/b/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/6/f/a^3/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f/a^4*b/(sin(f*x+e)-(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f/a^2/b/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/6/f/a^3/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-1/12/f/a^4*b/(sin(f*x+e)+(-a*b)^(1/2)/b)^2*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-7/12/f/a^2/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-13/6/f/a^3/(-a*b)^(1/2)*b/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)-19/12/f/a^4/(-a*b)^(1/2)/(sin(f*x+e)+(-a*b)^(1/2)/b)*(-b*cos(f*x+e)^2+(a*b+b^2)/b)^(1/2)*b^2-1/f/a^(5/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))-5/f/a^(7/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b-35/8/f/a^(9/2)*ln((2*a+2*a^(1/2)*(a+b*sin(f*x+e)^2)^(1/2))/sin(f*x+e))*b^2+1/f/a^3/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)+11/8/f/a^4*b/sin(f*x+e)^2*(a+b*sin(f*x+e)^2)^(1/2)-1/4/f/a^3/sin(f*x+e)^4*(a+b*sin(f*x+e)^2)^(1/2)","B"
538,1,667,318,3.495000," ","int(tan(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{-8 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2} \left(a -b \right) \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(13 a^{2}+2 a b -11 b^{2}\right) \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-2 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(2 a^{3}+3 a^{2} b -b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \left(a^{3}+3 a^{2} b +3 a \,b^{2}+b^{3}\right) \sin \left(f x +e \right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, b \left(5 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+2 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b \right) \left(\cos^{4}\left(f x +e \right)\right)-\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \left(5 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+7 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b -\EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-3 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{3}-8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right)^{4} \cos \left(f x +e \right) f}"," ",0,"-1/3*(-8*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^2*(a-b)*sin(f*x+e)*cos(f*x+e)^6+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(13*a^2+2*a*b-11*b^2)*cos(f*x+e)^4*sin(f*x+e)-2*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(2*a^3+3*a^2*b-b^3)*cos(f*x+e)^2*sin(f*x+e)+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(a^3+3*a^2*b+3*a*b^2+b^3)*sin(f*x+e)+(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*b*(5*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+2*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b-3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2+8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b)*cos(f*x+e)^4-(cos(f*x+e)^2)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(5*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+7*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b-EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-3*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^3-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3+8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)*cos(f*x+e)^2)/(a+b*sin(f*x+e)^2)^(3/2)/(1+sin(f*x+e))/(sin(f*x+e)-1)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)^4/cos(f*x+e)/f","B"
539,1,851,268,3.007000," ","int(tan(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b^{2} \left(7 a -b \right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, b \left(11 a^{2}+10 a b -b^{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, a \left(a^{2}+2 a b +b^{2}\right) \sin \left(f x +e \right)-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a b \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +\EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \left(\cos^{2}\left(f x +e \right)\right)+4 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+8 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +4 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}-7 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-6 \sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +\sqrt{-b \left(\cos^{4}\left(f x +e \right)\right)+\left(a +b \right) \left(\cos^{2}\left(f x +e \right)\right)}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2}}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{-\left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right) \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)}\, \left(a +b \right)^{3} a \cos \left(f x +e \right) f}"," ",0,"1/3*((-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b^2*(7*a-b)*sin(f*x+e)*cos(f*x+e)^4-(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*b*(11*a^2+10*a*b-b^2)*cos(f*x+e)^2*sin(f*x+e)+3*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*a*(a^2+2*a*b+b^2)*sin(f*x+e)-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*b*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a+EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*cos(f*x+e)^2+4*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+8*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+4*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2-7*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-6*(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+(-b*cos(f*x+e)^4+(a+b)*cos(f*x+e)^2)^(1/2)*(cos(f*x+e)^2)^(1/2)*(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2)/(a+b*sin(f*x+e)^2)^(3/2)/(-(a+b*sin(f*x+e)^2)*(sin(f*x+e)-1)*(1+sin(f*x+e)))^(1/2)/(a+b)^3/a/cos(f*x+e)/f","B"
540,1,547,245,2.089000," ","int(1/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)-4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{2}\left(f x +e \right)\right)-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{2}\left(f x +e \right)\right)+4 a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+2 b^{3} \left(\sin^{5}\left(f x +e \right)\right)+\sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}+a^{2} \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -4 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3}-2 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b +5 a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-a \,b^{2} \left(\sin^{3}\left(f x +e \right)\right)-2 b^{3} \left(\sin^{3}\left(f x +e \right)\right)-5 a^{2} b \sin \left(f x +e \right)-3 a \,b^{2} \sin \left(f x +e \right)}{3 \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} a^{2} \left(a +b \right)^{2} \cos \left(f x +e \right) f}"," ",0,"-1/3*((cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^2-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^2+4*a*b^2*sin(f*x+e)^5+2*b^3*sin(f*x+e)^5+(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3+a^2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-4*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3-2*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b+5*a^2*b*sin(f*x+e)^3-a*b^2*sin(f*x+e)^3-2*b^3*sin(f*x+e)^3-5*a^2*b*sin(f*x+e)-3*a*b^2*sin(f*x+e))/(a+b*sin(f*x+e)^2)^(3/2)/a^2/(a+b)^2/cos(f*x+e)/f","B"
541,1,411,261,1.987000," ","int(cot(f*x+e)^2/(a+b*sin(f*x+e)^2)^(5/2),x)","\frac{-\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a b \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b -7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a -8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b \right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\sqrt{-\frac{b \left(\cos^{2}\left(f x +e \right)\right)}{a}+\frac{a +b}{a}}\, \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, a \left(4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}+8 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b +4 \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}-7 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2}-15 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a b -8 \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) b^{2}\right) \sin \left(f x +e \right)+\left(-7 a \,b^{2}-8 b^{3}\right) \left(\cos^{6}\left(f x +e \right)\right)+\left(11 a^{2} b +26 a \,b^{2}+16 b^{3}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-3 a^{3}-14 a^{2} b -19 a \,b^{2}-8 b^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)}{3 \sin \left(f x +e \right) a^{3} \left(a +b \right) \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \cos \left(f x +e \right) f}"," ",0,"1/3*(-(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*b*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b)*sin(f*x+e)*cos(f*x+e)^2+(-b/a*cos(f*x+e)^2+(a+b)/a)^(1/2)*(cos(f*x+e)^2)^(1/2)*a*(4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2+8*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b+4*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*b^2-7*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2-15*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b-8*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*b^2)*sin(f*x+e)+(-7*a*b^2-8*b^3)*cos(f*x+e)^6+(11*a^2*b+26*a*b^2+16*b^3)*cos(f*x+e)^4+(-3*a^3-14*a^2*b-19*a*b^2-8*b^3)*cos(f*x+e)^2)/sin(f*x+e)/a^3/(a+b)/(a+b*sin(f*x+e)^2)^(3/2)/cos(f*x+e)/f","A"
542,1,633,318,1.934000," ","int(cot(f*x+e)^4/(a+b*sin(f*x+e)^2)^(5/2),x)","-\frac{5 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{5}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{5}\left(f x +e \right)\right)-16 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a \,b^{2} \left(\sin^{5}\left(f x +e \right)\right)+8 a \,b^{2} \left(\sin^{8}\left(f x +e \right)\right)+16 b^{3} \left(\sin^{8}\left(f x +e \right)\right)+5 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} \left(\sin^{3}\left(f x +e \right)\right)+8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticF \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{3}\left(f x +e \right)\right)-8 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{3} \left(\sin^{3}\left(f x +e \right)\right)-16 \sqrt{\frac{\cos \left(2 f x +2 e \right)}{2}+\frac{1}{2}}\, \sqrt{\frac{a +b \left(\sin^{2}\left(f x +e \right)\right)}{a}}\, \EllipticE \left(\sin \left(f x +e \right), \sqrt{-\frac{b}{a}}\right) a^{2} b \left(\sin^{3}\left(f x +e \right)\right)+13 a^{2} b \left(\sin^{6}\left(f x +e \right)\right)+16 a \,b^{2} \left(\sin^{6}\left(f x +e \right)\right)-16 b^{3} \left(\sin^{6}\left(f x +e \right)\right)+4 a^{3} \left(\sin^{4}\left(f x +e \right)\right)-7 a^{2} b \left(\sin^{4}\left(f x +e \right)\right)-24 a \,b^{2} \left(\sin^{4}\left(f x +e \right)\right)-5 a^{3} \left(\sin^{2}\left(f x +e \right)\right)-6 a^{2} b \left(\sin^{2}\left(f x +e \right)\right)+a^{3}}{3 \sin \left(f x +e \right)^{3} a^{4} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{\frac{3}{2}} \cos \left(f x +e \right) f}"," ",0,"-1/3*(5*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^5+8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^5-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^5-16*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a*b^2*sin(f*x+e)^5+8*a*b^2*sin(f*x+e)^8+16*b^3*sin(f*x+e)^8+5*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^3*sin(f*x+e)^3+8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticF(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^3-8*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^3*sin(f*x+e)^3-16*(cos(f*x+e)^2)^(1/2)*((a+b*sin(f*x+e)^2)/a)^(1/2)*EllipticE(sin(f*x+e),(-1/a*b)^(1/2))*a^2*b*sin(f*x+e)^3+13*a^2*b*sin(f*x+e)^6+16*a*b^2*sin(f*x+e)^6-16*b^3*sin(f*x+e)^6+4*a^3*sin(f*x+e)^4-7*a^2*b*sin(f*x+e)^4-24*a*b^2*sin(f*x+e)^4-5*a^3*sin(f*x+e)^2-6*a^2*b*sin(f*x+e)^2+a^3)/sin(f*x+e)^3/a^4/(a+b*sin(f*x+e)^2)^(3/2)/cos(f*x+e)/f","A"
543,0,0,112,4.010000," ","int((a+b*sin(f*x+e)^2)^p*(d*tan(f*x+e))^m,x)","\int \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p} \left(d \tan \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*sin(f*x+e)^2)^p*(d*tan(f*x+e))^m,x)","F"
544,0,0,100,2.011000," ","int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^3,x)","\int \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p} \left(\tan^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^3,x)","F"
545,0,0,59,2.293000," ","int((a+b*sin(d*x+c)^2)^p*tan(d*x+c),x)","\int \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p} \tan \left(d x +c \right)\, dx"," ",0,"int((a+b*sin(d*x+c)^2)^p*tan(d*x+c),x)","F"
546,0,0,54,2.253000," ","int(cot(d*x+c)*(a+b*sin(d*x+c)^2)^p,x)","\int \cot \left(d x +c \right) \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)*(a+b*sin(d*x+c)^2)^p,x)","F"
547,0,0,93,1.852000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c)^2)^p,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*sin(d*x+c)^2)^p,x)","F"
548,0,0,91,1.089000," ","int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^4,x)","\int \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p} \left(\tan^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^4,x)","F"
549,0,0,91,1.461000," ","int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^2,x)","\int \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p} \left(\tan^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^2)^p*tan(d*x+c)^2,x)","F"
550,0,0,89,1.524000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c)^2)^p,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*sin(d*x+c)^2)^p,x)","F"
551,0,0,91,1.109000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c)^2)^p,x)","\int \left(\cot^{4}\left(d x +c \right)\right) \left(a +b \left(\sin^{2}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^4*(a+b*sin(d*x+c)^2)^p,x)","F"
552,1,126,113,0.307000," ","int(cot(x)^3/(a+b*sin(x)^3),x)","-\frac{1}{2 a \sin \left(x \right)^{2}}-\frac{\ln \left(\sin \left(x \right)\right)}{a}-\frac{\ln \left(\sin \left(x \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\ln \left(\sin^{2}\left(x \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \sin \left(x \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \sin \left(x \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\ln \left(a +b \left(\sin^{3}\left(x \right)\right)\right)}{3 a}"," ",0,"-1/2/a/sin(x)^2-ln(sin(x))/a-1/3/a/(a/b)^(2/3)*ln(sin(x)+(a/b)^(1/3))+1/6/a/(a/b)^(2/3)*ln(sin(x)^2-(a/b)^(1/3)*sin(x)+(a/b)^(2/3))-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*sin(x)-1))+1/3*ln(a+b*sin(x)^3)/a","A"
553,1,34,33,1.934000," ","int(cot(x)*(a+b*sin(x)^3)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\sin^{3}\left(x \right)\right)}}{\sqrt{a}}\right) \sqrt{a}}{3}+\frac{2 \sqrt{a +b \left(\sin^{3}\left(x \right)\right)}}{3}"," ",0,"-2/3*arctanh((a+b*sin(x)^3)^(1/2)/a^(1/2))*a^(1/2)+2/3*(a+b*sin(x)^3)^(1/2)","A"
554,1,21,20,0.277000," ","int(cot(x)/(a+b*sin(x)^3)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\sin^{3}\left(x \right)\right)}}{\sqrt{a}}\right)}{3 \sqrt{a}}"," ",0,"-2/3*arctanh((a+b*sin(x)^3)^(1/2)/a^(1/2))/a^(1/2)","A"
555,0,0,47,1.729000," ","int(cot(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x)","\int \cot \left(d x +c \right) \sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}\, dx"," ",0,"int(cot(d*x+c)*(a+b*sin(d*x+c)^4)^(1/2),x)","F"
556,0,0,77,1.520000," ","int(tan(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\tan^{3}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(tan(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
557,1,72,43,0.514000," ","int(tan(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 b -2 b \left(\cos^{2}\left(d x +c \right)\right)+2 \sqrt{a +b}\, \sqrt{a +b -2 b \left(\cos^{2}\left(d x +c \right)\right)+b \left(\cos^{4}\left(d x +c \right)\right)}}{\cos \left(d x +c \right)^{2}}\right)}{2 d \sqrt{a +b}}"," ",0,"1/2/d/(a+b)^(1/2)*ln((2*a+2*b-2*b*cos(d*x+c)^2+2*(a+b)^(1/2)*(a+b-2*b*cos(d*x+c)^2+b*cos(d*x+c)^4)^(1/2))/cos(d*x+c)^2)","A"
558,0,0,27,1.546000," ","int(cot(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\cot \left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(cot(d*x+c)/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
559,0,0,58,1.811000," ","int(cot(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\cot^{3}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(cot(d*x+c)^3/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
560,0,0,94,1.881000," ","int(cot(d*x+c)^5/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\cot^{5}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(cot(d*x+c)^5/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
561,0,0,443,1.540000," ","int(tan(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\tan^{2}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(tan(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
562,1,396,181,3.392000," ","int(1/(a+b*sin(d*x+c)^4)^(1/2),x)","-\frac{\sqrt{\left(4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)\right) \left(\sin^{2}\left(2 d x +2 c \right)\right)}\, \sqrt{-a b}\, \sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \left(\cos \left(2 d x +2 c \right)+1\right)^{2} \sqrt{\frac{-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \sqrt{\frac{b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-b +\sqrt{-a b}\right) \left(-1+\cos \left(2 d x +2 c \right)\right)}{\sqrt{-a b}\, \left(\cos \left(2 d x +2 c \right)+1\right)}}, \sqrt{\frac{b +\sqrt{-a b}}{-b +\sqrt{-a b}}}\right)}{\left(-b +\sqrt{-a b}\right) \sqrt{\frac{\left(-1+\cos \left(2 d x +2 c \right)\right) \left(\cos \left(2 d x +2 c \right)+1\right) \left(-b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}+b \right) \left(b \cos \left(2 d x +2 c \right)+2 \sqrt{-a b}-b \right)}{b}}\, \sin \left(2 d x +2 c \right) \sqrt{4 a +\left(\cos^{2}\left(2 d x +2 c \right)\right) b +b -2 b \cos \left(2 d x +2 c \right)}\, d}"," ",0,"-((4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))*sin(2*d*x+2*c)^2)^(1/2)*(-a*b)^(1/2)*((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*(cos(2*d*x+2*c)+1)^2*((-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*((b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b)/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2)*EllipticF(((-b+(-a*b)^(1/2))*(-1+cos(2*d*x+2*c))/(-a*b)^(1/2)/(cos(2*d*x+2*c)+1))^(1/2),((b+(-a*b)^(1/2))/(-b+(-a*b)^(1/2)))^(1/2))/(-b+(-a*b)^(1/2))/(1/b*(-1+cos(2*d*x+2*c))*(cos(2*d*x+2*c)+1)*(-b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)+b)*(b*cos(2*d*x+2*c)+2*(-a*b)^(1/2)-b))^(1/2)/sin(2*d*x+2*c)/(4*a+cos(2*d*x+2*c)^2*b+b-2*b*cos(2*d*x+2*c))^(1/2)/d","B"
563,0,0,507,1.706000," ","int(cot(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","\int \frac{\cot^{2}\left(d x +c \right)}{\sqrt{a +b \left(\sin^{4}\left(d x +c \right)\right)}}\, dx"," ",0,"int(cot(d*x+c)^2/(a+b*sin(d*x+c)^4)^(1/2),x)","F"
564,0,0,25,5.071000," ","int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^m,x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p} \left(\tan^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^m,x)","F"
565,0,0,267,2.622000," ","int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^3,x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p} \left(\tan^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^3,x)","F"
566,0,0,135,4.725000," ","int((a+b*sin(d*x+c)^4)^p*tan(d*x+c),x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p} \tan \left(d x +c \right)\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p*tan(d*x+c),x)","F"
567,0,0,54,4.466000," ","int(cot(d*x+c)*(a+b*sin(d*x+c)^4)^p,x)","\int \cot \left(d x +c \right) \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)*(a+b*sin(d*x+c)^4)^p,x)","F"
568,0,0,123,2.487000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c)^4)^p,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*sin(d*x+c)^4)^p,x)","F"
569,0,0,25,1.658000," ","int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^4,x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p} \left(\tan^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^4,x)","F"
570,0,0,25,2.296000," ","int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^2,x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p} \left(\tan^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p*tan(d*x+c)^2,x)","F"
571,0,0,16,2.498000," ","int((a+b*sin(d*x+c)^4)^p,x)","\int \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sin(d*x+c)^4)^p,x)","F"
572,0,0,25,2.309000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c)^4)^p,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*sin(d*x+c)^4)^p,x)","F"
573,0,0,25,1.813000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c)^4)^p,x)","\int \left(\cot^{4}\left(d x +c \right)\right) \left(a +b \left(\sin^{4}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^4*(a+b*sin(d*x+c)^4)^p,x)","F"
574,-1,0,286,180.000000," ","int((a+b*sin(d*x+c)^n)^3*tan(d*x+c)^m,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{3} \left(\tan^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^3*tan(d*x+c)^m,x)","F"
575,-1,0,201,180.000000," ","int((a+b*sin(d*x+c)^n)^2*tan(d*x+c)^m,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{2} \left(\tan^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^2*tan(d*x+c)^m,x)","F"
576,-1,0,120,180.000000," ","int((a+b*sin(d*x+c)^n)*tan(d*x+c)^m,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right) \left(\tan^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)*tan(d*x+c)^m,x)","F"
577,0,0,25,1.567000," ","int(tan(d*x+c)^m/(a+b*sin(d*x+c)^n),x)","\int \frac{\tan^{m}\left(d x +c \right)}{a +b \left(\sin^{n}\left(d x +c \right)\right)}\, dx"," ",0,"int(tan(d*x+c)^m/(a+b*sin(d*x+c)^n),x)","F"
578,-1,0,25,180.000000," ","int(tan(d*x+c)^m/(a+b*sin(d*x+c)^n)^2,x)","\int \frac{\tan^{m}\left(d x +c \right)}{\left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{2}}\, dx"," ",0,"int(tan(d*x+c)^m/(a+b*sin(d*x+c)^n)^2,x)","F"
579,1,38,39,0.113000," ","int(cot(x)*(a+b*sin(x)^n)^(1/2),x)","\frac{2 \sqrt{a +b \left(\sin^{n}\left(x \right)\right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +b \left(\sin^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n}"," ",0,"1/n*(2*(a+b*sin(x)^n)^(1/2)-2*a^(1/2)*arctanh((a+b*sin(x)^n)^(1/2)/a^(1/2)))","A"
580,1,24,23,0.155000," ","int(cot(x)/(a+b*sin(x)^n)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\sin^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n \sqrt{a}}"," ",0,"-2*arctanh((a+b*sin(x)^n)^(1/2)/a^(1/2))/n/a^(1/2)","A"
581,0,0,25,3.743000," ","int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^m,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p} \left(\tan^{m}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^m,x)","F"
582,0,0,25,1.086000," ","int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^3,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p} \left(\tan^{3}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^3,x)","F"
583,0,0,23,1.032000," ","int((a+b*sin(d*x+c)^n)^p*tan(d*x+c),x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p} \tan \left(d x +c \right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p*tan(d*x+c),x)","F"
584,0,0,57,0.965000," ","int(cot(d*x+c)*(a+b*sin(d*x+c)^n)^p,x)","\int \cot \left(d x +c \right) \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)*(a+b*sin(d*x+c)^n)^p,x)","F"
585,0,0,135,1.059000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c)^n)^p,x)","\int \left(\cot^{3}\left(d x +c \right)\right) \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^3*(a+b*sin(d*x+c)^n)^p,x)","F"
586,0,0,25,0.961000," ","int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^4,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p} \left(\tan^{4}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^4,x)","F"
587,0,0,25,0.906000," ","int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^2,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p} \left(\tan^{2}\left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p*tan(d*x+c)^2,x)","F"
588,0,0,16,0.679000," ","int((a+b*sin(d*x+c)^n)^p,x)","\int \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int((a+b*sin(d*x+c)^n)^p,x)","F"
589,0,0,25,0.970000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c)^n)^p,x)","\int \left(\cot^{2}\left(d x +c \right)\right) \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^2*(a+b*sin(d*x+c)^n)^p,x)","F"
590,0,0,25,1.076000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c)^n)^p,x)","\int \left(\cot^{4}\left(d x +c \right)\right) \left(a +b \left(\sin^{n}\left(d x +c \right)\right)\right)^{p}\, dx"," ",0,"int(cot(d*x+c)^4*(a+b*sin(d*x+c)^n)^p,x)","F"
591,1,327,118,1.028000," ","int((a+b*sin(f*x+e)^2)/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x)","\frac{\left(-2 \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) a +\cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) b +\sqrt{2}\, \cos \left(f x +e \right) a +\sqrt{2}\, \cos \left(f x +e \right) b -\sqrt{2}\, a -\sqrt{2}\, b \right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{d \sin \left(f x +e \right)}}"," ",0,"1/3/f*(-2*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a+cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+2^(1/2)*cos(f*x+e)*a+2^(1/2)*cos(f*x+e)*b-2^(1/2)*a-2^(1/2)*b)*cos(f*x+e)*sin(f*x+e)/(-1+cos(f*x+e))/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2)*2^(1/2)","B"
592,0,0,125,8.127000," ","int((c*cos(f*x+e))^m*(d*sin(f*x+e))^n*(a+b*sin(f*x+e)^2)^p,x)","\int \left(c \cos \left(f x +e \right)\right)^{m} \left(d \sin \left(f x +e \right)\right)^{n} \left(a +b \left(\sin^{2}\left(f x +e \right)\right)\right)^{p}\, dx"," ",0,"int((c*cos(f*x+e))^m*(d*sin(f*x+e))^n*(a+b*sin(f*x+e)^2)^p,x)","F"
593,1,4067972,105,4.679000," ","int((a+(c*cos(f*x+e)+b*sin(f*x+e))^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
594,1,258179,105,3.765000," ","int(1/(a+(c*cos(f*x+e)+b*sin(f*x+e))^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"