1,1,12,11,0.047000," ","int(sin(b*x+a),x)","-\frac{\cos \left(b x +a \right)}{b}"," ",0,"-cos(b*x+a)/b","A"
2,1,27,21,0.045000," ","int(sin(b*x+a)^2,x)","\frac{-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}}{b}"," ",0,"1/b*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)","A"
3,1,22,25,0.120000," ","int(sin(b*x+a)^3,x)","-\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3 b}"," ",0,"-1/3/b*(2+sin(b*x+a)^2)*cos(b*x+a)","A"
4,1,38,40,0.136000," ","int(sin(b*x+a)^4,x)","\frac{-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}}{b}"," ",0,"1/b*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)","A"
5,1,32,38,0.103000," ","int(sin(b*x+a)^5,x)","-\frac{\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5 b}"," ",0,"-1/5/b*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a)","A"
6,1,48,59,0.101000," ","int(sin(b*x+a)^6,x)","\frac{-\frac{\left(\sin^{5}\left(b x +a \right)+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{4}+\frac{15 \sin \left(b x +a \right)}{8}\right) \cos \left(b x +a \right)}{6}+\frac{5 b x}{16}+\frac{5 a}{16}}{b}"," ",0,"1/b*(-1/6*(sin(b*x+a)^5+5/4*sin(b*x+a)^3+15/8*sin(b*x+a))*cos(b*x+a)+5/16*b*x+5/16*a)","A"
7,1,42,50,0.100000," ","int(sin(b*x+a)^7,x)","-\frac{\left(\frac{16}{5}+\sin^{6}\left(b x +a \right)+\frac{6 \left(\sin^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(b x +a \right)\right)}{5}\right) \cos \left(b x +a \right)}{7 b}"," ",0,"-1/7/b*(16/5+sin(b*x+a)^6+6/5*sin(b*x+a)^4+8/5*sin(b*x+a)^2)*cos(b*x+a)","A"
8,1,58,78,0.098000," ","int(sin(b*x+a)^8,x)","\frac{-\frac{\left(\sin^{7}\left(b x +a \right)+\frac{7 \left(\sin^{5}\left(b x +a \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(b x +a \right)\right)}{24}+\frac{35 \sin \left(b x +a \right)}{16}\right) \cos \left(b x +a \right)}{8}+\frac{35 b x}{128}+\frac{35 a}{128}}{b}"," ",0,"1/b*(-1/8*(sin(b*x+a)^7+7/6*sin(b*x+a)^5+35/24*sin(b*x+a)^3+35/16*sin(b*x+a))*cos(b*x+a)+35/128*b*x+35/128*a)","A"
9,1,84,73,0.171000," ","int(sin(b*x)^(7/2),x)","\frac{\frac{2 \sin \left(b x \right) \left(\cos^{4}\left(b x \right)\right)}{7}+\frac{5 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)}{21}-\frac{16 \left(\cos^{2}\left(b x \right)\right) \sin \left(b x \right)}{21}}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"(2/7*sin(b*x)*cos(b*x)^4+5/21*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))-16/21*cos(b*x)^2*sin(b*x))/cos(b*x)/sin(b*x)^(1/2)/b","A"
10,1,118,58,0.059000," ","int(sin(b*x)^(5/2),x)","\frac{\frac{2 \left(\sin^{4}\left(b x \right)\right)}{5}-\frac{2 \left(\sin^{2}\left(b x \right)\right)}{5}-\frac{6 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticE \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{3 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"(2/5*sin(b*x)^4-2/5*sin(b*x)^2-6/5*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticE((sin(b*x)+1)^(1/2),1/2*2^(1/2))+3/5*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2)))/cos(b*x)/sin(b*x)^(1/2)/b","B"
11,1,72,58,0.053000," ","int(sin(b*x)^(3/2),x)","\frac{\frac{\sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{2 \left(\cos^{2}\left(b x \right)\right) \sin \left(b x \right)}{3}}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"(1/3*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))-2/3*cos(b*x)^2*sin(b*x))/cos(b*x)/sin(b*x)^(1/2)/b","A"
12,1,77,42,0.056000," ","int(sin(b*x)^(1/2),x)","-\frac{\sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \left(2 \EllipticE \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"-(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*(2*EllipticE((sin(b*x)+1)^(1/2),1/2*2^(1/2))-EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2)))/cos(b*x)/sin(b*x)^(1/2)/b","A"
13,1,57,42,0.069000," ","int(1/sin(b*x)^(1/2),x)","\frac{\sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))/cos(b*x)/sin(b*x)^(1/2)/b","A"
14,1,110,58,0.066000," ","int(1/sin(b*x)^(3/2),x)","\frac{2 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticE \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x \right)\right)}{\cos \left(b x \right) \sqrt{\sin \left(b x \right)}\, b}"," ",0,"(2*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticE((sin(b*x)+1)^(1/2),1/2*2^(1/2))-(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))-2*cos(b*x)^2)/cos(b*x)/sin(b*x)^(1/2)/b","A"
15,1,72,58,0.055000," ","int(1/sin(b*x)^(5/2),x)","\frac{\sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right) \sin \left(b x \right)-2 \left(\cos^{2}\left(b x \right)\right)}{3 \sin \left(b x \right)^{\frac{3}{2}} \cos \left(b x \right) b}"," ",0,"1/3/sin(b*x)^(3/2)*((sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))*sin(b*x)-2*cos(b*x)^2)/cos(b*x)/b","A"
16,1,132,73,0.059000," ","int(1/sin(b*x)^(7/2),x)","\frac{6 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \left(\sin^{2}\left(b x \right)\right) \EllipticE \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\sin \left(b x \right)+1}\, \sqrt{-2 \sin \left(b x \right)+2}\, \sqrt{-\sin \left(b x \right)}\, \left(\sin^{2}\left(b x \right)\right) \EllipticF \left(\sqrt{\sin \left(b x \right)+1}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(b x \right)\right)-4 \left(\sin^{2}\left(b x \right)\right)-2}{5 \sin \left(b x \right)^{\frac{5}{2}} \cos \left(b x \right) b}"," ",0,"1/5/sin(b*x)^(5/2)*(6*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*sin(b*x)^2*EllipticE((sin(b*x)+1)^(1/2),1/2*2^(1/2))-3*(sin(b*x)+1)^(1/2)*(-2*sin(b*x)+2)^(1/2)*(-sin(b*x))^(1/2)*sin(b*x)^2*EllipticF((sin(b*x)+1)^(1/2),1/2*2^(1/2))+6*sin(b*x)^4-4*sin(b*x)^2-2)/cos(b*x)/b","A"
17,1,104,90,0.047000," ","int(sin(b*x+a)^(7/2),x)","\frac{\frac{2 \sin \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{7}+\frac{5 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{21}-\frac{16 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{21}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(2/7*sin(b*x+a)*cos(b*x+a)^4+5/21*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-16/21*cos(b*x+a)^2*sin(b*x+a))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
18,1,142,71,0.044000," ","int(sin(b*x+a)^(5/2),x)","\frac{\frac{2 \left(\sin^{4}\left(b x +a \right)\right)}{5}-\frac{2 \left(\sin^{2}\left(b x +a \right)\right)}{5}-\frac{6 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}+\frac{3 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{5}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(2/5*sin(b*x+a)^4-2/5*sin(b*x+a)^2-6/5*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+3/5*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2)))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
19,1,88,71,0.043000," ","int(sin(b*x+a)^(3/2),x)","\frac{\frac{\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{3}-\frac{2 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(1/3*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2/3*cos(b*x+a)^2*sin(b*x+a))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
20,1,91,51,0.040000," ","int(sin(b*x+a)^(1/2),x)","-\frac{\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \left(2 \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"-(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*(2*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2)))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
21,1,69,51,0.033000," ","int(1/sin(b*x+a)^(1/2),x)","\frac{\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
22,1,132,71,0.044000," ","int(1/sin(b*x+a)^(3/2),x)","\frac{2 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right)}{\cos \left(b x +a \right) \sqrt{\sin \left(b x +a \right)}\, b}"," ",0,"(2*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2)/cos(b*x+a)/sin(b*x+a)^(1/2)/b","A"
23,1,88,71,0.046000," ","int(1/sin(b*x+a)^(5/2),x)","\frac{\sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right)-2 \left(\cos^{2}\left(b x +a \right)\right)}{3 \sin \left(b x +a \right)^{\frac{3}{2}} \cos \left(b x +a \right) b}"," ",0,"1/3/sin(b*x+a)^(3/2)*((sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))*sin(b*x+a)-2*cos(b*x+a)^2)/cos(b*x+a)/b","A"
24,1,160,90,0.051000," ","int(1/sin(b*x+a)^(7/2),x)","\frac{6 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \left(\sin^{2}\left(b x +a \right)\right) \EllipticE \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\sin \left(b x +a \right)+1}\, \sqrt{-2 \sin \left(b x +a \right)+2}\, \sqrt{-\sin \left(b x +a \right)}\, \left(\sin^{2}\left(b x +a \right)\right) \EllipticF \left(\sqrt{\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(b x +a \right)\right)-4 \left(\sin^{2}\left(b x +a \right)\right)-2}{5 \sin \left(b x +a \right)^{\frac{5}{2}} \cos \left(b x +a \right) b}"," ",0,"1/5/sin(b*x+a)^(5/2)*(6*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*sin(b*x+a)^2*EllipticE((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-3*(sin(b*x+a)+1)^(1/2)*(-2*sin(b*x+a)+2)^(1/2)*(-sin(b*x+a))^(1/2)*sin(b*x+a)^2*EllipticF((sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+6*sin(b*x+a)^4-4*sin(b*x+a)^2-2)/cos(b*x+a)/b","A"
25,1,108,119,0.069000," ","int((c*sin(b*x+a))^(7/2),x)","-\frac{c^{4} \left(-6 \left(\sin^{5}\left(b x +a \right)\right)+5 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-4 \left(\sin^{3}\left(b x +a \right)\right)+10 \sin \left(b x +a \right)\right)}{21 \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-1/21*c^4*(-6*sin(b*x+a)^5+5*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-4*sin(b*x+a)^3+10*sin(b*x+a))/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
26,1,152,95,0.056000," ","int((c*sin(b*x+a))^(5/2),x)","-\frac{c^{3} \left(6 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{4}\left(b x +a \right)\right)+2 \left(\sin^{2}\left(b x +a \right)\right)\right)}{5 \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-1/5*c^3*(6*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticE((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-3*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*sin(b*x+a)^4+2*sin(b*x+a)^2)/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
27,1,97,95,0.054000," ","int((c*sin(b*x+a))^(3/2),x)","-\frac{c^{2} \left(\sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{3}\left(b x +a \right)\right)+2 \sin \left(b x +a \right)\right)}{3 \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-1/3*c^2*((-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*sin(b*x+a)^3+2*sin(b*x+a))/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
28,1,98,69,0.053000," ","int((c*sin(b*x+a))^(1/2),x)","-\frac{c \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \left(2 \EllipticE \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-c*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*(2*EllipticE((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2)))/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
29,1,74,69,0.046000," ","int(1/(c*sin(b*x+a))^(1/2),x)","-\frac{\sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)}{\cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
30,1,141,97,0.059000," ","int(1/(c*sin(b*x+a))^(3/2),x)","\frac{2 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sqrt{\sin}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right)}{c \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"1/c*(2*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticE((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(1/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2)/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
31,1,105,97,0.057000," ","int(1/(c*sin(b*x+a))^(5/2),x)","-\frac{\sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sin^{\frac{5}{2}}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{3}\left(b x +a \right)\right)+2 \sin \left(b x +a \right)}{3 c^{2} \sin \left(b x +a \right)^{2} \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"-1/3/c^2*((-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(5/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-2*sin(b*x+a)^3+2*sin(b*x+a))/sin(b*x+a)^2/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
32,1,168,121,0.066000," ","int(1/(c*sin(b*x+a))^(7/2),x)","\frac{6 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sin^{\frac{7}{2}}\left(b x +a \right)\right) \EllipticE \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\sin \left(b x +a \right)+1}\, \sqrt{2 \sin \left(b x +a \right)+2}\, \left(\sin^{\frac{7}{2}}\left(b x +a \right)\right) \EllipticF \left(\sqrt{-\sin \left(b x +a \right)+1}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{5}\left(b x +a \right)\right)-4 \left(\sin^{3}\left(b x +a \right)\right)-2 \sin \left(b x +a \right)}{5 c^{3} \sin \left(b x +a \right)^{3} \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}\, b}"," ",0,"1/5/c^3*(6*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(7/2)*EllipticE((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))-3*(-sin(b*x+a)+1)^(1/2)*(2*sin(b*x+a)+2)^(1/2)*sin(b*x+a)^(7/2)*EllipticF((-sin(b*x+a)+1)^(1/2),1/2*2^(1/2))+6*sin(b*x+a)^5-4*sin(b*x+a)^3-2*sin(b*x+a))/sin(b*x+a)^3/cos(b*x+a)/(c*sin(b*x+a))^(1/2)/b","A"
33,0,0,48,0.151000," ","int((c*sin(b*x+a))^(4/3),x)","\int \left(c \sin \left(b x +a \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((c*sin(b*x+a))^(4/3),x)","F"
34,0,0,48,0.171000," ","int((c*sin(b*x+a))^(2/3),x)","\int \left(c \sin \left(b x +a \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((c*sin(b*x+a))^(2/3),x)","F"
35,0,0,384,0.090000," ","int((c*sin(b*x+a))^(1/3),x)","\int \left(c \sin \left(b x +a \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((c*sin(b*x+a))^(1/3),x)","F"
36,0,0,189,0.072000," ","int(1/(c*sin(b*x+a))^(1/3),x)","\int \frac{1}{\left(c \sin \left(b x +a \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(c*sin(b*x+a))^(1/3),x)","F"
37,0,0,318,0.064000," ","int(1/(c*sin(b*x+a))^(2/3),x)","\int \frac{1}{\left(c \sin \left(b x +a \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(c*sin(b*x+a))^(2/3),x)","F"
38,0,0,48,0.050000," ","int(1/(c*sin(b*x+a))^(4/3),x)","\int \frac{1}{\left(c \sin \left(b x +a \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(c*sin(b*x+a))^(4/3),x)","F"
39,0,0,57,0.667000," ","int(sin(b*x+a)^n,x)","\int \sin^{n}\left(b x +a \right)\, dx"," ",0,"int(sin(b*x+a)^n,x)","F"
40,0,0,62,0.587000," ","int((c*sin(b*x+a))^n,x)","\int \left(c \sin \left(b x +a \right)\right)^{n}\, dx"," ",0,"int((c*sin(b*x+a))^n,x)","F"
41,0,0,79,1.083000," ","int((a*sin(f*x+e))^m*(b*sin(f*x+e))^n,x)","\int \left(a \sin \left(f x +e \right)\right)^{m} \left(b \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((a*sin(f*x+e))^m*(b*sin(f*x+e))^n,x)","F"
42,1,14,13,0.020000," ","int(cos(b*x+a)^3*sin(b*x+a),x)","-\frac{\cos^{4}\left(b x +a \right)}{4 b}"," ",0,"-1/4*cos(b*x+a)^4/b","A"
43,1,14,13,0.013000," ","int(cos(b*x+a)^2*sin(b*x+a),x)","-\frac{\cos^{3}\left(b x +a \right)}{3 b}"," ",0,"-1/3*cos(b*x+a)^3/b","A"
44,1,14,13,0.003000," ","int(cos(b*x+a)*sin(b*x+a),x)","\frac{\sin^{2}\left(b x +a \right)}{2 b}"," ",0,"1/2*sin(b*x+a)^2/b","A"
45,1,12,12,0.007000," ","int(sec(b*x+a)*sin(b*x+a),x)","\frac{\ln \left(\sec \left(b x +a \right)\right)}{b}"," ",0,"1/b*ln(sec(b*x+a))","A"
46,1,11,10,0.016000," ","int(sec(b*x+a)^2*sin(b*x+a),x)","\frac{\sec \left(b x +a \right)}{b}"," ",0,"sec(b*x+a)/b","A"
47,1,14,13,0.018000," ","int(sec(b*x+a)^3*sin(b*x+a),x)","\frac{\sec^{2}\left(b x +a \right)}{2 b}"," ",0,"1/2*sec(b*x+a)^2/b","A"
48,1,14,13,0.017000," ","int(sec(b*x+a)^4*sin(b*x+a),x)","\frac{\sec^{3}\left(b x +a \right)}{3 b}"," ",0,"1/3*sec(b*x+a)^3/b","A"
49,1,60,53,0.055000," ","int(cos(b*x+a)^7*sin(b*x+a)^2,x)","\frac{-\frac{\sin \left(b x +a \right) \left(\cos^{8}\left(b x +a \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{63}}{b}"," ",0,"1/b*(-1/9*sin(b*x+a)*cos(b*x+a)^8+1/63*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
50,1,50,40,0.051000," ","int(cos(b*x+a)^5*sin(b*x+a)^2,x)","\frac{-\frac{\sin \left(b x +a \right) \left(\cos^{6}\left(b x +a \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{35}}{b}"," ",0,"1/b*(-1/7*sin(b*x+a)*cos(b*x+a)^6+1/35*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
51,1,40,27,0.049000," ","int(cos(b*x+a)^3*sin(b*x+a)^2,x)","\frac{-\frac{\sin \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}}{b}"," ",0,"1/b*(-1/5*sin(b*x+a)*cos(b*x+a)^4+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))","A"
52,1,14,13,0.005000," ","int(cos(b*x+a)*sin(b*x+a)^2,x)","\frac{\sin^{3}\left(b x +a \right)}{3 b}"," ",0,"1/3*sin(b*x+a)^3/b","A"
53,1,19,14,0.026000," ","int(sec(b*x+a)^2*sin(b*x+a)^2,x)","\frac{\tan \left(b x +a \right)-b x -a}{b}"," ",0,"1/b*(tan(b*x+a)-b*x-a)","A"
54,1,22,13,0.033000," ","int(sec(b*x+a)^4*sin(b*x+a)^2,x)","\frac{\sin^{3}\left(b x +a \right)}{3 b \cos \left(b x +a \right)^{3}}"," ",0,"1/3/b*sin(b*x+a)^3/cos(b*x+a)^3","A"
55,1,42,27,0.035000," ","int(sec(b*x+a)^6*sin(b*x+a)^2,x)","\frac{\frac{\sin^{3}\left(b x +a \right)}{5 \cos \left(b x +a \right)^{5}}+\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{15 \cos \left(b x +a \right)^{3}}}{b}"," ",0,"1/b*(1/5*sin(b*x+a)^3/cos(b*x+a)^5+2/15*sin(b*x+a)^3/cos(b*x+a)^3)","A"
56,1,60,40,0.034000," ","int(sec(b*x+a)^8*sin(b*x+a)^2,x)","\frac{\frac{\sin^{3}\left(b x +a \right)}{7 \cos \left(b x +a \right)^{7}}+\frac{4 \left(\sin^{3}\left(b x +a \right)\right)}{35 \cos \left(b x +a \right)^{5}}+\frac{8 \left(\sin^{3}\left(b x +a \right)\right)}{105 \cos \left(b x +a \right)^{3}}}{b}"," ",0,"1/b*(1/7*sin(b*x+a)^3/cos(b*x+a)^7+4/35*sin(b*x+a)^3/cos(b*x+a)^5+8/105*sin(b*x+a)^3/cos(b*x+a)^3)","A"
57,1,78,53,0.037000," ","int(sec(b*x+a)^10*sin(b*x+a)^2,x)","\frac{\frac{\sin^{3}\left(b x +a \right)}{9 \cos \left(b x +a \right)^{9}}+\frac{2 \left(\sin^{3}\left(b x +a \right)\right)}{21 \cos \left(b x +a \right)^{7}}+\frac{8 \left(\sin^{3}\left(b x +a \right)\right)}{105 \cos \left(b x +a \right)^{5}}+\frac{16 \left(\sin^{3}\left(b x +a \right)\right)}{315 \cos \left(b x +a \right)^{3}}}{b}"," ",0,"1/b*(1/9*sin(b*x+a)^3/cos(b*x+a)^9+2/21*sin(b*x+a)^3/cos(b*x+a)^7+8/105*sin(b*x+a)^3/cos(b*x+a)^5+16/315*sin(b*x+a)^3/cos(b*x+a)^3)","A"
58,1,64,78,0.052000," ","int(cos(b*x+a)^6*sin(b*x+a)^2,x)","\frac{-\frac{\sin \left(b x +a \right) \left(\cos^{7}\left(b x +a \right)\right)}{8}+\frac{\left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)}{48}+\frac{5 b x}{128}+\frac{5 a}{128}}{b}"," ",0,"1/b*(-1/8*sin(b*x+a)*cos(b*x+a)^7+1/48*(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)+5/128*b*x+5/128*a)","A"
59,1,54,59,0.054000," ","int(cos(b*x+a)^4*sin(b*x+a)^2,x)","\frac{-\frac{\sin \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{6}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{24}+\frac{b x}{16}+\frac{a}{16}}{b}"," ",0,"1/b*(-1/6*sin(b*x+a)*cos(b*x+a)^5+1/24*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+1/16*b*x+1/16*a)","A"
60,1,43,40,0.020000," ","int(cos(b*x+a)^2*sin(b*x+a)^2,x)","\frac{-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{4}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{8}+\frac{b x}{8}+\frac{a}{8}}{b}"," ",0,"1/b*(-1/4*cos(b*x+a)^3*sin(b*x+a)+1/8*cos(b*x+a)*sin(b*x+a)+1/8*b*x+1/8*a)","A"
61,1,27,21,0.000000," ","int(sin(b*x+a)^2,x)","\frac{-\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{2}+\frac{b x}{2}+\frac{a}{2}}{b}"," ",0,"1/b*(-1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)","A"
62,1,31,23,0.027000," ","int(sec(b*x+a)*sin(b*x+a)^2,x)","-\frac{\sin \left(b x +a \right)}{b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"-sin(b*x+a)/b+1/b*ln(sec(b*x+a)+tan(b*x+a))","A"
63,1,53,30,0.028000," ","int(sec(b*x+a)^3*sin(b*x+a)^2,x)","\frac{\sin^{3}\left(b x +a \right)}{2 b \cos \left(b x +a \right)^{2}}+\frac{\sin \left(b x +a \right)}{2 b}-\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*sin(b*x+a)^3/cos(b*x+a)^2+1/2*sin(b*x+a)/b-1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
64,1,74,49,0.031000," ","int(sec(b*x+a)^5*sin(b*x+a)^2,x)","\frac{\sin^{3}\left(b x +a \right)}{4 b \cos \left(b x +a \right)^{4}}+\frac{\sin^{3}\left(b x +a \right)}{8 b \cos \left(b x +a \right)^{2}}+\frac{\sin \left(b x +a \right)}{8 b}-\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/4/b*sin(b*x+a)^3/cos(b*x+a)^4+1/8/b*sin(b*x+a)^3/cos(b*x+a)^2+1/8*sin(b*x+a)/b-1/8/b*ln(sec(b*x+a)+tan(b*x+a))","A"
65,1,95,68,0.036000," ","int(sec(b*x+a)^7*sin(b*x+a)^2,x)","\frac{\sin^{3}\left(b x +a \right)}{6 b \cos \left(b x +a \right)^{6}}+\frac{\sin^{3}\left(b x +a \right)}{8 b \cos \left(b x +a \right)^{4}}+\frac{\sin^{3}\left(b x +a \right)}{16 b \cos \left(b x +a \right)^{2}}+\frac{\sin \left(b x +a \right)}{16 b}-\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"1/6/b*sin(b*x+a)^3/cos(b*x+a)^6+1/8/b*sin(b*x+a)^3/cos(b*x+a)^4+1/16/b*sin(b*x+a)^3/cos(b*x+a)^2+1/16*sin(b*x+a)/b-1/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
66,1,34,27,0.021000," ","int(cos(b*x+a)^5*sin(b*x+a)^3,x)","\frac{-\frac{\left(\cos^{6}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{8}-\frac{\left(\cos^{6}\left(b x +a \right)\right)}{24}}{b}"," ",0,"1/b*(-1/8*cos(b*x+a)^6*sin(b*x+a)^2-1/24*cos(b*x+a)^6)","A"
67,1,34,27,0.023000," ","int(cos(b*x+a)^4*sin(b*x+a)^3,x)","\frac{-\frac{\left(\cos^{5}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(b x +a \right)\right)}{35}}{b}"," ",0,"1/b*(-1/7*cos(b*x+a)^5*sin(b*x+a)^2-2/35*cos(b*x+a)^5)","A"
68,1,34,27,0.020000," ","int(cos(b*x+a)^3*sin(b*x+a)^3,x)","\frac{-\frac{\left(\cos^{4}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{12}}{b}"," ",0,"1/b*(-1/6*cos(b*x+a)^4*sin(b*x+a)^2-1/12*cos(b*x+a)^4)","A"
69,1,34,27,0.023000," ","int(cos(b*x+a)^2*sin(b*x+a)^3,x)","\frac{-\frac{\left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(b x +a \right)\right)}{15}}{b}"," ",0,"1/b*(-1/5*cos(b*x+a)^3*sin(b*x+a)^2-2/15*cos(b*x+a)^3)","A"
70,1,14,13,0.006000," ","int(cos(b*x+a)*sin(b*x+a)^3,x)","\frac{\sin^{4}\left(b x +a \right)}{4 b}"," ",0,"1/4*sin(b*x+a)^4/b","A"
71,1,27,26,0.029000," ","int(sec(b*x+a)*sin(b*x+a)^3,x)","-\frac{\sin^{2}\left(b x +a \right)}{2 b}-\frac{\ln \left(\cos \left(b x +a \right)\right)}{b}"," ",0,"-1/2*sin(b*x+a)^2/b-ln(cos(b*x+a))/b","A"
72,1,40,21,0.029000," ","int(sec(b*x+a)^2*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{\cos \left(b x +a \right)}+\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{b}"," ",0,"1/b*(sin(b*x+a)^4/cos(b*x+a)+(2+sin(b*x+a)^2)*cos(b*x+a))","A"
73,1,26,25,0.032000," ","int(sec(b*x+a)^3*sin(b*x+a)^3,x)","\frac{\ln \left(\cos \left(b x +a \right)\right)}{b}+\frac{\tan^{2}\left(b x +a \right)}{2 b}"," ",0,"ln(cos(b*x+a))/b+1/2*tan(b*x+a)^2/b","A"
74,1,60,25,0.033000," ","int(sec(b*x+a)^4*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{3 \cos \left(b x +a \right)^{3}}-\frac{\sin^{4}\left(b x +a \right)}{3 \cos \left(b x +a \right)}-\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/3*sin(b*x+a)^4/cos(b*x+a)^3-1/3*sin(b*x+a)^4/cos(b*x+a)-1/3*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
75,1,22,13,0.035000," ","int(sec(b*x+a)^5*sin(b*x+a)^3,x)","\frac{\sin^{4}\left(b x +a \right)}{4 b \cos \left(b x +a \right)^{4}}"," ",0,"1/4/b*sin(b*x+a)^4/cos(b*x+a)^4","A"
76,1,78,27,0.033000," ","int(sec(b*x+a)^6*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{5 \cos \left(b x +a \right)^{5}}+\frac{\sin^{4}\left(b x +a \right)}{15 \cos \left(b x +a \right)^{3}}-\frac{\sin^{4}\left(b x +a \right)}{15 \cos \left(b x +a \right)}-\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{15}}{b}"," ",0,"1/b*(1/5*sin(b*x+a)^4/cos(b*x+a)^5+1/15*sin(b*x+a)^4/cos(b*x+a)^3-1/15*sin(b*x+a)^4/cos(b*x+a)-1/15*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
77,1,42,27,0.036000," ","int(sec(b*x+a)^7*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{6 \cos \left(b x +a \right)^{6}}+\frac{\sin^{4}\left(b x +a \right)}{12 \cos \left(b x +a \right)^{4}}}{b}"," ",0,"1/b*(1/6*sin(b*x+a)^4/cos(b*x+a)^6+1/12*sin(b*x+a)^4/cos(b*x+a)^4)","A"
78,1,96,27,0.038000," ","int(sec(b*x+a)^8*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{7 \cos \left(b x +a \right)^{7}}+\frac{3 \left(\sin^{4}\left(b x +a \right)\right)}{35 \cos \left(b x +a \right)^{5}}+\frac{\sin^{4}\left(b x +a \right)}{35 \cos \left(b x +a \right)^{3}}-\frac{\sin^{4}\left(b x +a \right)}{35 \cos \left(b x +a \right)}-\frac{\left(2+\sin^{2}\left(b x +a \right)\right) \cos \left(b x +a \right)}{35}}{b}"," ",0,"1/b*(1/7*sin(b*x+a)^4/cos(b*x+a)^7+3/35*sin(b*x+a)^4/cos(b*x+a)^5+1/35*sin(b*x+a)^4/cos(b*x+a)^3-1/35*sin(b*x+a)^4/cos(b*x+a)-1/35*(2+sin(b*x+a)^2)*cos(b*x+a))","B"
79,1,60,27,0.037000," ","int(sec(b*x+a)^9*sin(b*x+a)^3,x)","\frac{\frac{\sin^{4}\left(b x +a \right)}{8 \cos \left(b x +a \right)^{8}}+\frac{\sin^{4}\left(b x +a \right)}{12 \cos \left(b x +a \right)^{6}}+\frac{\sin^{4}\left(b x +a \right)}{24 \cos \left(b x +a \right)^{4}}}{b}"," ",0,"1/b*(1/8*sin(b*x+a)^4/cos(b*x+a)^8+1/12*sin(b*x+a)^4/cos(b*x+a)^6+1/24*sin(b*x+a)^4/cos(b*x+a)^4)","B"
80,1,78,53,0.026000," ","int(cos(b*x+a)^7*sin(b*x+a)^4,x)","\frac{-\frac{\left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{11}-\frac{\sin \left(b x +a \right) \left(\cos^{8}\left(b x +a \right)\right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{231}}{b}"," ",0,"1/b*(-1/11*sin(b*x+a)^3*cos(b*x+a)^8-1/33*sin(b*x+a)*cos(b*x+a)^8+1/231*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
81,1,68,40,0.024000," ","int(cos(b*x+a)^5*sin(b*x+a)^4,x)","\frac{-\frac{\left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{6}\left(b x +a \right)\right)}{9}-\frac{\sin \left(b x +a \right) \left(\cos^{6}\left(b x +a \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{105}}{b}"," ",0,"1/b*(-1/9*sin(b*x+a)^3*cos(b*x+a)^6-1/21*sin(b*x+a)*cos(b*x+a)^6+1/105*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
82,1,58,27,0.024000," ","int(cos(b*x+a)^3*sin(b*x+a)^4,x)","\frac{-\frac{\left(\cos^{4}\left(b x +a \right)\right) \left(\sin^{3}\left(b x +a \right)\right)}{7}-\frac{3 \sin \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{35}}{b}"," ",0,"1/b*(-1/7*cos(b*x+a)^4*sin(b*x+a)^3-3/35*sin(b*x+a)*cos(b*x+a)^4+1/35*(2+cos(b*x+a)^2)*sin(b*x+a))","B"
83,1,14,13,0.014000," ","int(cos(b*x+a)*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{5 b}"," ",0,"1/5*sin(b*x+a)^5/b","A"
84,1,54,34,0.029000," ","int(sec(b*x+a)^2*sin(b*x+a)^4,x)","\frac{\frac{\sin^{5}\left(b x +a \right)}{\cos \left(b x +a \right)}+\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)-\frac{3 b x}{2}-\frac{3 a}{2}}{b}"," ",0,"1/b*(sin(b*x+a)^5/cos(b*x+a)+(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)-3/2*b*x-3/2*a)","A"
85,1,28,26,0.033000," ","int(sec(b*x+a)^4*sin(b*x+a)^4,x)","\frac{\frac{\left(\tan^{3}\left(b x +a \right)\right)}{3}-\tan \left(b x +a \right)+b x +a}{b}"," ",0,"1/b*(1/3*tan(b*x+a)^3-tan(b*x+a)+b*x+a)","A"
86,1,22,13,0.035000," ","int(sec(b*x+a)^6*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{5 b \cos \left(b x +a \right)^{5}}"," ",0,"1/5/b*sin(b*x+a)^5/cos(b*x+a)^5","A"
87,1,42,27,0.037000," ","int(sec(b*x+a)^8*sin(b*x+a)^4,x)","\frac{\frac{\sin^{5}\left(b x +a \right)}{7 \cos \left(b x +a \right)^{7}}+\frac{2 \left(\sin^{5}\left(b x +a \right)\right)}{35 \cos \left(b x +a \right)^{5}}}{b}"," ",0,"1/b*(1/7*sin(b*x+a)^5/cos(b*x+a)^7+2/35*sin(b*x+a)^5/cos(b*x+a)^5)","A"
88,1,60,40,0.037000," ","int(sec(b*x+a)^10*sin(b*x+a)^4,x)","\frac{\frac{\sin^{5}\left(b x +a \right)}{9 \cos \left(b x +a \right)^{9}}+\frac{4 \left(\sin^{5}\left(b x +a \right)\right)}{63 \cos \left(b x +a \right)^{7}}+\frac{8 \left(\sin^{5}\left(b x +a \right)\right)}{315 \cos \left(b x +a \right)^{5}}}{b}"," ",0,"1/b*(1/9*sin(b*x+a)^5/cos(b*x+a)^9+4/63*sin(b*x+a)^5/cos(b*x+a)^7+8/315*sin(b*x+a)^5/cos(b*x+a)^5)","A"
89,1,82,99,0.025000," ","int(cos(b*x+a)^6*sin(b*x+a)^4,x)","\frac{-\frac{\left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{7}\left(b x +a \right)\right)}{10}-\frac{3 \sin \left(b x +a \right) \left(\cos^{7}\left(b x +a \right)\right)}{80}+\frac{\left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)}{160}+\frac{3 b x}{256}+\frac{3 a}{256}}{b}"," ",0,"1/b*(-1/10*sin(b*x+a)^3*cos(b*x+a)^7-3/80*sin(b*x+a)*cos(b*x+a)^7+1/160*(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)+3/256*b*x+3/256*a)","A"
90,1,72,80,0.025000," ","int(cos(b*x+a)^4*sin(b*x+a)^4,x)","\frac{-\frac{\left(\cos^{5}\left(b x +a \right)\right) \left(\sin^{3}\left(b x +a \right)\right)}{8}-\frac{\sin \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{16}+\frac{\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{64}+\frac{3 b x}{128}+\frac{3 a}{128}}{b}"," ",0,"1/b*(-1/8*cos(b*x+a)^5*sin(b*x+a)^3-1/16*sin(b*x+a)*cos(b*x+a)^5+1/64*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+3/128*b*x+3/128*a)","A"
91,1,61,61,0.021000," ","int(cos(b*x+a)^2*sin(b*x+a)^4,x)","\frac{-\frac{\left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{3}\left(b x +a \right)\right)}{6}-\frac{\left(\cos^{3}\left(b x +a \right)\right) \sin \left(b x +a \right)}{8}+\frac{\cos \left(b x +a \right) \sin \left(b x +a \right)}{16}+\frac{b x}{16}+\frac{a}{16}}{b}"," ",0,"1/b*(-1/6*cos(b*x+a)^3*sin(b*x+a)^3-1/8*cos(b*x+a)^3*sin(b*x+a)+1/16*cos(b*x+a)*sin(b*x+a)+1/16*b*x+1/16*a)","A"
92,1,38,40,0.000000," ","int(sin(b*x+a)^4,x)","\frac{-\frac{\left(\sin^{3}\left(b x +a \right)+\frac{3 \sin \left(b x +a \right)}{2}\right) \cos \left(b x +a \right)}{4}+\frac{3 b x}{8}+\frac{3 a}{8}}{b}"," ",0,"1/b*(-1/4*(sin(b*x+a)^3+3/2*sin(b*x+a))*cos(b*x+a)+3/8*b*x+3/8*a)","A"
93,1,44,36,0.027000," ","int(sec(b*x+a)*sin(b*x+a)^4,x)","-\frac{\sin^{3}\left(b x +a \right)}{3 b}-\frac{\sin \left(b x +a \right)}{b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/3*sin(b*x+a)^3/b-sin(b*x+a)/b+1/b*ln(sec(b*x+a)+tan(b*x+a))","A"
94,1,66,43,0.035000," ","int(sec(b*x+a)^3*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{2 b \cos \left(b x +a \right)^{2}}+\frac{\sin^{3}\left(b x +a \right)}{2 b}+\frac{3 \sin \left(b x +a \right)}{2 b}-\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*sin(b*x+a)^5/cos(b*x+a)^2+1/2*sin(b*x+a)^3/b+3/2*sin(b*x+a)/b-3/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
95,1,87,49,0.036000," ","int(sec(b*x+a)^5*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{4 b \cos \left(b x +a \right)^{4}}-\frac{\sin^{5}\left(b x +a \right)}{8 b \cos \left(b x +a \right)^{2}}-\frac{\sin^{3}\left(b x +a \right)}{8 b}-\frac{3 \sin \left(b x +a \right)}{8 b}+\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/4/b*sin(b*x+a)^5/cos(b*x+a)^4-1/8/b*sin(b*x+a)^5/cos(b*x+a)^2-1/8*sin(b*x+a)^3/b-3/8*sin(b*x+a)/b+3/8/b*ln(sec(b*x+a)+tan(b*x+a))","A"
96,1,108,70,0.039000," ","int(sec(b*x+a)^7*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{6 b \cos \left(b x +a \right)^{6}}+\frac{\sin^{5}\left(b x +a \right)}{24 b \cos \left(b x +a \right)^{4}}-\frac{\sin^{5}\left(b x +a \right)}{48 b \cos \left(b x +a \right)^{2}}-\frac{\sin^{3}\left(b x +a \right)}{48 b}-\frac{\sin \left(b x +a \right)}{16 b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"1/6/b*sin(b*x+a)^5/cos(b*x+a)^6+1/24/b*sin(b*x+a)^5/cos(b*x+a)^4-1/48/b*sin(b*x+a)^5/cos(b*x+a)^2-1/48*sin(b*x+a)^3/b-1/16*sin(b*x+a)/b+1/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
97,1,129,89,0.041000," ","int(sec(b*x+a)^9*sin(b*x+a)^4,x)","\frac{\sin^{5}\left(b x +a \right)}{8 b \cos \left(b x +a \right)^{8}}+\frac{\sin^{5}\left(b x +a \right)}{16 b \cos \left(b x +a \right)^{6}}+\frac{\sin^{5}\left(b x +a \right)}{64 b \cos \left(b x +a \right)^{4}}-\frac{\sin^{5}\left(b x +a \right)}{128 b \cos \left(b x +a \right)^{2}}-\frac{\sin^{3}\left(b x +a \right)}{128 b}-\frac{3 \sin \left(b x +a \right)}{128 b}+\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{128 b}"," ",0,"1/8/b*sin(b*x+a)^5/cos(b*x+a)^8+1/16/b*sin(b*x+a)^5/cos(b*x+a)^6+1/64/b*sin(b*x+a)^5/cos(b*x+a)^4-1/128/b*sin(b*x+a)^5/cos(b*x+a)^2-1/128*sin(b*x+a)^3/b-3/128*sin(b*x+a)/b+3/128/b*ln(sec(b*x+a)+tan(b*x+a))","A"
98,1,52,40,0.026000," ","int(cos(b*x+a)^7*sin(b*x+a)^5,x)","\frac{-\frac{\left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{12}-\frac{\left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{30}-\frac{\left(\cos^{8}\left(b x +a \right)\right)}{120}}{b}"," ",0,"1/b*(-1/12*sin(b*x+a)^4*cos(b*x+a)^8-1/30*sin(b*x+a)^2*cos(b*x+a)^8-1/120*cos(b*x+a)^8)","A"
99,1,52,40,0.026000," ","int(cos(b*x+a)^6*sin(b*x+a)^5,x)","\frac{-\frac{\left(\cos^{7}\left(b x +a \right)\right) \left(\sin^{4}\left(b x +a \right)\right)}{11}-\frac{4 \left(\cos^{7}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(b x +a \right)\right)}{693}}{b}"," ",0,"1/b*(-1/11*cos(b*x+a)^7*sin(b*x+a)^4-4/99*cos(b*x+a)^7*sin(b*x+a)^2-8/693*cos(b*x+a)^7)","A"
100,1,52,40,0.022000," ","int(cos(b*x+a)^5*sin(b*x+a)^5,x)","\frac{-\frac{\left(\cos^{6}\left(b x +a \right)\right) \left(\sin^{4}\left(b x +a \right)\right)}{10}-\frac{\left(\cos^{6}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{20}-\frac{\left(\cos^{6}\left(b x +a \right)\right)}{60}}{b}"," ",0,"1/b*(-1/10*cos(b*x+a)^6*sin(b*x+a)^4-1/20*cos(b*x+a)^6*sin(b*x+a)^2-1/60*cos(b*x+a)^6)","A"
101,1,52,40,0.023000," ","int(cos(b*x+a)^4*sin(b*x+a)^5,x)","\frac{-\frac{\left(\cos^{5}\left(b x +a \right)\right) \left(\sin^{4}\left(b x +a \right)\right)}{9}-\frac{4 \left(\cos^{5}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(b x +a \right)\right)}{315}}{b}"," ",0,"1/b*(-1/9*cos(b*x+a)^5*sin(b*x+a)^4-4/63*cos(b*x+a)^5*sin(b*x+a)^2-8/315*cos(b*x+a)^5)","A"
102,1,52,27,0.022000," ","int(cos(b*x+a)^3*sin(b*x+a)^5,x)","\frac{-\frac{\left(\cos^{4}\left(b x +a \right)\right) \left(\sin^{4}\left(b x +a \right)\right)}{8}-\frac{\left(\cos^{4}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{12}-\frac{\left(\cos^{4}\left(b x +a \right)\right)}{24}}{b}"," ",0,"1/b*(-1/8*cos(b*x+a)^4*sin(b*x+a)^4-1/12*cos(b*x+a)^4*sin(b*x+a)^2-1/24*cos(b*x+a)^4)","A"
103,1,52,40,0.024000," ","int(cos(b*x+a)^2*sin(b*x+a)^5,x)","\frac{-\frac{\left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{4}\left(b x +a \right)\right)}{7}-\frac{4 \left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{2}\left(b x +a \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(b x +a \right)\right)}{105}}{b}"," ",0,"1/b*(-1/7*cos(b*x+a)^3*sin(b*x+a)^4-4/35*cos(b*x+a)^3*sin(b*x+a)^2-8/105*cos(b*x+a)^3)","A"
104,1,14,13,0.004000," ","int(cos(b*x+a)*sin(b*x+a)^5,x)","\frac{\sin^{6}\left(b x +a \right)}{6 b}"," ",0,"1/6*sin(b*x+a)^6/b","A"
105,1,40,38,0.029000," ","int(sec(b*x+a)*sin(b*x+a)^5,x)","-\frac{\sin^{4}\left(b x +a \right)}{4 b}-\frac{\sin^{2}\left(b x +a \right)}{2 b}-\frac{\ln \left(\cos \left(b x +a \right)\right)}{b}"," ",0,"-1/4*sin(b*x+a)^4/b-1/2*sin(b*x+a)^2/b-ln(cos(b*x+a))/b","A"
106,1,50,35,0.028000," ","int(sec(b*x+a)^2*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{\cos \left(b x +a \right)}+\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{b}"," ",0,"1/b*(sin(b*x+a)^6/cos(b*x+a)+(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","A"
107,1,60,39,0.032000," ","int(sec(b*x+a)^3*sin(b*x+a)^5,x)","\frac{\sin^{6}\left(b x +a \right)}{2 b \cos \left(b x +a \right)^{2}}+\frac{\sin^{4}\left(b x +a \right)}{2 b}+\frac{\sin^{2}\left(b x +a \right)}{b}+\frac{2 \ln \left(\cos \left(b x +a \right)\right)}{b}"," ",0,"1/2/b*sin(b*x+a)^6/cos(b*x+a)^2+1/2*sin(b*x+a)^4/b+sin(b*x+a)^2/b+2*ln(cos(b*x+a))/b","A"
108,1,70,36,0.032000," ","int(sec(b*x+a)^4*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{3 \cos \left(b x +a \right)^{3}}-\frac{\sin^{6}\left(b x +a \right)}{\cos \left(b x +a \right)}-\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/3*sin(b*x+a)^6/cos(b*x+a)^3-sin(b*x+a)^6/cos(b*x+a)-(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","A"
109,1,40,39,0.035000," ","int(sec(b*x+a)^5*sin(b*x+a)^5,x)","-\frac{\ln \left(\cos \left(b x +a \right)\right)}{b}-\frac{\tan^{2}\left(b x +a \right)}{2 b}+\frac{\tan^{4}\left(b x +a \right)}{4 b}"," ",0,"-ln(cos(b*x+a))/b-1/2*tan(b*x+a)^2/b+1/4*tan(b*x+a)^4/b","A"
110,1,88,37,0.034000," ","int(sec(b*x+a)^6*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{5 \cos \left(b x +a \right)^{5}}-\frac{\sin^{6}\left(b x +a \right)}{15 \cos \left(b x +a \right)^{3}}+\frac{\sin^{6}\left(b x +a \right)}{5 \cos \left(b x +a \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{5}}{b}"," ",0,"1/b*(1/5*sin(b*x+a)^6/cos(b*x+a)^5-1/15*sin(b*x+a)^6/cos(b*x+a)^3+1/5*sin(b*x+a)^6/cos(b*x+a)+1/5*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","B"
111,1,22,13,0.036000," ","int(sec(b*x+a)^7*sin(b*x+a)^5,x)","\frac{\sin^{6}\left(b x +a \right)}{6 b \cos \left(b x +a \right)^{6}}"," ",0,"1/6/b*sin(b*x+a)^6/cos(b*x+a)^6","A"
112,1,106,40,0.037000," ","int(sec(b*x+a)^8*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{7 \cos \left(b x +a \right)^{7}}+\frac{\sin^{6}\left(b x +a \right)}{35 \cos \left(b x +a \right)^{5}}-\frac{\sin^{6}\left(b x +a \right)}{105 \cos \left(b x +a \right)^{3}}+\frac{\sin^{6}\left(b x +a \right)}{35 \cos \left(b x +a \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{35}}{b}"," ",0,"1/b*(1/7*sin(b*x+a)^6/cos(b*x+a)^7+1/35*sin(b*x+a)^6/cos(b*x+a)^5-1/105*sin(b*x+a)^6/cos(b*x+a)^3+1/35*sin(b*x+a)^6/cos(b*x+a)+1/35*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","B"
113,1,42,27,0.048000," ","int(sec(b*x+a)^9*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{8 \cos \left(b x +a \right)^{8}}+\frac{\sin^{6}\left(b x +a \right)}{24 \cos \left(b x +a \right)^{6}}}{b}"," ",0,"1/b*(1/8*sin(b*x+a)^6/cos(b*x+a)^8+1/24*sin(b*x+a)^6/cos(b*x+a)^6)","A"
114,1,124,40,0.034000," ","int(sec(b*x+a)^10*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{9 \cos \left(b x +a \right)^{9}}+\frac{\sin^{6}\left(b x +a \right)}{21 \cos \left(b x +a \right)^{7}}+\frac{\sin^{6}\left(b x +a \right)}{105 \cos \left(b x +a \right)^{5}}-\frac{\sin^{6}\left(b x +a \right)}{315 \cos \left(b x +a \right)^{3}}+\frac{\sin^{6}\left(b x +a \right)}{105 \cos \left(b x +a \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{105}}{b}"," ",0,"1/b*(1/9*sin(b*x+a)^6/cos(b*x+a)^9+1/21*sin(b*x+a)^6/cos(b*x+a)^7+1/105*sin(b*x+a)^6/cos(b*x+a)^5-1/315*sin(b*x+a)^6/cos(b*x+a)^3+1/105*sin(b*x+a)^6/cos(b*x+a)+1/105*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","B"
115,1,60,40,0.040000," ","int(sec(b*x+a)^11*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{10 \cos \left(b x +a \right)^{10}}+\frac{\sin^{6}\left(b x +a \right)}{20 \cos \left(b x +a \right)^{8}}+\frac{\sin^{6}\left(b x +a \right)}{60 \cos \left(b x +a \right)^{6}}}{b}"," ",0,"1/b*(1/10*sin(b*x+a)^6/cos(b*x+a)^10+1/20*sin(b*x+a)^6/cos(b*x+a)^8+1/60*sin(b*x+a)^6/cos(b*x+a)^6)","A"
116,1,142,40,0.041000," ","int(sec(b*x+a)^12*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{11 \cos \left(b x +a \right)^{11}}+\frac{5 \left(\sin^{6}\left(b x +a \right)\right)}{99 \cos \left(b x +a \right)^{9}}+\frac{5 \left(\sin^{6}\left(b x +a \right)\right)}{231 \cos \left(b x +a \right)^{7}}+\frac{\sin^{6}\left(b x +a \right)}{231 \cos \left(b x +a \right)^{5}}-\frac{\sin^{6}\left(b x +a \right)}{693 \cos \left(b x +a \right)^{3}}+\frac{\sin^{6}\left(b x +a \right)}{231 \cos \left(b x +a \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(b x +a \right)+\frac{4 \left(\sin^{2}\left(b x +a \right)\right)}{3}\right) \cos \left(b x +a \right)}{231}}{b}"," ",0,"1/b*(1/11*sin(b*x+a)^6/cos(b*x+a)^11+5/99*sin(b*x+a)^6/cos(b*x+a)^9+5/231*sin(b*x+a)^6/cos(b*x+a)^7+1/231*sin(b*x+a)^6/cos(b*x+a)^5-1/693*sin(b*x+a)^6/cos(b*x+a)^3+1/231*sin(b*x+a)^6/cos(b*x+a)+1/231*(8/3+sin(b*x+a)^4+4/3*sin(b*x+a)^2)*cos(b*x+a))","B"
117,1,78,40,0.043000," ","int(sec(b*x+a)^13*sin(b*x+a)^5,x)","\frac{\frac{\sin^{6}\left(b x +a \right)}{12 \cos \left(b x +a \right)^{12}}+\frac{\sin^{6}\left(b x +a \right)}{20 \cos \left(b x +a \right)^{10}}+\frac{\sin^{6}\left(b x +a \right)}{40 \cos \left(b x +a \right)^{8}}+\frac{\sin^{6}\left(b x +a \right)}{120 \cos \left(b x +a \right)^{6}}}{b}"," ",0,"1/b*(1/12*sin(b*x+a)^6/cos(b*x+a)^12+1/20*sin(b*x+a)^6/cos(b*x+a)^10+1/40*sin(b*x+a)^6/cos(b*x+a)^8+1/120*sin(b*x+a)^6/cos(b*x+a)^6)","A"
118,1,79,58,0.035000," ","int(sec(b*x+a)^3*sin(b*x+a)^6,x)","\frac{\sin^{7}\left(b x +a \right)}{2 b \cos \left(b x +a \right)^{2}}+\frac{\sin^{5}\left(b x +a \right)}{2 b}+\frac{5 \left(\sin^{3}\left(b x +a \right)\right)}{6 b}+\frac{5 \sin \left(b x +a \right)}{2 b}-\frac{5 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*sin(b*x+a)^7/cos(b*x+a)^2+1/2*sin(b*x+a)^5/b+5/6*sin(b*x+a)^3/b+5/2*sin(b*x+a)/b-5/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
119,1,96,48,0.037000," ","int(sec(b*x+a)^6*sin(b*x+a)^7,x)","\frac{\frac{\sin^{8}\left(b x +a \right)}{5 \cos \left(b x +a \right)^{5}}-\frac{\sin^{8}\left(b x +a \right)}{5 \cos \left(b x +a \right)^{3}}+\frac{\sin^{8}\left(b x +a \right)}{\cos \left(b x +a \right)}+\left(\frac{16}{5}+\sin^{6}\left(b x +a \right)+\frac{6 \left(\sin^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(b x +a \right)\right)}{5}\right) \cos \left(b x +a \right)}{b}"," ",0,"1/b*(1/5*sin(b*x+a)^8/cos(b*x+a)^5-1/5*sin(b*x+a)^8/cos(b*x+a)^3+sin(b*x+a)^8/cos(b*x+a)+(16/5+sin(b*x+a)^6+6/5*sin(b*x+a)^4+8/5*sin(b*x+a)^2)*cos(b*x+a))","A"
120,1,58,49,0.033000," ","int(cos(b*x+a)^6/sin(b*x+a),x)","\frac{\cos^{5}\left(b x +a \right)}{5 b}+\frac{\cos^{3}\left(b x +a \right)}{3 b}+\frac{\cos \left(b x +a \right)}{b}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/5*cos(b*x+a)^5/b+1/3*cos(b*x+a)^3/b+cos(b*x+a)/b+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
121,1,39,38,0.026000," ","int(cos(b*x+a)^5/sin(b*x+a),x)","\frac{\cos^{4}\left(b x +a \right)}{4 b}+\frac{\cos^{2}\left(b x +a \right)}{2 b}+\frac{\ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"1/4*cos(b*x+a)^4/b+1/2*cos(b*x+a)^2/b+ln(sin(b*x+a))/b","A"
122,1,45,36,0.024000," ","int(cos(b*x+a)^4/sin(b*x+a),x)","\frac{\cos^{3}\left(b x +a \right)}{3 b}+\frac{\cos \left(b x +a \right)}{b}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/3*cos(b*x+a)^3/b+cos(b*x+a)/b+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
123,1,26,25,0.028000," ","int(cos(b*x+a)^3/sin(b*x+a),x)","\frac{\cos^{2}\left(b x +a \right)}{2 b}+\frac{\ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"1/2*cos(b*x+a)^2/b+ln(sin(b*x+a))/b","A"
124,1,32,23,0.024000," ","int(cos(b*x+a)^2/sin(b*x+a),x)","\frac{\cos \left(b x +a \right)}{b}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"cos(b*x+a)/b+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
125,1,12,11,0.004000," ","int(cos(b*x+a)/sin(b*x+a),x)","\frac{\ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"ln(sin(b*x+a))/b","A"
126,1,12,11,0.037000," ","int(sec(b*x+a)/sin(b*x+a),x)","\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"ln(tan(b*x+a))/b","A"
127,1,34,23,0.038000," ","int(sec(b*x+a)^2/sin(b*x+a),x)","\frac{1}{b \cos \left(b x +a \right)}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/b/cos(b*x+a)+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
128,1,26,25,0.040000," ","int(sec(b*x+a)^3/sin(b*x+a),x)","\frac{1}{2 b \cos \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/2/b/cos(b*x+a)^2+ln(tan(b*x+a))/b","A"
129,1,47,36,0.041000," ","int(sec(b*x+a)^4/sin(b*x+a),x)","\frac{1}{3 b \cos \left(b x +a \right)^{3}}+\frac{1}{b \cos \left(b x +a \right)}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/3/b/cos(b*x+a)^3+1/b/cos(b*x+a)+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
130,1,39,37,0.040000," ","int(sec(b*x+a)^5/sin(b*x+a),x)","\frac{1}{4 b \cos \left(b x +a \right)^{4}}+\frac{1}{2 b \cos \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/4/b/cos(b*x+a)^4+1/2/b/cos(b*x+a)^2+ln(tan(b*x+a))/b","A"
131,1,60,49,0.043000," ","int(sec(b*x+a)^6/sin(b*x+a),x)","\frac{1}{5 b \cos \left(b x +a \right)^{5}}+\frac{1}{3 b \cos \left(b x +a \right)^{3}}+\frac{1}{b \cos \left(b x +a \right)}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"1/5/b/cos(b*x+a)^5+1/3/b/cos(b*x+a)^3+1/b/cos(b*x+a)+1/b*ln(csc(b*x+a)-cot(b*x+a))","A"
132,1,52,51,0.046000," ","int(sec(b*x+a)^7/sin(b*x+a),x)","\frac{1}{6 b \cos \left(b x +a \right)^{6}}+\frac{1}{4 b \cos \left(b x +a \right)^{4}}+\frac{1}{2 b \cos \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/6/b/cos(b*x+a)^6+1/4/b/cos(b*x+a)^4+1/2/b/cos(b*x+a)^2+ln(tan(b*x+a))/b","A"
133,1,62,48,0.021000," ","int(cos(b*x+a)^7/sin(b*x+a)^2,x)","\frac{-\frac{\cos^{8}\left(b x +a \right)}{\sin \left(b x +a \right)}-\left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{b}"," ",0,"1/b*(-1/sin(b*x+a)*cos(b*x+a)^8-(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
134,1,66,53,0.020000," ","int(cos(b*x+a)^6/sin(b*x+a)^2,x)","\frac{-\frac{\cos^{7}\left(b x +a \right)}{\sin \left(b x +a \right)}-\left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)-\frac{15 b x}{8}-\frac{15 a}{8}}{b}"," ",0,"1/b*(-1/sin(b*x+a)*cos(b*x+a)^7-(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)-15/8*b*x-15/8*a)","A"
135,1,52,36,0.021000," ","int(cos(b*x+a)^5/sin(b*x+a)^2,x)","\frac{-\frac{\cos^{6}\left(b x +a \right)}{\sin \left(b x +a \right)}-\left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{b}"," ",0,"1/b*(-cos(b*x+a)^6/sin(b*x+a)-(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
136,1,56,34,0.023000," ","int(cos(b*x+a)^4/sin(b*x+a)^2,x)","\frac{-\frac{\cos^{5}\left(b x +a \right)}{\sin \left(b x +a \right)}-\left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)-\frac{3 b x}{2}-\frac{3 a}{2}}{b}"," ",0,"1/b*(-cos(b*x+a)^5/sin(b*x+a)-(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)-3/2*b*x-3/2*a)","A"
137,1,42,23,0.019000," ","int(cos(b*x+a)^3/sin(b*x+a)^2,x)","\frac{-\frac{\cos^{4}\left(b x +a \right)}{\sin \left(b x +a \right)}-\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{b}"," ",0,"1/b*(-cos(b*x+a)^4/sin(b*x+a)-(2+cos(b*x+a)^2)*sin(b*x+a))","A"
138,1,21,15,0.021000," ","int(cos(b*x+a)^2/sin(b*x+a)^2,x)","\frac{-\cot \left(b x +a \right)-b x -a}{b}"," ",0,"1/b*(-cot(b*x+a)-b*x-a)","A"
139,1,14,11,0.005000," ","int(cos(b*x+a)/sin(b*x+a)^2,x)","-\frac{1}{b \sin \left(b x +a \right)}"," ",0,"-1/b/sin(b*x+a)","A"
140,1,33,23,0.029000," ","int(sec(b*x+a)/sin(b*x+a)^2,x)","-\frac{1}{b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/b/sin(b*x+a)+1/b*ln(sec(b*x+a)+tan(b*x+a))","A"
141,1,31,22,0.064000," ","int(sec(b*x+a)^2/sin(b*x+a)^2,x)","\frac{\frac{1}{\sin \left(b x +a \right) \cos \left(b x +a \right)}-2 \cot \left(b x +a \right)}{b}"," ",0,"1/b*(1/sin(b*x+a)/cos(b*x+a)-2*cot(b*x+a))","A"
142,1,55,43,0.038000," ","int(sec(b*x+a)^3/sin(b*x+a)^2,x)","\frac{1}{2 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{3}{2 b \sin \left(b x +a \right)}+\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b/sin(b*x+a)/cos(b*x+a)^2-3/2/b/sin(b*x+a)+3/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
143,1,50,36,0.038000," ","int(sec(b*x+a)^4/sin(b*x+a)^2,x)","\frac{\frac{1}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)^{3}}+\frac{4}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{8 \cot \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/3/sin(b*x+a)/cos(b*x+a)^3+4/3/sin(b*x+a)/cos(b*x+a)-8/3*cot(b*x+a))","A"
144,1,76,62,0.041000," ","int(sec(b*x+a)^5/sin(b*x+a)^2,x)","\frac{1}{4 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{4}}+\frac{5}{8 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{15}{8 b \sin \left(b x +a \right)}+\frac{15 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/4/b/sin(b*x+a)/cos(b*x+a)^4+5/8/b/sin(b*x+a)/cos(b*x+a)^2-15/8/b/sin(b*x+a)+15/8/b*ln(sec(b*x+a)+tan(b*x+a))","A"
145,1,74,52,0.021000," ","int(cos(b*x+a)^7/sin(b*x+a)^3,x)","-\frac{\cos^{8}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}-\frac{\cos^{6}\left(b x +a \right)}{2 b}-\frac{3 \left(\cos^{4}\left(b x +a \right)\right)}{4 b}-\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{2 b}-\frac{3 \ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"-1/2/b/sin(b*x+a)^2*cos(b*x+a)^8-1/2*cos(b*x+a)^6/b-3/4*cos(b*x+a)^4/b-3/2*cos(b*x+a)^2/b-3*ln(sin(b*x+a))/b","A"
146,1,81,58,0.023000," ","int(cos(b*x+a)^6/sin(b*x+a)^3,x)","-\frac{\cos^{7}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}-\frac{\cos^{5}\left(b x +a \right)}{2 b}-\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{6 b}-\frac{5 \cos \left(b x +a \right)}{2 b}-\frac{5 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2/b*cos(b*x+a)^7/sin(b*x+a)^2-1/2*cos(b*x+a)^5/b-5/6*cos(b*x+a)^3/b-5/2*cos(b*x+a)/b-5/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
147,1,61,39,0.022000," ","int(cos(b*x+a)^5/sin(b*x+a)^3,x)","-\frac{\cos^{6}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}-\frac{\cos^{4}\left(b x +a \right)}{2 b}-\frac{\cos^{2}\left(b x +a \right)}{b}-\frac{2 \ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"-1/2/b*cos(b*x+a)^6/sin(b*x+a)^2-1/2*cos(b*x+a)^4/b-cos(b*x+a)^2/b-2*ln(sin(b*x+a))/b","A"
148,1,68,43,0.025000," ","int(cos(b*x+a)^4/sin(b*x+a)^3,x)","-\frac{\cos^{5}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}-\frac{\cos^{3}\left(b x +a \right)}{2 b}-\frac{3 \cos \left(b x +a \right)}{2 b}-\frac{3 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2/b*cos(b*x+a)^5/sin(b*x+a)^2-1/2*cos(b*x+a)^3/b-3/2*cos(b*x+a)/b-3/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
149,1,27,26,0.023000," ","int(cos(b*x+a)^3/sin(b*x+a)^3,x)","-\frac{\cot^{2}\left(b x +a \right)}{2 b}-\frac{\ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"-1/2*cot(b*x+a)^2/b-ln(sin(b*x+a))/b","A"
150,1,55,30,0.020000," ","int(cos(b*x+a)^2/sin(b*x+a)^3,x)","-\frac{\cos^{3}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}-\frac{\cos \left(b x +a \right)}{2 b}-\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2/b*cos(b*x+a)^3/sin(b*x+a)^2-1/2*cos(b*x+a)/b-1/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
151,1,14,13,0.006000," ","int(cos(b*x+a)/sin(b*x+a)^3,x)","-\frac{1}{2 \sin \left(b x +a \right)^{2} b}"," ",0,"-1/2/sin(b*x+a)^2/b","A"
152,1,26,25,0.032000," ","int(sec(b*x+a)/sin(b*x+a)^3,x)","-\frac{1}{2 \sin \left(b x +a \right)^{2} b}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/2/sin(b*x+a)^2/b+ln(tan(b*x+a))/b","A"
153,1,57,43,0.033000," ","int(sec(b*x+a)^2/sin(b*x+a)^3,x)","-\frac{1}{2 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{3}{2 b \cos \left(b x +a \right)}+\frac{3 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2/b/sin(b*x+a)^2/cos(b*x+a)+3/2/b/cos(b*x+a)+3/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
154,1,48,39,0.038000," ","int(sec(b*x+a)^3/sin(b*x+a)^3,x)","\frac{1}{2 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{1}{\sin \left(b x +a \right)^{2} b}+\frac{2 \ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/2/b/sin(b*x+a)^2/cos(b*x+a)^2-1/sin(b*x+a)^2/b+2*ln(tan(b*x+a))/b","A"
155,1,78,58,0.039000," ","int(sec(b*x+a)^4/sin(b*x+a)^3,x)","\frac{1}{3 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{5}{6 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{5}{2 b \cos \left(b x +a \right)}+\frac{5 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"1/3/b/sin(b*x+a)^2/cos(b*x+a)^3-5/6/b/sin(b*x+a)^2/cos(b*x+a)+5/2/b/cos(b*x+a)+5/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
156,1,69,52,0.038000," ","int(sec(b*x+a)^5/sin(b*x+a)^3,x)","\frac{1}{4 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{4}}+\frac{3}{4 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{2 \sin \left(b x +a \right)^{2} b}+\frac{3 \ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/4/b/sin(b*x+a)^2/cos(b*x+a)^4+3/4/b/sin(b*x+a)^2/cos(b*x+a)^2-3/2/sin(b*x+a)^2/b+3*ln(tan(b*x+a))/b","A"
157,1,90,62,0.060000," ","int(cos(b*x+a)^9/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{10}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{7 \left(\cos^{10}\left(b x +a \right)\right)}{3 \sin \left(b x +a \right)}+\frac{7 \left(\frac{128}{35}+\cos^{8}\left(b x +a \right)+\frac{8 \left(\cos^{6}\left(b x +a \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(b x +a \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(b x +a \right)\right)}{35}\right) \sin \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(-1/3/sin(b*x+a)^3*cos(b*x+a)^10+7/3/sin(b*x+a)*cos(b*x+a)^10+7/3*(128/35+cos(b*x+a)^8+8/7*cos(b*x+a)^6+48/35*cos(b*x+a)^4+64/35*cos(b*x+a)^2)*sin(b*x+a))","A"
158,1,94,70,0.056000," ","int(cos(b*x+a)^8/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{9}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{2 \left(\cos^{9}\left(b x +a \right)\right)}{\sin \left(b x +a \right)}+2 \left(\cos^{7}\left(b x +a \right)+\frac{7 \left(\cos^{5}\left(b x +a \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(b x +a \right)\right)}{24}+\frac{35 \cos \left(b x +a \right)}{16}\right) \sin \left(b x +a \right)+\frac{35 b x}{8}+\frac{35 a}{8}}{b}"," ",0,"1/b*(-1/3/sin(b*x+a)^3*cos(b*x+a)^9+2/sin(b*x+a)*cos(b*x+a)^9+2*(cos(b*x+a)^7+7/6*cos(b*x+a)^5+35/24*cos(b*x+a)^3+35/16*cos(b*x+a))*sin(b*x+a)+35/8*b*x+35/8*a)","A"
159,1,80,49,0.021000," ","int(cos(b*x+a)^7/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{8}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{5 \left(\cos^{8}\left(b x +a \right)\right)}{3 \sin \left(b x +a \right)}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(-1/3/sin(b*x+a)^3*cos(b*x+a)^8+5/3/sin(b*x+a)*cos(b*x+a)^8+5/3*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
160,1,84,49,0.022000," ","int(cos(b*x+a)^6/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{7}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{4 \left(\cos^{7}\left(b x +a \right)\right)}{3 \sin \left(b x +a \right)}+\frac{4 \left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)}{3}+\frac{5 b x}{2}+\frac{5 a}{2}}{b}"," ",0,"1/b*(-1/3*cos(b*x+a)^7/sin(b*x+a)^3+4/3/sin(b*x+a)*cos(b*x+a)^7+4/3*(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)+5/2*b*x+5/2*a)","A"
161,1,68,35,0.023000," ","int(cos(b*x+a)^5/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{6}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{\cos^{6}\left(b x +a \right)}{\sin \left(b x +a \right)}+\left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{b}"," ",0,"1/b*(-1/3*cos(b*x+a)^6/sin(b*x+a)^3+cos(b*x+a)^6/sin(b*x+a)+(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
162,1,26,25,0.023000," ","int(cos(b*x+a)^4/sin(b*x+a)^4,x)","\frac{-\frac{\left(\cot^{3}\left(b x +a \right)\right)}{3}+\cot \left(b x +a \right)+b x +a}{b}"," ",0,"1/b*(-1/3*cot(b*x+a)^3+cot(b*x+a)+b*x+a)","A"
163,1,60,24,0.024000," ","int(cos(b*x+a)^3/sin(b*x+a)^4,x)","\frac{-\frac{\cos^{4}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3}}+\frac{\cos^{4}\left(b x +a \right)}{3 \sin \left(b x +a \right)}+\frac{\left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(-1/3*cos(b*x+a)^4/sin(b*x+a)^3+1/3*cos(b*x+a)^4/sin(b*x+a)+1/3*(2+cos(b*x+a)^2)*sin(b*x+a))","B"
164,1,22,13,0.022000," ","int(cos(b*x+a)^2/sin(b*x+a)^4,x)","-\frac{\cos^{3}\left(b x +a \right)}{3 \sin \left(b x +a \right)^{3} b}"," ",0,"-1/3*cos(b*x+a)^3/sin(b*x+a)^3/b","A"
165,1,14,13,0.005000," ","int(cos(b*x+a)/sin(b*x+a)^4,x)","-\frac{1}{3 \sin \left(b x +a \right)^{3} b}"," ",0,"-1/3/sin(b*x+a)^3/b","A"
166,1,46,36,0.033000," ","int(sec(b*x+a)/sin(b*x+a)^4,x)","-\frac{1}{3 \sin \left(b x +a \right)^{3} b}-\frac{1}{b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/3/sin(b*x+a)^3/b-1/b/sin(b*x+a)+1/b*ln(sec(b*x+a)+tan(b*x+a))","A"
167,1,50,35,0.035000," ","int(sec(b*x+a)^2/sin(b*x+a)^4,x)","\frac{-\frac{1}{3 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{4}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{8 \cot \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(-1/3/sin(b*x+a)^3/cos(b*x+a)+4/3/sin(b*x+a)/cos(b*x+a)-8/3*cot(b*x+a))","A"
168,1,76,58,0.040000," ","int(sec(b*x+a)^3/sin(b*x+a)^4,x)","-\frac{1}{3 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{5}{6 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{5}{2 b \sin \left(b x +a \right)}+\frac{5 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"-1/3/b/sin(b*x+a)^3/cos(b*x+a)^2+5/6/b/sin(b*x+a)/cos(b*x+a)^2-5/2/b/sin(b*x+a)+5/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
169,1,68,49,0.046000," ","int(sec(b*x+a)^4/sin(b*x+a)^4,x)","\frac{\frac{1}{3 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{3}}-\frac{2}{3 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{8}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{16 \cot \left(b x +a \right)}{3}}{b}"," ",0,"1/b*(1/3/sin(b*x+a)^3/cos(b*x+a)^3-2/3/sin(b*x+a)^3/cos(b*x+a)+8/3/sin(b*x+a)/cos(b*x+a)-16/3*cot(b*x+a))","A"
170,1,97,79,0.049000," ","int(sec(b*x+a)^5/sin(b*x+a)^4,x)","\frac{1}{4 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{4}}-\frac{7}{12 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{35}{24 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{35}{8 b \sin \left(b x +a \right)}+\frac{35 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/4/b/sin(b*x+a)^3/cos(b*x+a)^4-7/12/b/sin(b*x+a)^3/cos(b*x+a)^2+35/24/b/sin(b*x+a)/cos(b*x+a)^2-35/8/b/sin(b*x+a)+35/8/b*ln(sec(b*x+a)+tan(b*x+a))","A"
171,1,107,65,0.026000," ","int(cos(b*x+a)^9/sin(b*x+a)^5,x)","-\frac{\cos^{10}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}+\frac{3 \left(\cos^{10}\left(b x +a \right)\right)}{4 b \sin \left(b x +a \right)^{2}}+\frac{3 \left(\cos^{8}\left(b x +a \right)\right)}{4 b}+\frac{\cos^{6}\left(b x +a \right)}{b}+\frac{3 \left(\cos^{4}\left(b x +a \right)\right)}{2 b}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{b}+\frac{6 \ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"-1/4/b/sin(b*x+a)^4*cos(b*x+a)^10+3/4/b/sin(b*x+a)^2*cos(b*x+a)^10+3/4*cos(b*x+a)^8/b+cos(b*x+a)^6/b+3/2*cos(b*x+a)^4/b+3*cos(b*x+a)^2/b+6*ln(sin(b*x+a))/b","A"
172,1,115,79,0.023000," ","int(cos(b*x+a)^8/sin(b*x+a)^5,x)","-\frac{\cos^{9}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}+\frac{5 \left(\cos^{9}\left(b x +a \right)\right)}{8 b \sin \left(b x +a \right)^{2}}+\frac{5 \left(\cos^{7}\left(b x +a \right)\right)}{8 b}+\frac{7 \left(\cos^{5}\left(b x +a \right)\right)}{8 b}+\frac{35 \left(\cos^{3}\left(b x +a \right)\right)}{24 b}+\frac{35 \cos \left(b x +a \right)}{8 b}+\frac{35 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b*cos(b*x+a)^9/sin(b*x+a)^4+5/8/b/sin(b*x+a)^2*cos(b*x+a)^9+5/8*cos(b*x+a)^7/b+7/8*cos(b*x+a)^5/b+35/24*cos(b*x+a)^3/b+35/8*cos(b*x+a)/b+35/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
173,1,95,52,0.022000," ","int(cos(b*x+a)^7/sin(b*x+a)^5,x)","-\frac{\cos^{8}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}+\frac{\cos^{8}\left(b x +a \right)}{2 b \sin \left(b x +a \right)^{2}}+\frac{\cos^{6}\left(b x +a \right)}{2 b}+\frac{3 \left(\cos^{4}\left(b x +a \right)\right)}{4 b}+\frac{3 \left(\cos^{2}\left(b x +a \right)\right)}{2 b}+\frac{3 \ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"-1/4/b*cos(b*x+a)^8/sin(b*x+a)^4+1/2/b/sin(b*x+a)^2*cos(b*x+a)^8+1/2*cos(b*x+a)^6/b+3/4*cos(b*x+a)^4/b+3/2*cos(b*x+a)^2/b+3*ln(sin(b*x+a))/b","A"
174,1,102,62,0.023000," ","int(cos(b*x+a)^6/sin(b*x+a)^5,x)","-\frac{\cos^{7}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}+\frac{3 \left(\cos^{7}\left(b x +a \right)\right)}{8 b \sin \left(b x +a \right)^{2}}+\frac{3 \left(\cos^{5}\left(b x +a \right)\right)}{8 b}+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{8 b}+\frac{15 \cos \left(b x +a \right)}{8 b}+\frac{15 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b*cos(b*x+a)^7/sin(b*x+a)^4+3/8/b*cos(b*x+a)^7/sin(b*x+a)^2+3/8*cos(b*x+a)^5/b+5/8*cos(b*x+a)^3/b+15/8*cos(b*x+a)/b+15/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
175,1,39,38,0.022000," ","int(cos(b*x+a)^5/sin(b*x+a)^5,x)","\frac{\cot^{2}\left(b x +a \right)}{2 b}-\frac{\cot^{4}\left(b x +a \right)}{4 b}+\frac{\ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"1/2*cot(b*x+a)^2/b-1/4*cot(b*x+a)^4/b+ln(sin(b*x+a))/b","A"
176,1,89,49,0.024000," ","int(cos(b*x+a)^4/sin(b*x+a)^5,x)","-\frac{\cos^{5}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}+\frac{\cos^{5}\left(b x +a \right)}{8 b \sin \left(b x +a \right)^{2}}+\frac{\cos^{3}\left(b x +a \right)}{8 b}+\frac{3 \cos \left(b x +a \right)}{8 b}+\frac{3 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b*cos(b*x+a)^5/sin(b*x+a)^4+1/8/b*cos(b*x+a)^5/sin(b*x+a)^2+1/8*cos(b*x+a)^3/b+3/8*cos(b*x+a)/b+3/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
177,1,22,13,0.022000," ","int(cos(b*x+a)^3/sin(b*x+a)^5,x)","-\frac{\cos^{4}\left(b x +a \right)}{4 \sin \left(b x +a \right)^{4} b}"," ",0,"-1/4*cos(b*x+a)^4/sin(b*x+a)^4/b","A"
178,1,76,49,0.022000," ","int(cos(b*x+a)^2/sin(b*x+a)^5,x)","-\frac{\cos^{3}\left(b x +a \right)}{4 b \sin \left(b x +a \right)^{4}}-\frac{\cos^{3}\left(b x +a \right)}{8 b \sin \left(b x +a \right)^{2}}-\frac{\cos \left(b x +a \right)}{8 b}-\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b*cos(b*x+a)^3/sin(b*x+a)^4-1/8/b*cos(b*x+a)^3/sin(b*x+a)^2-1/8*cos(b*x+a)/b-1/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
179,1,14,13,0.006000," ","int(cos(b*x+a)/sin(b*x+a)^5,x)","-\frac{1}{4 \sin \left(b x +a \right)^{4} b}"," ",0,"-1/4/sin(b*x+a)^4/b","A"
180,1,39,38,0.032000," ","int(sec(b*x+a)/sin(b*x+a)^5,x)","-\frac{1}{4 \sin \left(b x +a \right)^{4} b}-\frac{1}{2 \sin \left(b x +a \right)^{2} b}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/4/sin(b*x+a)^4/b-1/2/sin(b*x+a)^2/b+ln(tan(b*x+a))/b","A"
181,1,78,62,0.033000," ","int(sec(b*x+a)^2/sin(b*x+a)^5,x)","-\frac{1}{4 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)}-\frac{5}{8 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{15}{8 b \cos \left(b x +a \right)}+\frac{15 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b/sin(b*x+a)^4/cos(b*x+a)-5/8/b/sin(b*x+a)^2/cos(b*x+a)+15/8/b/cos(b*x+a)+15/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
182,1,69,52,0.048000," ","int(sec(b*x+a)^3/sin(b*x+a)^5,x)","-\frac{1}{4 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{2}}+\frac{3}{4 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{2 \sin \left(b x +a \right)^{2} b}+\frac{3 \ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"-1/4/b/sin(b*x+a)^4/cos(b*x+a)^2+3/4/b/sin(b*x+a)^2/cos(b*x+a)^2-3/2/sin(b*x+a)^2/b+3*ln(tan(b*x+a))/b","A"
183,1,99,79,0.051000," ","int(sec(b*x+a)^4/sin(b*x+a)^5,x)","-\frac{1}{4 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{3}}+\frac{7}{12 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{35}{24 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{35}{8 b \cos \left(b x +a \right)}+\frac{35 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/4/b/sin(b*x+a)^4/cos(b*x+a)^3+7/12/b/sin(b*x+a)^2/cos(b*x+a)^3-35/24/b/sin(b*x+a)^2/cos(b*x+a)+35/8/b/cos(b*x+a)+35/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
184,1,90,65,0.051000," ","int(sec(b*x+a)^5/sin(b*x+a)^5,x)","\frac{1}{4 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{4}}-\frac{1}{2 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{2}}+\frac{3}{2 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{\sin \left(b x +a \right)^{2} b}+\frac{6 \ln \left(\tan \left(b x +a \right)\right)}{b}"," ",0,"1/4/b/sin(b*x+a)^4/cos(b*x+a)^4-1/2/b/sin(b*x+a)^4/cos(b*x+a)^2+3/2/b/sin(b*x+a)^2/cos(b*x+a)^2-3/sin(b*x+a)^2/b+6*ln(tan(b*x+a))/b","A"
185,1,22,13,0.017000," ","int(cos(x)^2/sin(x)^6,x)","-\frac{\cos^{3}\left(x \right)}{5 \sin \left(x \right)^{5}}-\frac{2 \left(\cos^{3}\left(x \right)\right)}{15 \sin \left(x \right)^{3}}"," ",0,"-1/5*cos(x)^3/sin(x)^5-2/15*cos(x)^3/sin(x)^3","A"
186,1,22,13,0.018000," ","int(cos(x)^3/sin(x)^7,x)","-\frac{\cos^{4}\left(x \right)}{6 \sin \left(x \right)^{6}}-\frac{\cos^{4}\left(x \right)}{12 \sin \left(x \right)^{4}}"," ",0,"-1/6/sin(x)^6*cos(x)^4-1/12*cos(x)^4/sin(x)^4","A"
187,1,19,18,0.019000," ","int((d*cos(b*x+a))^(3/2)*sin(b*x+a),x)","-\frac{2 \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}}}{5 b d}"," ",0,"-2/5*(d*cos(b*x+a))^(5/2)/b/d","A"
188,1,19,18,0.014000," ","int((d*cos(b*x+a))^(1/2)*sin(b*x+a),x)","-\frac{2 \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}}}{3 b d}"," ",0,"-2/3*(d*cos(b*x+a))^(3/2)/b/d","A"
189,1,19,18,0.016000," ","int(sin(b*x+a)/(d*cos(b*x+a))^(1/2),x)","-\frac{2 \sqrt{d \cos \left(b x +a \right)}}{b d}"," ",0,"-2*(d*cos(b*x+a))^(1/2)/b/d","A"
190,1,19,18,0.013000," ","int(sin(b*x+a)/(d*cos(b*x+a))^(3/2),x)","\frac{2}{b d \sqrt{d \cos \left(b x +a \right)}}"," ",0,"2/b/d/(d*cos(b*x+a))^(1/2)","A"
191,1,19,18,0.015000," ","int(sin(b*x+a)/(d*cos(b*x+a))^(5/2),x)","\frac{2}{3 b d \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}}}"," ",0,"2/3/b/d/(d*cos(b*x+a))^(3/2)","A"
192,1,19,18,0.014000," ","int(sin(b*x+a)/(d*cos(b*x+a))^(7/2),x)","\frac{2}{5 b d \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}}}"," ",0,"2/5/b/d/(d*cos(b*x+a))^(5/2)","A"
193,1,19,18,0.014000," ","int(sin(b*x+a)/(d*cos(b*x+a))^(9/2),x)","\frac{2}{7 b d \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}}}"," ",0,"2/7/b/d/(d*cos(b*x+a))^(7/2)","A"
194,1,249,134,0.137000," ","int((d*cos(b*x+a))^(9/2)*sin(b*x+a)^2,x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{5} \left(2880 \left(\cos^{15}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-11520 \left(\cos^{13}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+19280 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-17520 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+9284 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2808 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+425 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+21 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-21 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{585 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/585*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^5*(2880*cos(1/2*b*x+1/2*a)^15-11520*cos(1/2*b*x+1/2*a)^13+19280*cos(1/2*b*x+1/2*a)^11-17520*cos(1/2*b*x+1/2*a)^9+9284*cos(1/2*b*x+1/2*a)^7-2808*cos(1/2*b*x+1/2*a)^5+425*cos(1/2*b*x+1/2*a)^3+21*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-21*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
195,1,236,134,0.080000," ","int((d*cos(b*x+a))^(7/2)*sin(b*x+a)^2,x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{4} \left(672 \left(\cos^{13}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2352 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3312 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2400 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+922 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-159 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+5 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{231 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/231*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^4*(672*cos(1/2*b*x+1/2*a)^13-2352*cos(1/2*b*x+1/2*a)^11+3312*cos(1/2*b*x+1/2*a)^9-2400*cos(1/2*b*x+1/2*a)^7+922*cos(1/2*b*x+1/2*a)^5-159*cos(1/2*b*x+1/2*a)^3-5*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+5*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
196,1,223,110,0.086000," ","int((d*cos(b*x+a))^(5/2)*sin(b*x+a)^2,x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{3} \left(80 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-240 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+272 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-144 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+35 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-3 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{45 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/45*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^3*(80*cos(1/2*b*x+1/2*a)^11-240*cos(1/2*b*x+1/2*a)^9+272*cos(1/2*b*x+1/2*a)^7-144*cos(1/2*b*x+1/2*a)^5+35*cos(1/2*b*x+1/2*a)^3+3*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-3*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
197,1,208,110,0.079000," ","int((d*cos(b*x+a))^(3/2)*sin(b*x+a)^2,x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{2} \left(24 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-60 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+50 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-15 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+\cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{21 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/21*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^2*(24*cos(1/2*b*x+1/2*a)^9-60*cos(1/2*b*x+1/2*a)^7+50*cos(1/2*b*x+1/2*a)^5-15*cos(1/2*b*x+1/2*a)^3-(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
198,1,194,85,0.085000," ","int((d*cos(b*x+a))^(1/2)*sin(b*x+a)^2,x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d \left(4 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{5 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/5*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d*(4*cos(1/2*b*x+1/2*a)^7-8*cos(1/2*b*x+1/2*a)^5+5*cos(1/2*b*x+1/2*a)^3+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
199,1,188,85,0.072000," ","int(sin(b*x+a)^2/(d*cos(b*x+a))^(1/2),x)","\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(2 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/3*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4-(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
200,1,168,88,0.093000," ","int(sin(b*x+a)^2/(d*cos(b*x+a))^(3/2),x)","-\frac{4 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d}\, \left(\sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{d \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-4/d*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(1/2)*((2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
201,1,242,88,0.104000," ","int(sin(b*x+a)^2/(d*cos(b*x+a))^(5/2),x)","-\frac{4 \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{3 d^{2} \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-4/3*(2*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2-(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/d^2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
202,1,365,112,0.128000," ","int(sin(b*x+a)^2/(d*cos(b*x+a))^(7/2),x)","-\frac{4 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(4 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-4 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+8 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d}}{5 d^{4} \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-4/5*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/d^4/sin(1/2*b*x+1/2*a)^3/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)*(4*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^4-8*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)-4*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+8*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4+(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(1/2)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
203,1,396,112,0.099000," ","int(sin(b*x+a)^2/(d*cos(b*x+a))^(9/2),x)","\frac{4 \left(-8 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+12 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-6 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+8 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{21 d^{4} \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{3} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"4/21*(-8*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^6+12*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^4-8*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)-6*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+8*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/d^4*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)^3/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
204,1,63,37,0.062000," ","int((d*cos(b*x+a))^(1/2)*sin(b*x+a)^3,x)","-\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(6 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-9 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}{21 b}"," ",0,"-8/21*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(6*sin(1/2*b*x+1/2*a)^6-9*sin(1/2*b*x+1/2*a)^4+sin(1/2*b*x+1/2*a)^2+1)/b","A"
205,1,92,37,0.051000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(1/2),x)","\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{5 d b}"," ",0,"1/5*(8*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*sin(1/2*b*x+1/2*a)^4-8*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*sin(1/2*b*x+1/2*a)^2-8*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2))/d/b","B"
206,1,70,37,0.119000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(3/2),x)","-\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{3 d^{2} \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"-8/3/d^2*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2+1)/(2*sin(1/2*b*x+1/2*a)^2-1)/b","A"
207,1,85,37,0.148000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(5/2),x)","\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(3 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{3 d^{3} \left(4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"8/3/d^3/(4*sin(1/2*b*x+1/2*a)^4-4*sin(1/2*b*x+1/2*a)^2+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(3*sin(1/2*b*x+1/2*a)^4-3*sin(1/2*b*x+1/2*a)^2+1)/b","B"
208,1,98,37,0.244000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(7/2),x)","\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(5 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{5 d^{4} \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"8/5/d^4/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(5*sin(1/2*b*x+1/2*a)^4-5*sin(1/2*b*x+1/2*a)^2+1)/b","B"
209,1,111,37,0.250000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(9/2),x)","-\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(7 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{21 d^{5} \left(16 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"-8/21/d^5/(16*sin(1/2*b*x+1/2*a)^8-32*sin(1/2*b*x+1/2*a)^6+24*sin(1/2*b*x+1/2*a)^4-8*sin(1/2*b*x+1/2*a)^2+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(7*sin(1/2*b*x+1/2*a)^4-7*sin(1/2*b*x+1/2*a)^2+1)/b","B"
210,1,124,37,0.291000," ","int(sin(b*x+a)^3/(d*cos(b*x+a))^(11/2),x)","\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, \left(9 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-9 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{45 d^{6} \left(32 \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-80 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+80 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+10 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"8/45/d^6/(32*sin(1/2*b*x+1/2*a)^10-80*sin(1/2*b*x+1/2*a)^8+80*sin(1/2*b*x+1/2*a)^6-40*sin(1/2*b*x+1/2*a)^4+10*sin(1/2*b*x+1/2*a)^2-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*(9*sin(1/2*b*x+1/2*a)^4-9*sin(1/2*b*x+1/2*a)^2+1)/b","B"
211,1,275,160,0.119000," ","int((d*cos(b*x+a))^(9/2)*sin(b*x+a)^4,x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{5} \left(24960 \left(\cos^{19}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-124800 \left(\cos^{17}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+265440 \left(\cos^{15}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-312960 \left(\cos^{13}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+222520 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-96360 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+23866 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2652 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-35 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-21 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+21 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3315 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/3315*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^5*(24960*cos(1/2*b*x+1/2*a)^19-124800*cos(1/2*b*x+1/2*a)^17+265440*cos(1/2*b*x+1/2*a)^15-312960*cos(1/2*b*x+1/2*a)^13+222520*cos(1/2*b*x+1/2*a)^11-96360*cos(1/2*b*x+1/2*a)^9+23866*cos(1/2*b*x+1/2*a)^7-2652*cos(1/2*b*x+1/2*a)^5-35*cos(1/2*b*x+1/2*a)^3-21*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))+21*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
212,1,262,160,0.107000," ","int((d*cos(b*x+a))^(7/2)*sin(b*x+a)^4,x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{4} \left(4928 \left(\cos^{17}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-22176 \left(\cos^{15}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+41216 \left(\cos^{13}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-40768 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+22868 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-6994 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+926 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-5 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{1155 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/1155*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^4*(4928*cos(1/2*b*x+1/2*a)^17-22176*cos(1/2*b*x+1/2*a)^15+41216*cos(1/2*b*x+1/2*a)^13-40768*cos(1/2*b*x+1/2*a)^11+22868*cos(1/2*b*x+1/2*a)^9-6994*cos(1/2*b*x+1/2*a)^7+926*cos(1/2*b*x+1/2*a)^5+5*cos(1/2*b*x+1/2*a)^3+5*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-5*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
213,1,249,136,0.109000," ","int((d*cos(b*x+a))^(5/2)*sin(b*x+a)^4,x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{3} \left(480 \left(\cos^{15}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1920 \left(\cos^{13}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3040 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2400 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+958 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-156 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+3 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{195 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/195*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^3*(480*cos(1/2*b*x+1/2*a)^15-1920*cos(1/2*b*x+1/2*a)^13+3040*cos(1/2*b*x+1/2*a)^11-2400*cos(1/2*b*x+1/2*a)^9+958*cos(1/2*b*x+1/2*a)^7-156*cos(1/2*b*x+1/2*a)^5-5*cos(1/2*b*x+1/2*a)^3-3*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))+3*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
214,1,255,136,0.108000," ","int((d*cos(b*x+a))^(3/2)*sin(b*x+a)^4,x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{2} \left(112 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{12}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-280 \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+228 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-62 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{77 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/77*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^2*(112*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^12-280*sin(1/2*b*x+1/2*a)^10*cos(1/2*b*x+1/2*a)+228*sin(1/2*b*x+1/2*a)^8*cos(1/2*b*x+1/2*a)-62*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
215,1,221,111,0.102000," ","int((d*cos(b*x+a))^(1/2)*sin(b*x+a)^4,x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d \left(40 \left(\cos^{11}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-120 \left(\cos^{9}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+118 \left(\cos^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-36 \left(\cos^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5 \left(\cos^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+3 \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{45 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/45*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d*(40*cos(1/2*b*x+1/2*a)^11-120*cos(1/2*b*x+1/2*a)^9+118*cos(1/2*b*x+1/2*a)^7-36*cos(1/2*b*x+1/2*a)^5-5*cos(1/2*b*x+1/2*a)^3-3*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(-2*cos(1/2*b*x+1/2*a)^2+1)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))+3*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
216,1,208,111,0.100000," ","int(sin(b*x+a)^4/(d*cos(b*x+a))^(1/2),x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(4 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-6 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)+\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{7 \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/7*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*(4*sin(1/2*b*x+1/2*a)^8*cos(1/2*b*x+1/2*a)-6*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)+(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))+sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
217,1,213,114,0.110000," ","int(sin(b*x+a)^4/(d*cos(b*x+a))^(3/2),x)","-\frac{8 \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d}\, \left(-2 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-3 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{5 d \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/5/d*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)+2*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4+3*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-3*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
218,1,286,114,0.109000," ","int(sin(b*x+a)^4/(d*cos(b*x+a))^(5/2),x)","-\frac{8 \left(-2 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{3 d^{2} \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/3*(-2*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)+2*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+2*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4-(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/d^2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
219,1,366,114,0.159000," ","int(sin(b*x+a)^4/(d*cos(b*x+a))^(7/2),x)","-\frac{8 \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-14 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+14 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-3 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d}}{5 d^{4} \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-8/5*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/d^4/sin(1/2*b*x+1/2*a)^3/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)*(12*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^4-14*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)-12*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+14*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4+3*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))-3*sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(1/2)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
220,1,398,114,0.116000," ","int(sin(b*x+a)^4/(d*cos(b*x+a))^(9/2),x)","\frac{8 \left(8 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-6 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+6 \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}}{7 d^{4} \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{3} \sqrt{-d \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"8/7*(8*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^6-12*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^4-6*sin(1/2*b*x+1/2*a)^6*cos(1/2*b*x+1/2*a)+6*(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*sin(1/2*b*x+1/2*a)^2+6*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4-(sin(1/2*b*x+1/2*a)^2)^(1/2)*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))-sin(1/2*b*x+1/2*a)^2*cos(1/2*b*x+1/2*a))/d^4*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(2*cos(1/2*b*x+1/2*a)^2-1)^3/(-d*(2*sin(1/2*b*x+1/2*a)^4-sin(1/2*b*x+1/2*a)^2))^(1/2)/sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
221,1,103,40,0.129000," ","int(cos(b*x+a)^(3/2)*sin(b*x+a)^5,x)","-\frac{32 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1}\, \left(180 \left(\sin^{12}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-540 \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+545 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-190 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2\right)}{585 b}"," ",0,"-32/585*(-2*sin(1/2*b*x+1/2*a)^2+1)^(1/2)*(180*sin(1/2*b*x+1/2*a)^12-540*sin(1/2*b*x+1/2*a)^10+545*sin(1/2*b*x+1/2*a)^8-190*sin(1/2*b*x+1/2*a)^6+3*sin(1/2*b*x+1/2*a)^4+2*sin(1/2*b*x+1/2*a)^2+2)/b","B"
222,1,318,80,0.200000," ","int((d*cos(b*x+a))^(9/2)*csc(b*x+a),x)","-\frac{16 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{4} \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{7 b}-\frac{d^{\frac{9}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 b}-\frac{d^{\frac{9}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 b}+\frac{24 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{4} \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{7 b}-\frac{64 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{4} \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{21 b}-\frac{d^{5} \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}+\frac{20 d^{4} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{21 b}"," ",0,"-16/7/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^4*sin(1/2*b*x+1/2*a)^6-1/2/b*d^(9/2)*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))-1/2/b*d^(9/2)*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))+24/7/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^4*sin(1/2*b*x+1/2*a)^4-64/21/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^4*sin(1/2*b*x+1/2*a)^2-1/(-d)^(1/2)/b*d^5*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))+20/21/b*d^4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
223,1,280,81,0.176000," ","int((d*cos(b*x+a))^(7/2)*csc(b*x+a),x)","\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{3} \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{5 b}-\frac{d^{\frac{7}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 b}-\frac{d^{\frac{7}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 b}-\frac{8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{3} \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{5 b}+\frac{12 d^{3} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{5 b}+\frac{d^{4} \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}"," ",0,"8/5/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^3*sin(1/2*b*x+1/2*a)^4-1/2/b*d^(7/2)*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))-1/2/b*d^(7/2)*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))-8/5/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^3*sin(1/2*b*x+1/2*a)^2+12/5/b*d^3*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+1/(-d)^(1/2)/b*d^4*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))","B"
224,1,244,62,0.181000," ","int((d*cos(b*x+a))^(5/2)*csc(b*x+a),x)","-\frac{d^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 b}-\frac{d^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 b}-\frac{4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{2} \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 b}+\frac{2 d^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{3 b}-\frac{d^{3} \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}"," ",0,"-1/2/b*d^(5/2)*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))-1/2/b*d^(5/2)*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))-4/3/b*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^2*sin(1/2*b*x+1/2*a)^2+2/3/b*d^2*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-1/(-d)^(1/2)/b*d^3*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))","B"
225,1,204,63,0.171000," ","int((d*cos(b*x+a))^(3/2)*csc(b*x+a),x)","-\frac{d^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 b}-\frac{d^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 b}+\frac{2 d \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{b}+\frac{d^{2} \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}"," ",0,"-1/2/b*d^(3/2)*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))-1/2/b*d^(3/2)*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))+2/b*d*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+1/(-d)^(1/2)/b*d^2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))","B"
226,1,179,46,0.172000," ","int((d*cos(b*x+a))^(1/2)*csc(b*x+a),x)","-\frac{\sqrt{d}\, \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 b}-\frac{\sqrt{d}\, \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 b}-\frac{d \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}"," ",0,"-1/2/b*d^(1/2)*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))-1/2/b*d^(1/2)*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))-1/(-d)^(1/2)/b*d*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))","B"
227,1,177,47,0.198000," ","int(csc(b*x+a)/(d*cos(b*x+a))^(1/2),x)","-\frac{\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{2 \sqrt{d}\, b}-\frac{\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{2 \sqrt{d}\, b}+\frac{\ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\sqrt{-d}\, b}"," ",0,"-1/2/d^(1/2)/b*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))-1/2/d^(1/2)/b*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))+1/(-d)^(1/2)/b*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))","B"
228,1,422,64,0.327000," ","int(csc(b*x+a)/(d*cos(b*x+a))^(3/2),x)","\frac{-\left(4 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{5}{2}}+2 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{2}+2 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{5}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{3}{2}} \sqrt{-d}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{2}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{2}}{2 d^{\frac{7}{2}} \sqrt{-d}\, \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"1/2*(-(4*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(5/2)+2*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2+2*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2)*sin(1/2*b*x+1/2*a)^2+2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(5/2)-4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(3/2)*(-d)^(1/2)+ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2+ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2)/d^(7/2)/(-d)^(1/2)/(2*sin(1/2*b*x+1/2*a)^2-1)/b","B"
229,1,624,65,0.308000," ","int(csc(b*x+a)/(d*cos(b*x+a))^(5/2),x)","\frac{\left(24 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}-12 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}-12 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\left(-24 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}+12 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}+12 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}+4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{5}{2}} \sqrt{-d}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}}{6 d^{\frac{11}{2}} \sqrt{-d}\, \left(4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"1/6*((24*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)-12*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-12*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^4+(-24*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)+12*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3+12*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^2+6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)+4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(5/2)*(-d)^(1/2)-3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)/d^(11/2)/(-d)^(1/2)/(4*sin(1/2*b*x+1/2*a)^4-4*sin(1/2*b*x+1/2*a)^2+1)/b","B"
230,1,882,82,0.320000," ","int(csc(b*x+a)/(d*cos(b*x+a))^(7/2),x)","\frac{10 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-24 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}-40 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+20 \left(6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-10 \left(6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-8 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{10 d^{\frac{15}{2}} \sqrt{-d}\, \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"1/10/d^(15/2)/(-d)^(1/2)/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)*(10*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-24*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+5*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+5*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4-40*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)+ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^6+20*(6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^4-10*(6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-8*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^2)/b","B"
231,1,1086,83,0.372000," ","int(csc(b*x+a)/(d*cos(b*x+a))^(9/2),x)","\frac{42 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{11}{2}}+40 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{9}{2}} \sqrt{-d}-21 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{5}-21 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{5}+336 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{11}{2}}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{5}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{5}\right) \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-672 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{11}{2}}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{5}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{5}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-56 \left(6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{11}{2}}+2 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{9}{2}} \sqrt{-d}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{5}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{5}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+56 \left(18 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{11}{2}}+2 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{9}{2}} \sqrt{-d}-9 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{5}-9 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{5}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{42 d^{\frac{19}{2}} \sqrt{-d}\, \left(16 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"1/42/d^(19/2)/(-d)^(1/2)/(16*sin(1/2*b*x+1/2*a)^8-32*sin(1/2*b*x+1/2*a)^6+24*sin(1/2*b*x+1/2*a)^4-8*sin(1/2*b*x+1/2*a)^2+1)*(42*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(11/2)+40*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(9/2)*(-d)^(1/2)-21*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5-21*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5+336*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(11/2)-ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5-ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5)*sin(1/2*b*x+1/2*a)^8-672*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(11/2)-ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5-ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5)*sin(1/2*b*x+1/2*a)^6-56*(6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(11/2)+2*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(9/2)*(-d)^(1/2)-3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5-3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5)*sin(1/2*b*x+1/2*a)^2+56*(18*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(11/2)+2*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(9/2)*(-d)^(1/2)-9*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5-9*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^5)*sin(1/2*b*x+1/2*a)^4)/b","B"
232,1,242,134,0.276000," ","int((d*cos(b*x+a))^(11/2)*csc(b*x+a)^2,x)","-\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{7} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(-128 \left(\sin^{12}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+384 \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-576 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+30 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+512 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-204 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+12 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+7\right)}{14 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-1/14*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^7/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(-128*sin(1/2*b*x+1/2*a)^12+384*sin(1/2*b*x+1/2*a)^10-576*sin(1/2*b*x+1/2*a)^8+30*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+512*sin(1/2*b*x+1/2*a)^6-204*sin(1/2*b*x+1/2*a)^4+12*sin(1/2*b*x+1/2*a)^2+7)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
233,1,229,110,0.266000," ","int((d*cos(b*x+a))^(9/2)*csc(b*x+a)^2,x)","\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{6} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(-64 \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+160 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+42 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-104 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+22 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5\right)}{10 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"1/10*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^6/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(-64*sin(1/2*b*x+1/2*a)^10+160*sin(1/2*b*x+1/2*a)^8+42*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)-104*sin(1/2*b*x+1/2*a)^6-4*sin(1/2*b*x+1/2*a)^4+22*sin(1/2*b*x+1/2*a)^2-5)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
234,1,216,110,0.245000," ","int((d*cos(b*x+a))^(7/2)*csc(b*x+a)^2,x)","-\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{5} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(-32 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+10 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+64 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-28 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3\right)}{6 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-1/6*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^5/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(-32*sin(1/2*b*x+1/2*a)^8+10*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+64*sin(1/2*b*x+1/2*a)^6-28*sin(1/2*b*x+1/2*a)^4-4*sin(1/2*b*x+1/2*a)^2+3)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
235,1,203,86,0.252000," ","int((d*cos(b*x+a))^(5/2)*csc(b*x+a)^2,x)","\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{4} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(6 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}{2 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"1/2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^4/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(6*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
236,1,190,86,0.264000," ","int((d*cos(b*x+a))^(3/2)*csc(b*x+a)^2,x)","-\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{3} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(2 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{2 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-1/2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^3/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(2*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+4*sin(1/2*b*x+1/2*a)^4-4*sin(1/2*b*x+1/2*a)^2+1)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
237,1,203,85,0.362000," ","int((d*cos(b*x+a))^(1/2)*csc(b*x+a)^2,x)","\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d^{2} \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(2 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}{2 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"1/2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)*d^2/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)*(2*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
238,1,188,84,0.261000," ","int(csc(b*x+a)^2/(d*cos(b*x+a))^(1/2),x)","\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, d \sin \left(\frac{b x}{2}+\frac{a}{2}\right) \left(2 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-4 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+4 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}{2 \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"1/2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*d*sin(1/2*b*x+1/2*a)*(2*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)-4*sin(1/2*b*x+1/2*a)^4+4*sin(1/2*b*x+1/2*a)^2-1)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
239,1,209,112,0.328000," ","int(csc(b*x+a)^2/(d*cos(b*x+a))^(3/2),x)","-\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \left(6 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{2 d^{3} \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{5} \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{2} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-1/2*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/d^3/sin(1/2*b*x+1/2*a)^5/(2*sin(1/2*b*x+1/2*a)^2-1)^2/cos(1/2*b*x+1/2*a)*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)*(6*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+12*sin(1/2*b*x+1/2*a)^4-12*sin(1/2*b*x+1/2*a)^2+1)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
240,1,190,112,0.377000," ","int(csc(b*x+a)^2/(d*cos(b*x+a))^(5/2),x)","\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(10 \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticF \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-20 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+20 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3\right) \sin \left(\frac{b x}{2}+\frac{a}{2}\right)}{6 d \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"1/6*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/d/(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/cos(1/2*b*x+1/2*a)*(10*(2*sin(1/2*b*x+1/2*a)^2-1)^(3/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticF(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)-20*sin(1/2*b*x+1/2*a)^4+20*sin(1/2*b*x+1/2*a)^2-3)*sin(1/2*b*x+1/2*a)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","A"
241,1,408,136,0.389000," ","int(csc(b*x+a)^2/(d*cos(b*x+a))^(7/2),x)","-\frac{\sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}\, \left(168 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+336 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-168 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-672 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+42 \sqrt{2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(b x +a \right)}{2}}\, \EllipticE \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right), \sqrt{2}\right) \cos \left(\frac{b x}{2}+\frac{a}{2}\right)+448 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-112 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5\right) \left(-2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +\left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d \right)^{\frac{3}{2}}}{10 d^{5} \left(2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{5} \cos \left(\frac{b x}{2}+\frac{a}{2}\right) \left(8 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}\, b}"," ",0,"-1/10*(d*(2*cos(1/2*b*x+1/2*a)^2-1)*sin(1/2*b*x+1/2*a)^2)^(1/2)/d^5/(2*sin(1/2*b*x+1/2*a)^2-1)/sin(1/2*b*x+1/2*a)^5/cos(1/2*b*x+1/2*a)/(8*sin(1/2*b*x+1/2*a)^6-12*sin(1/2*b*x+1/2*a)^4+6*sin(1/2*b*x+1/2*a)^2-1)*(168*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^4+336*sin(1/2*b*x+1/2*a)^8-168*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)*sin(1/2*b*x+1/2*a)^2-672*sin(1/2*b*x+1/2*a)^6+42*(2*sin(1/2*b*x+1/2*a)^2-1)^(1/2)*(sin(1/2*b*x+1/2*a)^2)^(1/2)*EllipticE(cos(1/2*b*x+1/2*a),2^(1/2))*cos(1/2*b*x+1/2*a)+448*sin(1/2*b*x+1/2*a)^4-112*sin(1/2*b*x+1/2*a)^2+5)*(-2*sin(1/2*b*x+1/2*a)^4*d+sin(1/2*b*x+1/2*a)^2*d)^(3/2)/(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)/b","B"
242,1,433,107,0.296000," ","int((d*cos(b*x+a))^(11/2)*csc(b*x+a)^3,x)","-\frac{8 d^{5} \left(\cos^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{5 b}+\frac{8 d^{5} \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{5 b}+\frac{8 d^{5} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{5 b}-\frac{6 d^{5} \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}}{b}+\frac{9 d^{\frac{11}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}-\frac{d^{5} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}+\frac{9 d^{\frac{11}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}-\frac{9 d^{6} \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}-\frac{d^{5} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{d^{5} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"-8/5/b*d^5*cos(1/2*b*x+1/2*a)^4*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+8/5/b*d^5*cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+8/5/b*d^5*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)-6/b*d^5*(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)+9/8/b*d^(11/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b*d^5/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+9/8/b*d^(11/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))-9/4/b*d^6/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))-1/8/b*d^5/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b*d^5/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
243,1,394,89,0.310000," ","int((d*cos(b*x+a))^(9/2)*csc(b*x+a)^3,x)","-\frac{4 d^{4} \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{3 b}-\frac{4 d^{4} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{3 b}+\frac{2 d^{4} \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}}{b}+\frac{7 d^{\frac{9}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}-\frac{d^{4} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}+\frac{7 d^{\frac{9}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}+\frac{7 d^{5} \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}+\frac{d^{4} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{d^{4} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"-4/3/b*d^4*cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)-4/3/b*d^4*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+2/b*d^4*(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)+7/8/b*d^(9/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b*d^4/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+7/8/b*d^(9/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))+7/4/b*d^5/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))+1/8/b*d^4/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b*d^4/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
244,1,327,89,0.285000," ","int((d*cos(b*x+a))^(7/2)*csc(b*x+a)^3,x)","-\frac{2 d^{3} \sqrt{d \left(2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right)}}{b}+\frac{5 d^{\frac{7}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}-\frac{d^{3} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}+\frac{5 d^{\frac{7}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}-\frac{5 d^{4} \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}-\frac{d^{3} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{d^{3} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"-2/b*d^3*(d*(2*cos(1/2*b*x+1/2*a)^2-1))^(1/2)+5/8/b*d^(7/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b*d^3/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+5/8/b*d^(7/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))-5/4/b*d^4/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))-1/8/b*d^3/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b*d^3/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
245,1,300,71,0.408000," ","int((d*cos(b*x+a))^(5/2)*csc(b*x+a)^3,x)","\frac{3 d^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}-\frac{d^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}+\frac{3 d^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}+\frac{3 d^{3} \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}+\frac{d^{2} \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{d^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"3/8/b*d^(5/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b*d^2/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+3/8/b*d^(5/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))+3/4/b*d^3/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))+1/8/b*d^2/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b*d^2/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
246,1,294,71,0.278000," ","int((d*cos(b*x+a))^(3/2)*csc(b*x+a)^3,x)","\frac{d^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}-\frac{d \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}+\frac{d^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}-\frac{d^{2} \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}-\frac{d \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{d \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"1/8/b*d^(3/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b*d/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+1/8/b*d^(3/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))-1/4/b*d^2/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))-1/8/b*d/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b*d/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
247,1,289,73,0.279000," ","int((d*cos(b*x+a))^(1/2)*csc(b*x+a)^3,x)","-\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}-\frac{\sqrt{d}\, \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 b}+\frac{\sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}-\frac{d \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}+\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}-\frac{\sqrt{d}\, \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 b}"," ",0,"-1/16/b/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-1/8/b*d^(1/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))+1/8/b/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)-1/4/b*d/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))+1/16/b/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-1/8/b*d^(1/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))","B"
248,1,297,73,0.283000," ","int(csc(b*x+a)^3/(d*cos(b*x+a))^(1/2),x)","-\frac{3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right)}{8 \sqrt{d}\, b}-\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b d \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}-\frac{3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right)}{8 \sqrt{d}\, b}+\frac{3 \ln \left(\frac{-2 d +2 \sqrt{-d}\, \sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{4 b \sqrt{-d}}-\frac{\sqrt{2 \left(\cos^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d -d}}{8 b d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)^{2}}+\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}}{16 b d \left(\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}"," ",0,"-3/8/b/d^(1/2)*ln((4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)-1))-1/16/b/d/(cos(1/2*b*x+1/2*a)+1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-3/8/b/d^(1/2)*ln((-4*d*cos(1/2*b*x+1/2*a)+2*d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d)/(cos(1/2*b*x+1/2*a)+1))+3/4/b/(-d)^(1/2)*ln((-2*d+2*(-d)^(1/2)*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2))/cos(1/2*b*x+1/2*a))-1/8/b/d/cos(1/2*b*x+1/2*a)^2*(2*cos(1/2*b*x+1/2*a)^2*d-d)^(1/2)+1/16/b/d/(cos(1/2*b*x+1/2*a)-1)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)","B"
249,1,705,91,0.539000," ","int(csc(b*x+a)^3/(d*cos(b*x+a))^(3/2),x)","\frac{-\sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{3}{2}} \sqrt{-d}-\left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \left(20 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{5}{2}}+10 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{2}+10 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{2}\right)+5 \left(6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{5}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{3}{2}} \sqrt{-d}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{2}+3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{2}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-5 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{5}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{3}{2}} \sqrt{-d}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{2}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{2}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{8 d^{\frac{7}{2}} \sqrt{-d}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{2} \left(2 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"1/8/d^(7/2)/(-d)^(1/2)/sin(1/2*b*x+1/2*a)^2/(2*sin(1/2*b*x+1/2*a)^4-3*sin(1/2*b*x+1/2*a)^2+1)*(-(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(3/2)*(-d)^(1/2)-sin(1/2*b*x+1/2*a)^6*(20*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(5/2)+10*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2+10*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2)+5*(6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(5/2)-4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(3/2)*(-d)^(1/2)+3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2+3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2)*sin(1/2*b*x+1/2*a)^4-5*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(5/2)-4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(3/2)*(-d)^(1/2)+ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2+ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^2)*sin(1/2*b*x+1/2*a)^2)/b","B"
250,1,909,91,0.465000," ","int(csc(b*x+a)^3/(d*cos(b*x+a))^(5/2),x)","\frac{3 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{5}{2}} \sqrt{-d}+84 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-168 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}-\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-7 \left(6 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}+4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{5}{2}} \sqrt{-d}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}-3 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+7 \left(30 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{7}{2}}+4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{5}{2}} \sqrt{-d}-15 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{3}-15 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{3}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{24 d^{\frac{11}{2}} \sqrt{-d}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{2} \left(4 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+5 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-1\right) b}"," ",0,"1/24/d^(11/2)/(-d)^(1/2)/sin(1/2*b*x+1/2*a)^2/(4*sin(1/2*b*x+1/2*a)^6-8*sin(1/2*b*x+1/2*a)^4+5*sin(1/2*b*x+1/2*a)^2-1)*(3*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(5/2)*(-d)^(1/2)+84*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)-ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^8-168*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)-ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^6-7*(6*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)+4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(5/2)*(-d)^(1/2)-3*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-3*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^2+7*(30*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(7/2)+4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(5/2)*(-d)^(1/2)-15*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3-15*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^3)*sin(1/2*b*x+1/2*a)^4)/b","B"
251,1,1165,109,0.520000," ","int(csc(b*x+a)^3/(d*cos(b*x+a))^(7/2),x)","\frac{-5 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}-360 \left(2 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}+\ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{10}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+180 \left(10 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-90 \left(18 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-16 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+9 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}+9 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+9 \left(70 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-104 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+35 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}+35 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-9 \left(10 \ln \left(\frac{2 \sqrt{-d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)}\right) d^{\frac{9}{2}}-24 \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}\, d^{\frac{7}{2}} \sqrt{-d}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}-4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\right) \sqrt{-d}\, d^{4}+5 \ln \left(\frac{2 \sqrt{d}\, \sqrt{-2 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) d +d}+4 d \cos \left(\frac{b x}{2}+\frac{a}{2}\right)-2 d}{\cos \left(\frac{b x}{2}+\frac{a}{2}\right)-1}\right) \sqrt{-d}\, d^{4}\right) \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{40 d^{\frac{15}{2}} \sqrt{-d}\, \sin \left(\frac{b x}{2}+\frac{a}{2}\right)^{2} \left(8 \left(\sin^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-20 \left(\sin^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+18 \left(\sin^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right) b}"," ",0,"1/40/d^(15/2)/(-d)^(1/2)/sin(1/2*b*x+1/2*a)^2/(8*sin(1/2*b*x+1/2*a)^8-20*sin(1/2*b*x+1/2*a)^6+18*sin(1/2*b*x+1/2*a)^4-7*sin(1/2*b*x+1/2*a)^2+1)*(-5*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)-360*(2*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)+ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^10+180*(10*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-4*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+5*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+5*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^8-90*(18*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-16*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+9*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+9*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^6+9*(70*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-104*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+35*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+35*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^4-9*(10*ln(2/cos(1/2*b*x+1/2*a)*((-d)^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-d))*d^(9/2)-24*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)*d^(7/2)*(-d)^(1/2)+5*ln(2/(cos(1/2*b*x+1/2*a)+1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)-2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4+5*ln(2/(cos(1/2*b*x+1/2*a)-1)*(d^(1/2)*(-2*sin(1/2*b*x+1/2*a)^2*d+d)^(1/2)+2*d*cos(1/2*b*x+1/2*a)-d))*(-d)^(1/2)*d^4)*sin(1/2*b*x+1/2*a)^2)/b","B"
252,1,19,18,0.014000," ","int((d*cos(b*x+a))^(1/5)*sin(b*x+a),x)","-\frac{5 \left(d \cos \left(b x +a \right)\right)^{\frac{6}{5}}}{6 b d}"," ",0,"-5/6*(d*cos(b*x+a))^(6/5)/b/d","A"
253,1,14,13,0.066000," ","int(cos(x)^3*sin(x)^(1/2),x)","\frac{2 \left(\sin^{\frac{3}{2}}\left(x \right)\right)}{3}-\frac{2 \left(\sin^{\frac{7}{2}}\left(x \right)\right)}{7}"," ",0,"2/3*sin(x)^(3/2)-2/7*sin(x)^(7/2)","A"
254,1,14,13,0.055000," ","int(cos(x)^3*sin(x)^(3/2),x)","\frac{2 \left(\sin^{\frac{5}{2}}\left(x \right)\right)}{5}-\frac{2 \left(\sin^{\frac{9}{2}}\left(x \right)\right)}{9}"," ",0,"2/5*sin(x)^(5/2)-2/9*sin(x)^(9/2)","A"
255,1,14,13,0.053000," ","int(cos(x)^3*sin(x)^(5/2),x)","\frac{2 \left(\sin^{\frac{7}{2}}\left(x \right)\right)}{7}-\frac{2 \left(\sin^{\frac{11}{2}}\left(x \right)\right)}{11}"," ",0,"2/7*sin(x)^(7/2)-2/11*sin(x)^(11/2)","A"
256,1,14,13,0.059000," ","int(cos(x)^3/sin(x)^(1/2),x)","-\frac{2 \left(\sin^{\frac{5}{2}}\left(x \right)\right)}{5}+2 \left(\sqrt{\sin}\left(x \right)\right)"," ",0,"-2/5*sin(x)^(5/2)+2*sin(x)^(1/2)","A"
257,1,532,137,0.291000," ","int((d*cos(b*x+a))^(9/2)*(c*sin(b*x+a))^(1/2),x)","-\frac{\sqrt{c \sin \left(b x +a \right)}\, \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}} \left(12 \left(\cos^{6}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-21 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+42 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+42 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-21 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{120 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{5}}"," ",0,"-1/120/b*(c*sin(b*x+a))^(1/2)*(d*cos(b*x+a))^(9/2)*(12*cos(b*x+a)^6*2^(1/2)+2*cos(b*x+a)^4*2^(1/2)-21*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+42*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-21*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+42*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+7*cos(b*x+a)^2*2^(1/2)-21*cos(b*x+a)*2^(1/2))/sin(b*x+a)/cos(b*x+a)^5*2^(1/2)","B"
258,1,518,106,0.177000," ","int((d*cos(b*x+a))^(5/2)*(c*sin(b*x+a))^(1/2),x)","-\frac{\sqrt{c \sin \left(b x +a \right)}\, \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}} \left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{12 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{3}}"," ",0,"-1/12/b*(c*sin(b*x+a))^(1/2)*(d*cos(b*x+a))^(5/2)*(2*cos(b*x+a)^4*2^(1/2)-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2))/sin(b*x+a)/cos(b*x+a)^3*2^(1/2)","B"
259,1,505,73,0.135000," ","int((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(1/2),x)","-\frac{\left(2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}\right) \sqrt{d \cos \left(b x +a \right)}\, \sqrt{c \sin \left(b x +a \right)}\, \sqrt{2}}{2 b \sin \left(b x +a \right) \cos \left(b x +a \right)}"," ",0,"-1/2/b*(2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(1/2)/sin(b*x+a)/cos(b*x+a)*2^(1/2)","B"
260,1,493,108,0.169000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(3/2),x)","\frac{\left(2 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \sqrt{c \sin \left(b x +a \right)}\, \cos \left(b x +a \right) \sqrt{2}}{b \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"1/b*(2*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)*2^(1/2)+2^(1/2))*(c*sin(b*x+a))^(1/2)*cos(b*x+a)/(d*cos(b*x+a))^(3/2)/sin(b*x+a)*2^(1/2)","B"
261,1,528,139,0.186000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(7/2),x)","\frac{\left(4 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+4 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\sqrt{2}\right) \sqrt{c \sin \left(b x +a \right)}\, \cos \left(b x +a \right) \sqrt{2}}{5 b \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}} \sin \left(b x +a \right)}"," ",0,"1/5/b*(4*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+4*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)+cos(b*x+a)^2*2^(1/2)+2^(1/2))*(c*sin(b*x+a))^(1/2)*cos(b*x+a)/(d*cos(b*x+a))^(7/2)/sin(b*x+a)*2^(1/2)","B"
262,1,514,238,0.116000," ","int((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(1/2),x)","\frac{\left(-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \sqrt{c \sin \left(b x +a \right)}\, \sin \left(b x +a \right) \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{2}}"," ",0,"1/8/b*(-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(b*x+a)^2*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(1/2)*sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^2*2^(1/2)","C"
263,1,271,209,0.112000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(1/2),x)","-\frac{\sqrt{c \sin \left(b x +a \right)}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sin \left(b x +a \right) \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \sqrt{d \cos \left(b x +a \right)}}"," ",0,"-1/2/b*(c*sin(b*x+a))^(1/2)*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(1/2)*2^(1/2)","C"
264,1,38,31,0.136000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(5/2),x)","\frac{2 \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{c \sin \left(b x +a \right)}}{3 b \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}}}"," ",0,"2/3/b*sin(b*x+a)*cos(b*x+a)*(c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(5/2)","A"
265,1,50,63,0.144000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(9/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)+3\right) \sqrt{c \sin \left(b x +a \right)}\, \cos \left(b x +a \right) \sin \left(b x +a \right)}{21 b \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}}}"," ",0,"2/21/b*(4*cos(b*x+a)^2+3)*(c*sin(b*x+a))^(1/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(9/2)","A"
266,1,60,94,0.213000," ","int((c*sin(b*x+a))^(1/2)/(d*cos(b*x+a))^(13/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)+24 \left(\cos^{2}\left(b x +a \right)\right)+21\right) \sqrt{c \sin \left(b x +a \right)}\, \cos \left(b x +a \right) \sin \left(b x +a \right)}{231 b \left(d \cos \left(b x +a \right)\right)^{\frac{13}{2}}}"," ",0,"2/231/b*(32*cos(b*x+a)^4+24*cos(b*x+a)^2+21)*(c*sin(b*x+a))^(1/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(13/2)","A"
267,1,216,136,0.200000," ","int((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(3/2),x)","-\frac{\left(\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \sqrt{2}}{12 b \sin \left(b x +a \right) \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{2}}"," ",0,"-1/12/b*(sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)^4*2^(1/2)-2*cos(b*x+a)^3*2^(1/2)-cos(b*x+a)^2*2^(1/2)+cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^(3/2)/sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^2*2^(1/2)","A"
268,1,182,106,0.148000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(1/2),x)","-\frac{\left(\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \sqrt{d \cos \left(b x +a \right)}\, \sin \left(b x +a \right)}"," ",0,"-1/2/b*(sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2))*(c*sin(b*x+a))^(3/2)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(1/2)/sin(b*x+a)*2^(1/2)","A"
269,1,186,109,0.123000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(5/2),x)","\frac{\left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)+\cos \left(b x +a \right) \sqrt{2}-\sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sqrt{2}}{3 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}} \sin \left(b x +a \right)}"," ",0,"1/3/b*(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)+cos(b*x+a)*2^(1/2)-2^(1/2))*(c*sin(b*x+a))^(3/2)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(5/2)/sin(b*x+a)*2^(1/2)","A"
270,1,215,138,0.142000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(9/2),x)","\frac{\left(2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)-\left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}-3 \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sqrt{2}}{21 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}} \sin \left(b x +a \right)}"," ",0,"1/21/b*(2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)^3-cos(b*x+a)^3*2^(1/2)+cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2)-3*2^(1/2))*(c*sin(b*x+a))^(3/2)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(9/2)/sin(b*x+a)*2^(1/2)","A"
271,1,656,237,0.112000," ","int((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(3/2),x)","\frac{\left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \sqrt{d \cos \left(b x +a \right)}\, \left(i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \sqrt{2}}{8 b \sin \left(b x +a \right) \cos \left(b x +a \right) \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"1/8/b*(c*sin(b*x+a))^(3/2)*(d*cos(b*x+a))^(1/2)*(I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2))/sin(b*x+a)/cos(b*x+a)/(-1+cos(b*x+a))*2^(1/2)","C"
272,1,642,237,0.128000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(3/2),x)","\frac{\left(i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}-2 \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \sin \left(b x +a \right)}"," ",0,"1/2/b*(I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)-I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2)-2*2^(1/2))*(c*sin(b*x+a))^(3/2)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(3/2)/sin(b*x+a)*2^(1/2)","C"
273,1,38,31,0.102000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(7/2),x)","\frac{2 \sin \left(b x +a \right) \cos \left(b x +a \right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}}}{5 b \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}}}"," ",0,"2/5/b*sin(b*x+a)*cos(b*x+a)*(c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(7/2)","A"
274,1,50,88,0.106000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(11/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{45 b \left(d \cos \left(b x +a \right)\right)^{\frac{11}{2}}}"," ",0,"2/45/b*(4*cos(b*x+a)^2+5)*(c*sin(b*x+a))^(3/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(11/2)","A"
275,1,60,117,0.158000," ","int((c*sin(b*x+a))^(3/2)/(d*cos(b*x+a))^(15/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)+40 \left(\cos^{2}\left(b x +a \right)\right)+45\right) \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{585 b \left(d \cos \left(b x +a \right)\right)^{\frac{15}{2}}}"," ",0,"2/585/b*(32*cos(b*x+a)^4+40*cos(b*x+a)^2+45)*(c*sin(b*x+a))^(3/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(15/2)","A"
276,1,545,165,0.164000," ","int((d*cos(b*x+a))^(9/2)*(c*sin(b*x+a))^(5/2),x)","\frac{\left(40 \left(\cos^{8}\left(b x +a \right)\right) \sqrt{2}-52 \left(\cos^{6}\left(b x +a \right)\right) \sqrt{2}-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+21 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-42 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+21 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-7 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+21 \cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}} \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \sqrt{2}}{560 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{5}}"," ",0,"1/560/b*(40*cos(b*x+a)^8*2^(1/2)-52*cos(b*x+a)^6*2^(1/2)-2*cos(b*x+a)^4*2^(1/2)+21*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-42*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+21*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-42*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-7*cos(b*x+a)^2*2^(1/2)+21*cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(9/2)*(c*sin(b*x+a))^(5/2)/sin(b*x+a)^3/cos(b*x+a)^5*2^(1/2)","B"
277,1,532,136,0.112000," ","int((d*cos(b*x+a))^(5/2)*(c*sin(b*x+a))^(5/2),x)","\frac{\left(4 \left(\cos^{6}\left(b x +a \right)\right) \sqrt{2}-6 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+3 \cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}} \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \sqrt{2}}{40 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{3}}"," ",0,"1/40/b*(4*cos(b*x+a)^6*2^(1/2)-6*cos(b*x+a)^4*2^(1/2)-6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^2*2^(1/2)+3*cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(5/2)*(c*sin(b*x+a))^(5/2)/sin(b*x+a)^3/cos(b*x+a)^3*2^(1/2)","B"
278,1,519,106,0.151000," ","int((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(5/2),x)","-\frac{\left(6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+5 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{d \cos \left(b x +a \right)}\, \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \sqrt{2}}{12 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}"," ",0,"-1/12/b*(6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^4*2^(1/2)+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+5*cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^(5/2)/sin(b*x+a)^3/cos(b*x+a)*2^(1/2)","B"
279,1,508,109,0.127000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(3/2),x)","\frac{\left(6 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-3 \cos \left(b x +a \right) \sqrt{2}+2 \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sqrt{2}}{2 b \sin \left(b x +a \right)^{3} \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}}}"," ",0,"1/2/b*(6*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+cos(b*x+a)^2*2^(1/2)-3*cos(b*x+a)*2^(1/2)+2*2^(1/2))*(c*sin(b*x+a))^(5/2)*cos(b*x+a)/sin(b*x+a)^3/(d*cos(b*x+a))^(3/2)*2^(1/2)","B"
280,1,531,138,0.142000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(7/2),x)","-\frac{\left(6 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+4 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sqrt{2}}{5 b \sin \left(b x +a \right)^{3} \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}}}"," ",0,"-1/5/b*(6*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-3*cos(b*x+a)^3*2^(1/2)+4*cos(b*x+a)^2*2^(1/2)-2^(1/2))*(c*sin(b*x+a))^(5/2)*cos(b*x+a)/sin(b*x+a)^3/(d*cos(b*x+a))^(7/2)*2^(1/2)","B"
281,1,544,167,0.119000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(11/2),x)","\frac{\left(-12 \left(\cos^{5}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{5}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-12 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticE \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{5}\left(b x +a \right)\right) \sqrt{2}-3 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-8 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+5 \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sqrt{2}}{45 b \sin \left(b x +a \right)^{3} \left(d \cos \left(b x +a \right)\right)^{\frac{11}{2}}}"," ",0,"1/45/b*(-12*cos(b*x+a)^5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-12*cos(b*x+a)^4*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticE(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^4*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+6*cos(b*x+a)^5*2^(1/2)-3*cos(b*x+a)^4*2^(1/2)-8*cos(b*x+a)^2*2^(1/2)+5*2^(1/2))*(c*sin(b*x+a))^(5/2)*cos(b*x+a)/sin(b*x+a)^3/(d*cos(b*x+a))^(11/2)*2^(1/2)","B"
282,1,510,238,0.148000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(1/2),x)","-\frac{\left(3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \sqrt{2}}{8 b \left(-1+\cos \left(b x +a \right)\right) \sqrt{d \cos \left(b x +a \right)}\, \sin \left(b x +a \right)}"," ",0,"-1/8/b*(3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(b*x+a)^2*2^(1/2)-2*cos(b*x+a)*2^(1/2))*(c*sin(b*x+a))^(5/2)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(1/2)/sin(b*x+a)*2^(1/2)","C"
283,1,532,238,0.126000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(5/2),x)","\frac{\left(3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)+2 \cos \left(b x +a \right) \sqrt{2}-2 \sqrt{2}\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sqrt{2}}{6 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}} \sin \left(b x +a \right)}"," ",0,"1/6/b*(3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)-3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)+2*cos(b*x+a)*2^(1/2)-2*2^(1/2))*(c*sin(b*x+a))^(5/2)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(5/2)/sin(b*x+a)*2^(1/2)","C"
284,1,38,31,0.098000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(9/2),x)","\frac{2 \sin \left(b x +a \right) \cos \left(b x +a \right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}}}{7 b \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}}}"," ",0,"2/7/b*sin(b*x+a)*cos(b*x+a)*(c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(9/2)","A"
285,1,50,88,0.105000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(13/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)+7\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{77 b \left(d \cos \left(b x +a \right)\right)^{\frac{13}{2}}}"," ",0,"2/77/b*(4*cos(b*x+a)^2+7)*(c*sin(b*x+a))^(5/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(13/2)","A"
286,1,60,117,0.153000," ","int((c*sin(b*x+a))^(5/2)/(d*cos(b*x+a))^(17/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)+56 \left(\cos^{2}\left(b x +a \right)\right)+77\right) \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}} \cos \left(b x +a \right) \sin \left(b x +a \right)}{1155 b \left(d \cos \left(b x +a \right)\right)^{\frac{17}{2}}}"," ",0,"2/1155/b*(32*cos(b*x+a)^4+56*cos(b*x+a)^2+77)*(c*sin(b*x+a))^(5/2)*cos(b*x+a)*sin(b*x+a)/(d*cos(b*x+a))^(17/2)","A"
287,1,692,180,0.160000," ","int(sin(b*x+a)^(7/2)/cos(b*x+a)^(7/2),x)","-\frac{\left(5 i \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-5 i \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+5 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-10 \left(\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+12 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}-12 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-2 \cos \left(b x +a \right) \sqrt{2}+2 \sqrt{2}\right) \left(\sqrt{\sin}\left(b x +a \right)\right) \sqrt{2}}{10 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{\frac{5}{2}}}"," ",0,"-1/10/b*(5*I*cos(b*x+a)^2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*I*cos(b*x+a)^2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*cos(b*x+a)^2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*cos(b*x+a)^2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-10*cos(b*x+a)^2*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+12*cos(b*x+a)^3*2^(1/2)-12*cos(b*x+a)^2*2^(1/2)-2*cos(b*x+a)*2^(1/2)+2*2^(1/2))*sin(b*x+a)^(1/2)/(-1+cos(b*x+a))/cos(b*x+a)^(5/2)*2^(1/2)","C"
288,1,33,10,0.063000," ","int(sin(x)^(3/2)/cos(x)^(7/2),x)","\frac{\left(-\left(\sin^{2}\left(x \right)\right)+\cos^{2}\left(x \right)-2 \cos \left(x \right)+1\right) \left(\sin^{\frac{5}{2}}\left(x \right)\right)}{5 \left(-1+\cos \left(x \right)\right) \cos \left(x \right)^{\frac{7}{2}}}"," ",0,"1/5*(-sin(x)^2+cos(x)^2-2*cos(x)+1)*sin(x)^(5/2)/(-1+cos(x))/cos(x)^(7/2)","B"
289,1,166,87,0.061000," ","int(sin(x)^(1/2)/cos(x)^(1/2),x)","-\frac{\left(\sin^{\frac{3}{2}}\left(x \right)\right) \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{1-\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{2}}{2 \left(-1+\cos \left(x \right)\right) \sqrt{\cos \left(x \right)}}"," ",0,"-1/2*sin(x)^(3/2)*(I*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*((-1+cos(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((1-cos(x)+sin(x))/sin(x))^(1/2)/(-1+cos(x))/cos(x)^(1/2)*2^(1/2)","C"
290,1,2595,97,0.149000," ","int(sin(x)^(5/2)/cos(x)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/32*sin(x)^(3/2)*(-6*cos(x)^2*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-4*sin(x)^2*2^(1/2)-16*cos(x)^3*2^(1/2)+4*cos(x)^4*2^(1/2)+24*cos(x)^2*2^(1/2)-16*cos(x)*2^(1/2)+4*2^(1/2)-3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*cos(x)^2*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*cos(x)*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*cos(x)*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*sin(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*sin(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*cos(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*cos(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+6*I*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+8*cos(x)*sin(x)^2*2^(1/2)-4*cos(x)^2*sin(x)^2*2^(1/2)+6*I*cos(x)^2*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-6*I*cos(x)^2*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*I*cos(x)*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*I*cos(x)*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(x)+12*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(x)-3*sin(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*sin(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*cos(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*cos(x)^4*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-6*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*cos(x)^3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*cos(x)^3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-18*cos(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-18*cos(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*I*sin(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*I*cos(x)^3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*I*cos(x)^3*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))+18*I*cos(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-18*I*cos(x)^2*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-12*I*cos(x)*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+12*I*cos(x)*((1-cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*EllipticPi(((1-cos(x)+sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2)))/(-1+cos(x))^3/cos(x)^(1/2)*2^(1/2)","C"
291,1,216,137,0.140000," ","int((d*cos(b*x+a))^(7/2)/(c*sin(b*x+a))^(1/2),x)","\frac{\left(2 \left(\cos^{4}\left(b x +a \right)\right) \sqrt{2}-5 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+5 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-5 \cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}} \sin \left(b x +a \right) \sqrt{2}}{12 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{4} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"1/12/b*(2*cos(b*x+a)^4*2^(1/2)-5*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-2*cos(b*x+a)^3*2^(1/2)+5*cos(b*x+a)^2*2^(1/2)-5*cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(7/2)*sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^4/(c*sin(b*x+a))^(1/2)*2^(1/2)","A"
292,1,188,105,0.115000," ","int((d*cos(b*x+a))^(3/2)/(c*sin(b*x+a))^(1/2),x)","-\frac{\left(\sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}+\cos \left(b x +a \right) \sqrt{2}\right) \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \sin \left(b x +a \right) \sqrt{2}}{2 b \left(-1+\cos \left(b x +a \right)\right) \cos \left(b x +a \right)^{2} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"-1/2/b*(sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))-cos(b*x+a)^2*2^(1/2)+cos(b*x+a)*2^(1/2))*(d*cos(b*x+a))^(3/2)*sin(b*x+a)/(-1+cos(b*x+a))/cos(b*x+a)^2/(c*sin(b*x+a))^(1/2)*2^(1/2)","A"
293,1,151,73,0.104000," ","int(1/(d*cos(b*x+a))^(1/2)/(c*sin(b*x+a))^(1/2),x)","-\frac{\EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(\sin^{2}\left(b x +a \right)\right) \sqrt{2}}{b \sqrt{c \sin \left(b x +a \right)}\, \left(-1+\cos \left(b x +a \right)\right) \sqrt{d \cos \left(b x +a \right)}}"," ",0,"-1/b*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*sin(b*x+a)^2/(c*sin(b*x+a))^(1/2)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(1/2)*2^(1/2)","B"
294,1,184,108,0.126000," ","int(1/(d*cos(b*x+a))^(5/2)/(c*sin(b*x+a))^(1/2),x)","-\frac{\left(2 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{2}}{3 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"-1/3/b*(2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)-cos(b*x+a)*2^(1/2)+2^(1/2))*sin(b*x+a)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(5/2)/(c*sin(b*x+a))^(1/2)*2^(1/2)","A"
295,1,212,139,0.164000," ","int(1/(d*cos(b*x+a))^(9/2)/(c*sin(b*x+a))^(1/2),x)","-\frac{\left(4 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \left(\cos^{3}\left(b x +a \right)\right)-2 \left(\cos^{3}\left(b x +a \right)\right) \sqrt{2}+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}-\cos \left(b x +a \right) \sqrt{2}+\sqrt{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right) \sqrt{2}}{7 b \left(-1+\cos \left(b x +a \right)\right) \left(d \cos \left(b x +a \right)\right)^{\frac{9}{2}} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"-1/7/b*(4*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)^3-2*cos(b*x+a)^3*2^(1/2)+2*cos(b*x+a)^2*2^(1/2)-cos(b*x+a)*2^(1/2)+2^(1/2))*sin(b*x+a)*cos(b*x+a)/(-1+cos(b*x+a))/(d*cos(b*x+a))^(9/2)/(c*sin(b*x+a))^(1/2)*2^(1/2)","A"
296,1,312,208,0.114000," ","int((d*cos(b*x+a))^(1/2)/(c*sin(b*x+a))^(1/2),x)","-\frac{\sqrt{d \cos \left(b x +a \right)}\, \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)\right) \left(\sin^{2}\left(b x +a \right)\right) \sqrt{2}}{2 b \sqrt{c \sin \left(b x +a \right)}\, \cos \left(b x +a \right) \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/2/b*(d*cos(b*x+a))^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2)))*sin(b*x+a)^2/(c*sin(b*x+a))^(1/2)/cos(b*x+a)/(-1+cos(b*x+a))*2^(1/2)","C"
297,1,38,31,0.105000," ","int(1/(d*cos(b*x+a))^(3/2)/(c*sin(b*x+a))^(1/2),x)","\frac{2 \sin \left(b x +a \right) \cos \left(b x +a \right)}{b \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"2/b*sin(b*x+a)*cos(b*x+a)/(d*cos(b*x+a))^(3/2)/(c*sin(b*x+a))^(1/2)","A"
298,1,50,63,0.113000," ","int(1/(d*cos(b*x+a))^(7/2)/(c*sin(b*x+a))^(1/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(b x +a \right)\right)+1\right) \sin \left(b x +a \right) \cos \left(b x +a \right)}{5 b \left(d \cos \left(b x +a \right)\right)^{\frac{7}{2}} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"2/5/b*(4*cos(b*x+a)^2+1)*sin(b*x+a)*cos(b*x+a)/(d*cos(b*x+a))^(7/2)/(c*sin(b*x+a))^(1/2)","A"
299,1,60,94,0.126000," ","int(1/(d*cos(b*x+a))^(11/2)/(c*sin(b*x+a))^(1/2),x)","\frac{2 \left(32 \left(\cos^{4}\left(b x +a \right)\right)+8 \left(\cos^{2}\left(b x +a \right)\right)+5\right) \sin \left(b x +a \right) \cos \left(b x +a \right)}{45 b \left(d \cos \left(b x +a \right)\right)^{\frac{11}{2}} \sqrt{c \sin \left(b x +a \right)}}"," ",0,"2/45/b*(32*cos(b*x+a)^4+8*cos(b*x+a)^2+5)*sin(b*x+a)*cos(b*x+a)/(d*cos(b*x+a))^(11/2)/(c*sin(b*x+a))^(1/2)","A"
300,1,292,138,0.120000," ","int(cos(b*x+a)^(1/2)/sin(b*x+a)^(1/2),x)","-\frac{\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)\right) \left(\sin^{\frac{3}{2}}\left(b x +a \right)\right) \sqrt{2}}{2 b \sqrt{\cos \left(b x +a \right)}\, \left(-1+\cos \left(b x +a \right)\right)}"," ",0,"-1/2/b/cos(b*x+a)^(1/2)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*(I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2)))*sin(b*x+a)^(3/2)/(-1+cos(b*x+a))*2^(1/2)","C"
301,1,937,160,0.108000," ","int(cos(b*x+a)^(3/2)/sin(b*x+a)^(3/2),x)","-\frac{\left(i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)+i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(b x +a \right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(b x +a \right) \sqrt{2}\right) \sqrt{2}}{2 b \sqrt{\sin \left(b x +a \right)}\, \sqrt{\cos \left(b x +a \right)}}"," ",0,"-1/2/b*(I*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)-I*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)+I*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(b*x+a)*2^(1/2))/sin(b*x+a)^(1/2)/cos(b*x+a)^(1/2)*2^(1/2)","C"
302,1,1261,159,0.123000," ","int(cos(b*x+a)^(5/2)/sin(b*x+a)^(5/2),x)","-\frac{4 \left(\cos^{\frac{5}{2}}\left(b x +a \right)\right) \left(-1+\cos \left(b x +a \right)\right)^{3} \left(3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)-3 i \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)+3 i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)+3 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)-6 \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right) \sin \left(b x +a \right) \cos \left(b x +a \right)+3 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \sin \left(b x +a \right) \sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \sqrt{\frac{-1+\cos \left(b x +a \right)}{\sin \left(b x +a \right)}}\, \EllipticF \left(\sqrt{\frac{1-\cos \left(b x +a \right)+\sin \left(b x +a \right)}{\sin \left(b x +a \right)}}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(b x +a \right)\right) \sqrt{2}\right) \sqrt{2}}{3 b \sin \left(b x +a \right)^{\frac{3}{2}} \left(-1+\cos \left(b x +a \right)+\sin \left(b x +a \right)\right)^{3} \left(-1+\cos \left(b x +a \right)-\sin \left(b x +a \right)\right)^{3}}"," ",0,"-4/3/b*cos(b*x+a)^(5/2)*(-1+cos(b*x+a))^3*(3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)-3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)+3*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)-3*I*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)+3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)-6*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))*sin(b*x+a)*cos(b*x+a)+3*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+3*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*sin(b*x+a)*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticF(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2*2^(1/2))+2*cos(b*x+a)^2*2^(1/2))/sin(b*x+a)^(3/2)/(-1+cos(b*x+a)+sin(b*x+a))^3/(-1+cos(b*x+a)-sin(b*x+a))^3*2^(1/2)","C"
303,1,1934,181,0.138000," ","int(cos(b*x+a)^(7/2)/sin(b*x+a)^(7/2),x)","\text{Expression too large to display}"," ",0,"-8/5/b*cos(b*x+a)^(7/2)*(-1+cos(b*x+a))^4*(5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)^3+5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)^2-5*I*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*cos(b*x+a)+5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)-5*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*cos(b*x+a)^3*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)^3-5*I*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)-5*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))-5*cos(b*x+a)^2*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))-5*I*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)^2+5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(b*x+a)+5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(b*x+a)+5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2-1/2*I,1/2*2^(1/2))+5*((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2)*((-1+cos(b*x+a))/sin(b*x+a))^(1/2)*EllipticPi(((1-cos(b*x+a)+sin(b*x+a))/sin(b*x+a))^(1/2),1/2+1/2*I,1/2*2^(1/2))+12*cos(b*x+a)^3*2^(1/2)-10*cos(b*x+a)*2^(1/2))/sin(b*x+a)^(5/2)/(-1+cos(b*x+a)+sin(b*x+a))^4/(-1+cos(b*x+a)-sin(b*x+a))^4*2^(1/2)","C"
304,0,0,48,0.227000," ","int(cos(f*x+e)^4*(b*sin(f*x+e))^(1/3),x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(f*x+e)^4*(b*sin(f*x+e))^(1/3),x)","F"
305,0,0,48,0.125000," ","int(cos(f*x+e)^2*(b*sin(f*x+e))^(1/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(b*sin(f*x+e))^(1/3),x)","F"
306,0,0,48,0.103000," ","int((b*sin(f*x+e))^(1/3),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(1/3),x)","F"
307,0,0,48,0.097000," ","int(sec(f*x+e)^2*(b*sin(f*x+e))^(1/3),x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(f*x+e)^2*(b*sin(f*x+e))^(1/3),x)","F"
308,0,0,48,0.106000," ","int(sec(f*x+e)^4*(b*sin(f*x+e))^(1/3),x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(sec(f*x+e)^4*(b*sin(f*x+e))^(1/3),x)","F"
309,0,0,48,0.183000," ","int(cos(f*x+e)^4*(b*sin(f*x+e))^(5/3),x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(cos(f*x+e)^4*(b*sin(f*x+e))^(5/3),x)","F"
310,0,0,48,0.122000," ","int(cos(f*x+e)^2*(b*sin(f*x+e))^(5/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(b*sin(f*x+e))^(5/3),x)","F"
311,0,0,48,0.026000," ","int((b*sin(f*x+e))^(5/3),x)","\int \left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int((b*sin(f*x+e))^(5/3),x)","F"
312,0,0,48,0.092000," ","int(sec(f*x+e)^2*(b*sin(f*x+e))^(5/3),x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(f*x+e)^2*(b*sin(f*x+e))^(5/3),x)","F"
313,0,0,48,0.107000," ","int(sec(f*x+e)^4*(b*sin(f*x+e))^(5/3),x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}\, dx"," ",0,"int(sec(f*x+e)^4*(b*sin(f*x+e))^(5/3),x)","F"
314,0,0,48,0.143000," ","int(cos(f*x+e)^4/(b*sin(f*x+e))^(1/3),x)","\int \frac{\cos^{4}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(f*x+e)^4/(b*sin(f*x+e))^(1/3),x)","F"
315,0,0,48,0.092000," ","int(cos(f*x+e)^2/(b*sin(f*x+e))^(1/3),x)","\int \frac{\cos^{2}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(f*x+e)^2/(b*sin(f*x+e))^(1/3),x)","F"
316,0,0,48,0.084000," ","int(1/(b*sin(f*x+e))^(1/3),x)","\int \frac{1}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(b*sin(f*x+e))^(1/3),x)","F"
317,0,0,48,0.090000," ","int(sec(f*x+e)^2/(b*sin(f*x+e))^(1/3),x)","\int \frac{\sec^{2}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(f*x+e)^2/(b*sin(f*x+e))^(1/3),x)","F"
318,0,0,48,0.100000," ","int(sec(f*x+e)^4/(b*sin(f*x+e))^(1/3),x)","\int \frac{\sec^{4}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(f*x+e)^4/(b*sin(f*x+e))^(1/3),x)","F"
319,0,0,48,0.138000," ","int(cos(f*x+e)^4/(b*sin(f*x+e))^(5/3),x)","\int \frac{\cos^{4}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(cos(f*x+e)^4/(b*sin(f*x+e))^(5/3),x)","F"
320,0,0,48,0.090000," ","int(cos(f*x+e)^2/(b*sin(f*x+e))^(5/3),x)","\int \frac{\cos^{2}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(cos(f*x+e)^2/(b*sin(f*x+e))^(5/3),x)","F"
321,0,0,48,0.024000," ","int(1/(b*sin(f*x+e))^(5/3),x)","\int \frac{1}{\left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(1/(b*sin(f*x+e))^(5/3),x)","F"
322,0,0,48,0.089000," ","int(sec(f*x+e)^2/(b*sin(f*x+e))^(5/3),x)","\int \frac{\sec^{2}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(f*x+e)^2/(b*sin(f*x+e))^(5/3),x)","F"
323,0,0,48,0.101000," ","int(sec(f*x+e)^4/(b*sin(f*x+e))^(5/3),x)","\int \frac{\sec^{4}\left(f x +e \right)}{\left(b \sin \left(f x +e \right)\right)^{\frac{5}{3}}}\, dx"," ",0,"int(sec(f*x+e)^4/(b*sin(f*x+e))^(5/3),x)","F"
324,0,0,103,0.140000," ","int(sin(b*x+a)^(1/3)/cos(b*x+a)^(1/3),x)","\int \frac{\sin^{\frac{1}{3}}\left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(sin(b*x+a)^(1/3)/cos(b*x+a)^(1/3),x)","F"
325,0,0,178,0.094000," ","int(sin(b*x+a)^(2/3)/cos(b*x+a)^(2/3),x)","\int \frac{\sin^{\frac{2}{3}}\left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(sin(b*x+a)^(2/3)/cos(b*x+a)^(2/3),x)","F"
326,0,0,199,0.066000," ","int(sin(b*x+a)^(4/3)/cos(b*x+a)^(4/3),x)","\int \frac{\sin^{\frac{4}{3}}\left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{4}{3}}}\, dx"," ",0,"int(sin(b*x+a)^(4/3)/cos(b*x+a)^(4/3),x)","F"
327,0,0,124,0.072000," ","int(sin(b*x+a)^(5/3)/cos(b*x+a)^(5/3),x)","\int \frac{\sin^{\frac{5}{3}}\left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{5}{3}}}\, dx"," ",0,"int(sin(b*x+a)^(5/3)/cos(b*x+a)^(5/3),x)","F"
328,0,0,124,0.072000," ","int(sin(b*x+a)^(7/3)/cos(b*x+a)^(7/3),x)","\int \frac{\sin^{\frac{7}{3}}\left(b x +a \right)}{\cos \left(b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(sin(b*x+a)^(7/3)/cos(b*x+a)^(7/3),x)","F"
329,0,0,103,0.085000," ","int(cos(b*x+a)^(1/3)/sin(b*x+a)^(1/3),x)","\int \frac{\cos^{\frac{1}{3}}\left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(cos(b*x+a)^(1/3)/sin(b*x+a)^(1/3),x)","F"
330,0,0,179,0.084000," ","int(cos(b*x+a)^(2/3)/sin(b*x+a)^(2/3),x)","\int \frac{\cos^{\frac{2}{3}}\left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(cos(b*x+a)^(2/3)/sin(b*x+a)^(2/3),x)","F"
331,0,0,200,0.067000," ","int(cos(b*x+a)^(4/3)/sin(b*x+a)^(4/3),x)","\int \frac{\cos^{\frac{4}{3}}\left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{4}{3}}}\, dx"," ",0,"int(cos(b*x+a)^(4/3)/sin(b*x+a)^(4/3),x)","F"
332,0,0,124,0.066000," ","int(cos(b*x+a)^(5/3)/sin(b*x+a)^(5/3),x)","\int \frac{\cos^{\frac{5}{3}}\left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{5}{3}}}\, dx"," ",0,"int(cos(b*x+a)^(5/3)/sin(b*x+a)^(5/3),x)","F"
333,0,0,124,0.067000," ","int(cos(b*x+a)^(7/3)/sin(b*x+a)^(7/3),x)","\int \frac{\cos^{\frac{7}{3}}\left(b x +a \right)}{\sin \left(b x +a \right)^{\frac{7}{3}}}\, dx"," ",0,"int(cos(b*x+a)^(7/3)/sin(b*x+a)^(7/3),x)","F"
334,0,0,10,0.062000," ","int(cos(x)^(2/3)/sin(x)^(8/3),x)","\int \frac{\cos^{\frac{2}{3}}\left(x \right)}{\sin \left(x \right)^{\frac{8}{3}}}\, dx"," ",0,"int(cos(x)^(2/3)/sin(x)^(8/3),x)","F"
335,0,0,10,0.061000," ","int(sin(x)^(2/3)/cos(x)^(8/3),x)","\int \frac{\sin^{\frac{2}{3}}\left(x \right)}{\cos \left(x \right)^{\frac{8}{3}}}\, dx"," ",0,"int(sin(x)^(2/3)/cos(x)^(8/3),x)","F"
336,0,0,70,0.579000," ","int(cos(f*x+e)^n*sin(f*x+e)^m,x)","\int \left(\cos^{n}\left(f x +e \right)\right) \left(\sin^{m}\left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^n*sin(f*x+e)^m,x)","F"
337,0,0,75,0.548000," ","int((d*cos(f*x+e))^n*sin(f*x+e)^m,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(\sin^{m}\left(f x +e \right)\right)\, dx"," ",0,"int((d*cos(f*x+e))^n*sin(f*x+e)^m,x)","F"
338,0,0,73,0.531000," ","int(cos(f*x+e)^n*(b*sin(f*x+e))^m,x)","\int \left(\cos^{n}\left(f x +e \right)\right) \left(b \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cos(f*x+e)^n*(b*sin(f*x+e))^m,x)","F"
339,0,0,78,0.567000," ","int((d*cos(f*x+e))^n*(b*sin(f*x+e))^m,x)","\int \left(d \cos \left(f x +e \right)\right)^{n} \left(b \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((d*cos(f*x+e))^n*(b*sin(f*x+e))^m,x)","F"
340,0,0,74,1.782000," ","int(cos(b*x+a)^5*(c*sin(b*x+a))^m,x)","\int \left(\cos^{5}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(cos(b*x+a)^5*(c*sin(b*x+a))^m,x)","F"
341,0,0,50,1.166000," ","int(cos(b*x+a)^3*(c*sin(b*x+a))^m,x)","\int \left(\cos^{3}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(cos(b*x+a)^3*(c*sin(b*x+a))^m,x)","F"
342,1,25,24,0.002000," ","int(cos(b*x+a)*(c*sin(b*x+a))^m,x)","\frac{\left(c \sin \left(b x +a \right)\right)^{1+m}}{b c \left(1+m \right)}"," ",0,"(c*sin(b*x+a))^(1+m)/b/c/(1+m)","A"
343,0,0,46,0.385000," ","int(sec(b*x+a)*(c*sin(b*x+a))^m,x)","\int \sec \left(b x +a \right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(sec(b*x+a)*(c*sin(b*x+a))^m,x)","F"
344,0,0,46,0.371000," ","int(sec(b*x+a)^3*(c*sin(b*x+a))^m,x)","\int \left(\sec^{3}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(sec(b*x+a)^3*(c*sin(b*x+a))^m,x)","F"
345,0,0,62,1.260000," ","int(cos(b*x+a)^4*(c*sin(b*x+a))^m,x)","\int \left(\cos^{4}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(cos(b*x+a)^4*(c*sin(b*x+a))^m,x)","F"
346,0,0,62,1.114000," ","int(cos(b*x+a)^2*(c*sin(b*x+a))^m,x)","\int \left(\cos^{2}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(cos(b*x+a)^2*(c*sin(b*x+a))^m,x)","F"
347,0,0,62,0.483000," ","int((c*sin(b*x+a))^m,x)","\int \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((c*sin(b*x+a))^m,x)","F"
348,0,0,62,0.379000," ","int(sec(b*x+a)^2*(c*sin(b*x+a))^m,x)","\int \left(\sec^{2}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(sec(b*x+a)^2*(c*sin(b*x+a))^m,x)","F"
349,0,0,62,0.380000," ","int(sec(b*x+a)^4*(c*sin(b*x+a))^m,x)","\int \left(\sec^{4}\left(b x +a \right)\right) \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int(sec(b*x+a)^4*(c*sin(b*x+a))^m,x)","F"
350,0,0,67,0.116000," ","int((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x)","\int \left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}} \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((d*cos(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x)","F"
351,0,0,67,0.106000," ","int((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x)","\int \sqrt{d \cos \left(b x +a \right)}\, \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((d*cos(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x)","F"
352,0,0,67,0.100000," ","int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(1/2),x)","\int \frac{\left(c \sin \left(b x +a \right)\right)^{m}}{\sqrt{d \cos \left(b x +a \right)}}\, dx"," ",0,"int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(1/2),x)","F"
353,0,0,69,0.096000," ","int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(3/2),x)","\int \frac{\left(c \sin \left(b x +a \right)\right)^{m}}{\left(d \cos \left(b x +a \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(3/2),x)","F"
354,0,0,69,0.103000," ","int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(5/2),x)","\int \frac{\left(c \sin \left(b x +a \right)\right)^{m}}{\left(d \cos \left(b x +a \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((c*sin(b*x+a))^m/(d*cos(b*x+a))^(5/2),x)","F"
355,0,0,76,1.292000," ","int((d*cos(b*x+a))^n*sin(b*x+a)^5,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\sin^{5}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*sin(b*x+a)^5,x)","F"
356,1,1076,50,2.144000," ","int((d*cos(b*x+a))^n*sin(b*x+a)^3,x)","-\frac{\left({\mathrm e}^{i \left(b x +a \right)}\right)^{-n} d^{n} \left(\frac{1}{2}\right)^{n} \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{n} \left(n +9\right) {\mathrm e}^{-\frac{i \left(\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{3}-\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2}-\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)+\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)-\pi  n \,\mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)+\pi  n \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{3}-\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+2 b x +2 a \right)}{2}}}{8 \left(3+n \right) \left(1+n \right) b}-\frac{\left({\mathrm e}^{i \left(b x +a \right)}\right)^{-n} d^{n} \left(\frac{1}{2}\right)^{n} \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{n} \left(n +9\right) {\mathrm e}^{\frac{i \left(-\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{3}+\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2}+\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)-\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)+\pi  n \,\mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}-\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)-\pi  n \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{3}+\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+2 b x +2 a \right)}{2}}}{8 \left(3+n \right) \left(1+n \right) b}+\frac{\left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{n} \left(\frac{1}{2}\right)^{n} d^{n} \left({\mathrm e}^{i \left(b x +a \right)}\right)^{-n} {\mathrm e}^{-\frac{i \left(\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{3}-\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2}-\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)-\pi  n \,\mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)+\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)+\pi  n \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{3}-\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+6 b x +6 a \right)}{2}}}{8 n b +24 b}+\frac{\left({\mathrm e}^{i \left(b x +a \right)}\right)^{-n} d^{n} \left(\frac{1}{2}\right)^{n} \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)^{n} {\mathrm e}^{\frac{i \left(-\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{3}+\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2}+\pi  n \mathrm{csgn}\left(i \cos \left(b x +a \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)-\pi  n \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i \left(b x +a \right)}+1\right)\right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i \left(b x +a \right)}\right)+\pi  n \,\mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}-\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i \cos \left(b x +a \right)\right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)-\pi  n \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{3}+\pi  n \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d \cos \left(b x +a \right)\right)^{2}+6 b x +6 a \right)}{2}}}{8 n b +24 b}"," ",0,"-1/8*exp(I*(b*x+a))^(-n)*d^n*(1/2)^n*(exp(2*I*(b*x+a))+1)^n/(3+n)/(1+n)/b*(n+9)*exp(-1/2*I*(Pi*n*csgn(I*cos(b*x+a))^3-Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))^2-Pi*n*csgn(I*cos(b*x+a))^2*csgn(I*exp(-I*(b*x+a)))+Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))*csgn(I*exp(-I*(b*x+a)))-Pi*n*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))^2+Pi*n*csgn(I*d)*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))+Pi*n*csgn(I*d*cos(b*x+a))^3-Pi*n*csgn(I*d)*csgn(I*d*cos(b*x+a))^2+2*b*x+2*a))-1/8*exp(I*(b*x+a))^(-n)*d^n*(1/2)^n*(exp(2*I*(b*x+a))+1)^n/(3+n)/(1+n)/b*(n+9)*exp(1/2*I*(-Pi*n*csgn(I*cos(b*x+a))^3+Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))^2+Pi*n*csgn(I*cos(b*x+a))^2*csgn(I*exp(-I*(b*x+a)))-Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))*csgn(I*exp(-I*(b*x+a)))+Pi*n*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))^2-Pi*n*csgn(I*d)*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))-Pi*n*csgn(I*d*cos(b*x+a))^3+Pi*n*csgn(I*d)*csgn(I*d*cos(b*x+a))^2+2*b*x+2*a))+1/8/(b*n+3*b)*(exp(2*I*(b*x+a))+1)^n*(1/2)^n*d^n*exp(I*(b*x+a))^(-n)*exp(-1/2*I*(Pi*n*csgn(I*cos(b*x+a))^3-Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))^2-Pi*n*csgn(I*cos(b*x+a))^2*csgn(I*exp(-I*(b*x+a)))-Pi*n*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))^2+Pi*n*csgn(I*d)*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))+Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))*csgn(I*exp(-I*(b*x+a)))+Pi*n*csgn(I*d*cos(b*x+a))^3-Pi*n*csgn(I*d)*csgn(I*d*cos(b*x+a))^2+6*b*x+6*a))+1/8*exp(I*(b*x+a))^(-n)*d^n*(1/2)^n*(exp(2*I*(b*x+a))+1)^n/(b*n+3*b)*exp(1/2*I*(-Pi*n*csgn(I*cos(b*x+a))^3+Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))^2+Pi*n*csgn(I*cos(b*x+a))^2*csgn(I*exp(-I*(b*x+a)))-Pi*n*csgn(I*(exp(2*I*(b*x+a))+1))*csgn(I*cos(b*x+a))*csgn(I*exp(-I*(b*x+a)))+Pi*n*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))^2-Pi*n*csgn(I*d)*csgn(I*cos(b*x+a))*csgn(I*d*cos(b*x+a))-Pi*n*csgn(I*d*cos(b*x+a))^3+Pi*n*csgn(I*d)*csgn(I*d*cos(b*x+a))^2+6*b*x+6*a))","C"
357,1,26,25,0.000000," ","int((d*cos(b*x+a))^n*sin(b*x+a),x)","-\frac{\left(d \cos \left(b x +a \right)\right)^{1+n}}{b d \left(1+n \right)}"," ",0,"-(d*cos(b*x+a))^(1+n)/b/d/(1+n)","A"
358,0,0,47,0.536000," ","int((d*cos(b*x+a))^n*csc(b*x+a),x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \csc \left(b x +a \right)\, dx"," ",0,"int((d*cos(b*x+a))^n*csc(b*x+a),x)","F"
359,0,0,47,0.561000," ","int((d*cos(b*x+a))^n*csc(b*x+a)^3,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\csc^{3}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*csc(b*x+a)^3,x)","F"
360,0,0,47,0.303000," ","int((d*cos(b*x+a))^n*csc(b*x+a)^5,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\csc^{5}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*csc(b*x+a)^5,x)","F"
361,0,0,63,0.984000," ","int((d*cos(b*x+a))^n*sin(b*x+a)^4,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\sin^{4}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*sin(b*x+a)^4,x)","F"
362,0,0,63,1.280000," ","int((d*cos(b*x+a))^n*sin(b*x+a)^2,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*sin(b*x+a)^2,x)","F"
363,0,0,63,0.224000," ","int((d*cos(b*x+a))^n,x)","\int \left(d \cos \left(b x +a \right)\right)^{n}\, dx"," ",0,"int((d*cos(b*x+a))^n,x)","F"
364,0,0,63,0.407000," ","int((d*cos(b*x+a))^n*csc(b*x+a)^2,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\csc^{2}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*csc(b*x+a)^2,x)","F"
365,0,0,63,0.294000," ","int((d*cos(b*x+a))^n*csc(b*x+a)^4,x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(\csc^{4}\left(b x +a \right)\right)\, dx"," ",0,"int((d*cos(b*x+a))^n*csc(b*x+a)^4,x)","F"
366,0,0,68,0.123000," ","int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(5/2),x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(c \sin \left(b x +a \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(5/2),x)","F"
367,0,0,68,0.110000," ","int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(3/2),x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(3/2),x)","F"
368,0,0,68,0.115000," ","int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(1/2),x)","\int \left(d \cos \left(b x +a \right)\right)^{n} \sqrt{c \sin \left(b x +a \right)}\, dx"," ",0,"int((d*cos(b*x+a))^n*(c*sin(b*x+a))^(1/2),x)","F"
369,0,0,68,0.094000," ","int((d*cos(b*x+a))^n/(c*sin(b*x+a))^(1/2),x)","\int \frac{\left(d \cos \left(b x +a \right)\right)^{n}}{\sqrt{c \sin \left(b x +a \right)}}\, dx"," ",0,"int((d*cos(b*x+a))^n/(c*sin(b*x+a))^(1/2),x)","F"
370,0,0,70,0.092000," ","int((d*cos(b*x+a))^n/(c*sin(b*x+a))^(3/2),x)","\int \frac{\left(d \cos \left(b x +a \right)\right)^{n}}{\left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*cos(b*x+a))^n/(c*sin(b*x+a))^(3/2),x)","F"
371,1,517,71,0.382000," ","int(sin(f*x+e)^7*(b*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(60 \left(\cos^{7}\left(f x +e \right)\right)-260 \left(\cos^{5}\left(f x +e \right)\right)+468 \left(\cos^{3}\left(f x +e \right)\right)+195 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-195 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+195 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-195 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-780 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{390 f \sin \left(f x +e \right)^{4}}"," ",0,"1/390/f*(-1+cos(f*x+e))^2*(60*cos(f*x+e)^7-260*cos(f*x+e)^5+468*cos(f*x+e)^3+195*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-195*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+195*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-195*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-780*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^4","B"
372,1,507,53,0.192000," ","int(sin(f*x+e)^5*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(20 \left(\cos^{5}\left(f x +e \right)\right)-72 \left(\cos^{3}\left(f x +e \right)\right)-45 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+45 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-45 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+45 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+180 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{90 f \sin \left(f x +e \right)^{4}}"," ",0,"-1/90/f*(-1+cos(f*x+e))^2*(20*cos(f*x+e)^5-72*cos(f*x+e)^3-45*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+45*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+180*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^4","B"
373,1,497,35,0.213000," ","int(sin(f*x+e)^3*(b*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(4 \left(\cos^{3}\left(f x +e \right)\right)-5 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+5 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-5 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+5 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-20 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{10 f \sin \left(f x +e \right)^{4}}"," ",0,"1/10/f*(-1+cos(f*x+e))^2*(4*cos(f*x+e)^3-5*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-20*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^4","B"
374,1,17,16,0.033000," ","int(sin(f*x+e)*(b*sec(f*x+e))^(1/2),x)","-\frac{2 b}{f \sqrt{b \sec \left(f x +e \right)}}"," ",0,"-2*b/f/(b*sec(f*x+e))^(1/2)","A"
375,1,169,46,0.185000," ","int(csc(f*x+e)*(b*sec(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(\ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{2 f \sin \left(f x +e \right)^{2} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"1/2/f*(b/cos(f*x+e))^(1/2)*cos(f*x+e)*(ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))*(-1+cos(f*x+e))/sin(f*x+e)^2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
376,1,603,73,0.221000," ","int(csc(f*x+e)^3*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+16 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+8 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+\ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)\right) \cos \left(f x +e \right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{8 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{4}}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+16*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2))*cos(f*x+e)*(b/cos(f*x+e))^(1/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^4","B"
377,1,1089,99,0.230000," ","int(csc(f*x+e)^5*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(72 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+56 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-11 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+32 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-21 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-104 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+44 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+11 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-32 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+21 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-88 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-88 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+11 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-32 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+21 \cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+44 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-11 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+32 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-21 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)\right) \cos \left(f x +e \right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{64 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{4}}"," ",0,"-1/64/f*(72*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+56*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-11*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+32*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*cos(f*x+e)^3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-104*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+44*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+11*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-32*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+21*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-88*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-88*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+11*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-32*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+21*cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+44*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-11*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+32*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))*cos(f*x+e)*(b/cos(f*x+e))^(1/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^4","B"
378,1,165,131,0.345000," ","int(sin(f*x+e)^6*(b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(7 \left(\cos^{6}\left(f x +e \right)\right)-7 \left(\cos^{5}\left(f x +e \right)\right)+40 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-24 \left(\cos^{4}\left(f x +e \right)\right)+24 \left(\cos^{3}\left(f x +e \right)\right)+37 \left(\cos^{2}\left(f x +e \right)\right)-37 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{77 f \sin \left(f x +e \right)^{3}}"," ",0,"-2/77/f*(-1+cos(f*x+e))*(7*cos(f*x+e)^6-7*cos(f*x+e)^5+40*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-24*cos(f*x+e)^4+24*cos(f*x+e)^3+37*cos(f*x+e)^2-37*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^3","C"
379,1,143,107,0.226000," ","int(sin(f*x+e)^4*(b*sec(f*x+e))^(1/2),x)","\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(-4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{4}\left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)-3 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{7 f \sin \left(f x +e \right)^{3}}"," ",0,"2/7/f*(-1+cos(f*x+e))*(-4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e)^4-cos(f*x+e)^3-3*cos(f*x+e)^2+3*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^3","C"
380,1,123,83,0.194000," ","int(sin(f*x+e)^2*(b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{3 f \sin \left(f x +e \right)^{3}}"," ",0,"-2/3/f*(-1+cos(f*x+e))*(2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e)^2-cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^3","C"
381,1,98,60,0.170000," ","int((b*sec(f*x+e))^(1/2),x)","-\frac{2 i \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \left(\cos \left(f x +e \right)+1\right)^{2}}{f \sin \left(f x +e \right)^{2}}"," ",0,"-2*I/f*(b/cos(f*x+e))^(1/2)*(-1+cos(f*x+e))*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(cos(f*x+e)+1)^2/sin(f*x+e)^2","C"
382,1,184,82,0.195000," ","int(csc(f*x+e)^2*(b*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right)^{5}}"," ",0,"1/f*(-1+cos(f*x+e))^2*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^5","C"
383,1,335,107,0.229000," ","int(csc(f*x+e)^4*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(5 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-5 \left(\cos^{3}\left(f x +e \right)\right)+7 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{6 f \sin \left(f x +e \right)^{7}}"," ",0,"-1/6/f*(-1+cos(f*x+e))^2*(5*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)-5*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-5*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-5*cos(f*x+e)^3+7*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^7","C"
384,1,485,131,0.249000," ","int(csc(f*x+e)^6*(b*sec(f*x+e))^(1/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-30 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-30 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-15 \left(\cos^{5}\left(f x +e \right)\right)+36 \left(\cos^{3}\left(f x +e \right)\right)-25 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{20 f \sin \left(f x +e \right)^{9}}"," ",0,"1/20/f*(-1+cos(f*x+e))^2*(15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^5*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-30*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-30*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-15*cos(f*x+e)^5+36*cos(f*x+e)^3-25*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^9","C"
385,1,969,71,0.321000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^7,x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(28 \left(\cos^{7}\left(f x +e \right)\right)+77 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-77 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+231 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-231 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-132 \left(\cos^{5}\left(f x +e \right)\right)+231 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-231 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+77 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-77 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+308 \left(\cos^{3}\left(f x +e \right)\right)+308 \cos \left(f x +e \right)\right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{154 f \sin \left(f x +e \right)^{4}}"," ",0,"1/154/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(28*cos(f*x+e)^7+77*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-77*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-231*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-132*cos(f*x+e)^5+231*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-231*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+77*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-77*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+308*cos(f*x+e)^3+308*cos(f*x+e))*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^4","B"
386,1,959,53,0.227000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^5,x)","-\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(-21 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+21 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-63 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+63 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+12 \left(\cos^{5}\left(f x +e \right)\right)-63 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+63 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-21 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+21 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-56 \left(\cos^{3}\left(f x +e \right)\right)-84 \cos \left(f x +e \right)\right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{42 f \sin \left(f x +e \right)^{4}}"," ",0,"-1/42/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(-21*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+21*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-63*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+63*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+12*cos(f*x+e)^5-63*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+63*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+21*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-56*cos(f*x+e)^3-84*cos(f*x+e))*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^4","B"
387,1,949,35,0.192000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^3,x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+9 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-9 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+9 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-9 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-3 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \left(\cos^{3}\left(f x +e \right)\right)+12 \cos \left(f x +e \right)\right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{6 f \sin \left(f x +e \right)^{4}}"," ",0,"1/6/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(3*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-9*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-9*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)^3+12*cos(f*x+e))*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^4","B"
388,1,17,16,0.024000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e),x)","\frac{2 b \sqrt{b \sec \left(f x +e \right)}}{f}"," ",0,"2*b*(b*sec(f*x+e))^(1/2)/f","A"
389,1,235,63,0.214000," ","int(csc(f*x+e)*(b*sec(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{3} \left(4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+\cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+\cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{2 f \sin \left(f x +e \right)^{6} \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(-1+cos(f*x+e))^3*(4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*(b/cos(f*x+e))^(3/2)*cos(f*x+e)^2/sin(f*x+e)^6/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)","B"
390,1,644,89,0.194000," ","int(csc(f*x+e)^3*(b*sec(f*x+e))^(3/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right) \left(-1+\cos \left(f x +e \right)\right)^{3} \left(4 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-16 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-5 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+4 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+5 \cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+\cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+16 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)\right)}{8 f \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{8}}"," ",0,"1/8/f*(cos(f*x+e)+1)*(-1+cos(f*x+e))^3*(4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-16*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+16*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*(b/cos(f*x+e))^(3/2)*cos(f*x+e)^2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/sin(f*x+e)^8","B"
391,1,330,138,0.287000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^6,x)","\frac{2 \left(\cos^{6}\left(f x +e \right)-24 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+24 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-24 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+24 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-5 \left(\cos^{4}\left(f x +e \right)\right)+19 \left(\cos^{2}\left(f x +e \right)\right)-24 \cos \left(f x +e \right)+9\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{9 f \sin \left(f x +e \right)}"," ",0,"2/9/f*(cos(f*x+e)^6-24*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+24*I*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-24*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+24*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-5*cos(f*x+e)^4+19*cos(f*x+e)^2-24*cos(f*x+e)+9)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)","C"
392,1,320,112,0.227000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^4,x)","-\frac{2 \left(12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-12 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-12 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\cos^{4}\left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+12 \cos \left(f x +e \right)-5\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{5 f \sin \left(f x +e \right)}"," ",0,"-2/5/f*(12*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-12*I*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+12*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-12*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^4-8*cos(f*x+e)^2+12*cos(f*x+e)-5)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)","C"
393,1,310,86,0.204000," ","int((b*sec(f*x+e))^(3/2)*sin(f*x+e)^2,x)","\frac{2 \left(-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+2 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+2 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{f \sin \left(f x +e \right)}"," ",0,"2/f*(-2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+2*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^2-2*cos(f*x+e)+1)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)","C"
394,1,322,86,0.259000," ","int((b*sec(f*x+e))^(3/2),x)","\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{f \sin \left(f x +e \right)^{5}}"," ",0,"2/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)+1)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^5","C"
395,1,322,108,0.198000," ","int(csc(f*x+e)^2*(b*sec(f*x+e))^(3/2),x)","-\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \cos \left(f x +e \right)-2\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{f \sin \left(f x +e \right)^{5}}"," ",0,"-1/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*cos(f*x+e)-2)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^5","C"
396,1,622,132,0.222000," ","int(csc(f*x+e)^4*(b*sec(f*x+e))^(3/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(21 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-21 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+21 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+21 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 \left(\cos^{3}\left(f x +e \right)\right)-14 \left(\cos^{2}\left(f x +e \right)\right)-21 \cos \left(f x +e \right)+12\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}{6 f \sin \left(f x +e \right)^{7}}"," ",0,"1/6/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*cos(f*x+e)^3-14*cos(f*x+e)^2-21*cos(f*x+e)+12)*cos(f*x+e)*(b/cos(f*x+e))^(3/2)/sin(f*x+e)^7","C"
397,1,532,71,0.210000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^7,x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(20 \left(\cos^{6}\left(f x +e \right)\right)-108 \left(\cos^{4}\left(f x +e \right)\right)-135 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+135 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-135 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+135 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+540 \left(\cos^{2}\left(f x +e \right)\right)+60\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{90 f \sin \left(f x +e \right)^{4}}"," ",0,"1/90/f*(-1+cos(f*x+e))^2*(20*cos(f*x+e)^6-108*cos(f*x+e)^4-135*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+135*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-135*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+135*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+540*cos(f*x+e)^2+60)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^4","B"
398,1,522,53,0.204000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^5,x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(6 \left(\cos^{4}\left(f x +e \right)\right)-15 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+15 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-15 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+15 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-60 \left(\cos^{2}\left(f x +e \right)\right)-10\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{15 f \sin \left(f x +e \right)^{4}}"," ",0,"-1/15/f*(-1+cos(f*x+e))^2*(6*cos(f*x+e)^4-15*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+15*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-15*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+15*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-60*cos(f*x+e)^2-10)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^4","B"
399,1,357,35,0.175000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^3,x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{6 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{2}}"," ",0,"-1/6/f*(-1+cos(f*x+e))*(12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+12*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*cos(f*x+e)*(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^2","B"
400,1,17,16,0.023000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e),x)","\frac{2 b \left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}}}{3 f}"," ",0,"2/3*b*(b*sec(f*x+e))^(3/2)/f","A"
401,1,237,62,0.168000," ","int(csc(f*x+e)*(b*sec(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right) \left(3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{6 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{2}}"," ",0,"1/6/f*(-1+cos(f*x+e))*(3*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*cos(f*x+e)*(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^2","B"
402,1,699,89,0.222000," ","int(csc(f*x+e)^3*(b*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(24 \left(\cos^{4}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+48 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-3 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+24 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-21 \left(\cos^{4}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+24 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-4 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-28 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-24 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+21 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+16 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+16 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{24 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{4}}"," ",0,"-1/24/f*(-1+cos(f*x+e))*(24*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+48*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*cos(f*x+e)^4*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+24*cos(f*x+e)^4*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*cos(f*x+e)^4*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+24*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-28*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-24*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+21*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+16*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+16*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*cos(f*x+e)*(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^4","B"
403,1,1161,115,0.179000," ","int(csc(f*x+e)^5*(b*sec(f*x+e))^(5/2),x)","-\frac{\left(408 \left(\cos^{5}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+360 \left(\cos^{4}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+288 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-231 \left(\cos^{5}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-57 \left(\cos^{5}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-504 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-288 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+231 \left(\cos^{4}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+100 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+57 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-456 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-288 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)+231 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-456 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+57 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+288 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right)-231 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+484 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-57 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-128 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right) \cos \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{192 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{4}}"," ",0,"-1/192/f*(408*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+360*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+288*cos(f*x+e)^5*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-231*cos(f*x+e)^5*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-57*cos(f*x+e)^5*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-504*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-288*cos(f*x+e)^4*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*cos(f*x+e)^4*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+100*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+57*cos(f*x+e)^4*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-456*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-288*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*cos(f*x+e)^3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-456*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+57*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+288*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-231*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+484*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-57*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-128*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*cos(f*x+e)*(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^4","B"
404,1,168,138,0.240000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^6,x)","-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(-40 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{5}\left(f x +e \right)\right)-3 \left(\cos^{4}\left(f x +e \right)\right)-16 \left(\cos^{3}\left(f x +e \right)\right)+16 \left(\cos^{2}\left(f x +e \right)\right)-7 \cos \left(f x +e \right)+7\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{21 f \sin \left(f x +e \right)^{3}}"," ",0,"-2/21/f*(-1+cos(f*x+e))*(-40*I*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*cos(f*x+e)^5-3*cos(f*x+e)^4-16*cos(f*x+e)^3+16*cos(f*x+e)^2-7*cos(f*x+e)+7)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^3","C"
405,1,144,112,0.195000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^4,x)","\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)-1\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{3 f \sin \left(f x +e \right)^{3}}"," ",0,"2/3/f*(-1+cos(f*x+e))*(4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+cos(f*x+e)^3-cos(f*x+e)^2+cos(f*x+e)-1)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^3","C"
406,1,126,86,0.176000," ","int((b*sec(f*x+e))^(5/2)*sin(f*x+e)^2,x)","\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-1\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{3 f \sin \left(f x +e \right)^{3}}"," ",0,"2/3/f*(-1+cos(f*x+e))*(2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)+cos(f*x+e)-1)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^3","C"
407,1,128,86,0.170000," ","int((b*sec(f*x+e))^(5/2),x)","-\frac{2 \left(-1+\cos \left(f x +e \right)\right) \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{3 f \sin \left(f x +e \right)^{3}}"," ",0,"-2/3/f*(-1+cos(f*x+e))*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-cos(f*x+e)+1)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^3","C"
408,1,202,110,0.191000," ","int(csc(f*x+e)^2*(b*sec(f*x+e))^(5/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(5 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-5 \left(\cos^{2}\left(f x +e \right)\right)+2\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{3 f \sin \left(f x +e \right)^{5}}"," ",0,"1/3/f*(-1+cos(f*x+e))^2*(5*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)+5*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-5*cos(f*x+e)^2+2)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^5","C"
409,1,352,133,0.231000," ","int(csc(f*x+e)^4*(b*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+15 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-15 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-15 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-15 \left(\cos^{4}\left(f x +e \right)\right)+21 \left(\cos^{2}\left(f x +e \right)\right)-4\right) \cos \left(f x +e \right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}{6 f \sin \left(f x +e \right)^{7}}"," ",0,"-1/6/f*(-1+cos(f*x+e))^2*(15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+15*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)-15*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)-15*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-15*cos(f*x+e)^4+21*cos(f*x+e)^2-4)*cos(f*x+e)*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(5/2)/sin(f*x+e)^7","C"
410,1,56,71,0.217000," ","int(sin(f*x+e)^7/(b*sec(f*x+e))^(1/2),x)","\frac{2 \left(77 \left(\cos^{6}\left(f x +e \right)\right)-315 \left(\cos^{4}\left(f x +e \right)\right)+495 \left(\cos^{2}\left(f x +e \right)\right)-385\right) \cos \left(f x +e \right)}{1155 f \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"2/1155/f*(77*cos(f*x+e)^6-315*cos(f*x+e)^4+495*cos(f*x+e)^2-385)*cos(f*x+e)/(b/cos(f*x+e))^(1/2)","A"
411,1,46,53,0.172000," ","int(sin(f*x+e)^5/(b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(21 \left(\cos^{4}\left(f x +e \right)\right)-66 \left(\cos^{2}\left(f x +e \right)\right)+77\right) \cos \left(f x +e \right)}{231 f \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-2/231/f*(21*cos(f*x+e)^4-66*cos(f*x+e)^2+77)*cos(f*x+e)/(b/cos(f*x+e))^(1/2)","A"
412,1,36,35,0.164000," ","int(sin(f*x+e)^3/(b*sec(f*x+e))^(1/2),x)","\frac{2 \left(3 \left(\cos^{2}\left(f x +e \right)\right)-7\right) \cos \left(f x +e \right)}{21 f \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"2/21/f*(3*cos(f*x+e)^2-7)*cos(f*x+e)/(b/cos(f*x+e))^(1/2)","A"
413,1,17,16,0.032000," ","int(sin(f*x+e)/(b*sec(f*x+e))^(1/2),x)","-\frac{2 b}{3 f \left(b \sec \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-2/3*b/f/(b*sec(f*x+e))^(3/2)","A"
414,1,161,47,0.175000," ","int(csc(f*x+e)/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(\ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{2 f \sin \left(f x +e \right)^{2} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-1/2/f*(ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))*(-1+cos(f*x+e))/sin(f*x+e)^2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/(b/cos(f*x+e))^(1/2)","B"
415,1,425,73,0.211000," ","int(csc(f*x+e)^3/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+16 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+8 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+\ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)\right)}{8 f \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)^{4} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+16*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-4*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2))/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)/sin(f*x+e)^4/(b/cos(f*x+e))^(1/2)","B"
416,1,729,99,0.217000," ","int(csc(f*x+e)^5/(b*sec(f*x+e))^(1/2),x)","-\frac{40 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+24 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-20 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-5 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-5 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-72 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+40 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+5 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+5 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-56 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-20 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+5 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+5 \cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-5 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-5 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)}{64 f \sin \left(f x +e \right)^{4} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"-1/64/f*(40*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+24*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-20*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-5*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*cos(f*x+e)^3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-72*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+5*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-56*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-20*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+5*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-5*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))/sin(f*x+e)^4/(b/cos(f*x+e))^(1/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
417,1,338,131,0.245000," ","int(sin(f*x+e)^6/(b*sec(f*x+e))^(1/2),x)","\frac{2 \left(9 \left(\cos^{8}\left(f x +e \right)\right)-37 \left(\cos^{6}\left(f x +e \right)\right)+24 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-24 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+24 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-24 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+59 \left(\cos^{4}\left(f x +e \right)\right)-55 \left(\cos^{2}\left(f x +e \right)\right)+24 \cos \left(f x +e \right)\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{117 f \sin \left(f x +e \right) b}"," ",0,"2/117/f*(9*cos(f*x+e)^8-37*cos(f*x+e)^6+24*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-24*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+24*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+59*cos(f*x+e)^4-55*cos(f*x+e)^2+24*cos(f*x+e))*(b/cos(f*x+e))^(1/2)/sin(f*x+e)/b","C"
418,1,328,107,0.202000," ","int(sin(f*x+e)^4/(b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(5 \left(\cos^{6}\left(f x +e \right)\right)+12 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+12 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-16 \left(\cos^{4}\left(f x +e \right)\right)+23 \left(\cos^{2}\left(f x +e \right)\right)-12 \cos \left(f x +e \right)\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{45 f \sin \left(f x +e \right) b}"," ",0,"-2/45/f*(5*cos(f*x+e)^6+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-16*cos(f*x+e)^4+23*cos(f*x+e)^2-12*cos(f*x+e))*(b/cos(f*x+e))^(1/2)/sin(f*x+e)/b","C"
419,1,318,83,0.227000," ","int(sin(f*x+e)^2/(b*sec(f*x+e))^(1/2),x)","-\frac{2 \left(2 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+2 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right)-2 \cos \left(f x +e \right)\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{5 f \sin \left(f x +e \right) b}"," ",0,"-2/5/f*(2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+2*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^4+3*cos(f*x+e)^2-2*cos(f*x+e))*(b/cos(f*x+e))^(1/2)/sin(f*x+e)/b","C"
420,1,306,60,0.187000," ","int(1/(b*sec(f*x+e))^(1/2),x)","\frac{2 \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{f \sin \left(f x +e \right) b}"," ",0,"2/f*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-cos(f*x+e)^2+cos(f*x+e))*(b/cos(f*x+e))^(1/2)/sin(f*x+e)/b","C"
421,1,316,83,0.192000," ","int(csc(f*x+e)^2/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{f b \sin \left(f x +e \right)^{5}}"," ",0,"-1/f*(-1+cos(f*x+e))^2*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/b/sin(f*x+e)^5","C"
422,1,618,107,0.236000," ","int(csc(f*x+e)^4/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-3 \left(\cos^{3}\left(f x +e \right)\right)+2 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{6 f b \sin \left(f x +e \right)^{7}}"," ",0,"-1/6/f*(-1+cos(f*x+e))^2*(3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-3*cos(f*x+e)^3+2*cos(f*x+e)^2+3*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/b/sin(f*x+e)^7","C"
423,1,918,131,0.254000," ","int(csc(f*x+e)^6/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(-21 i \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+42 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-42 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-42 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-21 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+42 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 \left(\cos^{5}\left(f x +e \right)\right)-14 \left(\cos^{4}\left(f x +e \right)\right)-42 \left(\cos^{3}\left(f x +e \right)\right)+26 \left(\cos^{2}\left(f x +e \right)\right)+21 \cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{60 f b \sin \left(f x +e \right)^{9}}"," ",0,"-1/60/f*(-1+cos(f*x+e))^2*(21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+42*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)-21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*cos(f*x+e)^5*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*sin(f*x+e)-21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+42*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)+21*I*cos(f*x+e)^5*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*sin(f*x+e)+21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*sin(f*x+e)-42*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*sin(f*x+e)+21*cos(f*x+e)^5-14*cos(f*x+e)^4-42*cos(f*x+e)^3+26*cos(f*x+e)^2+21*cos(f*x+e))*(cos(f*x+e)+1)^2*(b/cos(f*x+e))^(1/2)/b/sin(f*x+e)^9","C"
424,1,56,71,0.214000," ","int(sin(f*x+e)^7/(b*sec(f*x+e))^(3/2),x)","\frac{2 \left(195 \left(\cos^{6}\left(f x +e \right)\right)-765 \left(\cos^{4}\left(f x +e \right)\right)+1105 \left(\cos^{2}\left(f x +e \right)\right)-663\right) \cos \left(f x +e \right)}{3315 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3315/f*(195*cos(f*x+e)^6-765*cos(f*x+e)^4+1105*cos(f*x+e)^2-663)*cos(f*x+e)/(b/cos(f*x+e))^(3/2)","A"
425,1,46,53,0.165000," ","int(sin(f*x+e)^5/(b*sec(f*x+e))^(3/2),x)","-\frac{2 \left(45 \left(\cos^{4}\left(f x +e \right)\right)-130 \left(\cos^{2}\left(f x +e \right)\right)+117\right) \cos \left(f x +e \right)}{585 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/585/f*(45*cos(f*x+e)^4-130*cos(f*x+e)^2+117)*cos(f*x+e)/(b/cos(f*x+e))^(3/2)","A"
426,1,36,35,0.146000," ","int(sin(f*x+e)^3/(b*sec(f*x+e))^(3/2),x)","\frac{2 \left(5 \left(\cos^{2}\left(f x +e \right)\right)-9\right) \cos \left(f x +e \right)}{45 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"2/45/f*(5*cos(f*x+e)^2-9)*cos(f*x+e)/(b/cos(f*x+e))^(3/2)","A"
427,1,17,16,0.025000," ","int(sin(f*x+e)/(b*sec(f*x+e))^(3/2),x)","-\frac{2 b}{5 f \left(b \sec \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"-2/5*b/f/(b*sec(f*x+e))^(5/2)","A"
428,1,221,64,0.170000," ","int(csc(f*x+e)/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right)}{2 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"-1/2/f*(-1+cos(f*x+e))*(4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))/cos(f*x+e)/sin(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
429,1,426,73,0.180000," ","int(csc(f*x+e)^3/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+16 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+\left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+8 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+\ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)\right)}{8 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{4} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+16*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2))/cos(f*x+e)/sin(f*x+e)^4/(b/cos(f*x+e))^(3/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
430,1,729,99,0.194000," ","int(csc(f*x+e)^5/(b*sec(f*x+e))^(3/2),x)","-\frac{8 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-3 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-40 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+12 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-24 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-24 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+12 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-3 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)}{64 f \cos \left(f x +e \right) \sin \left(f x +e \right)^{4} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"-1/64/f*(8*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-40*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+12*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-24*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-24*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+12*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))/cos(f*x+e)/sin(f*x+e)^4/(b/cos(f*x+e))^(3/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
431,1,173,134,0.227000," ","int(sin(f*x+e)^4/(b*sec(f*x+e))^(3/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(-7 \left(\cos^{6}\left(f x +e \right)\right)+4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+7 \left(\cos^{5}\left(f x +e \right)\right)+13 \left(\cos^{4}\left(f x +e \right)\right)-13 \left(\cos^{3}\left(f x +e \right)\right)-4 \left(\cos^{2}\left(f x +e \right)\right)+4 \cos \left(f x +e \right)\right)}{77 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{3} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/77/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))*(-7*cos(f*x+e)^6+4*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+7*cos(f*x+e)^5+13*cos(f*x+e)^4-13*cos(f*x+e)^3-4*cos(f*x+e)^2+4*cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^3/(b/cos(f*x+e))^(3/2)","C"
432,1,153,110,0.187000," ","int(sin(f*x+e)^2/(b*sec(f*x+e))^(3/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+3 \left(\cos^{4}\left(f x +e \right)\right)-3 \left(\cos^{3}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)\right)}{21 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{3} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-2/21/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))*(2*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+3*cos(f*x+e)^4-3*cos(f*x+e)^3-2*cos(f*x+e)^2+2*cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^3/(b/cos(f*x+e))^(3/2)","C"
433,1,131,88,0.176000," ","int(1/(b*sec(f*x+e))^(3/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)\right)}{3 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{3}}"," ",0,"-2/3/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^2+cos(f*x+e))/(b/cos(f*x+e))^(3/2)/cos(f*x+e)^2/sin(f*x+e)^3","C"
434,1,191,88,0.179000," ","int(csc(f*x+e)^2/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos \left(f x +e \right)\right) \left(\cos \left(f x +e \right)+1\right)^{2}}{f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{5} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/f*(-1+cos(f*x+e))^2*(I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+cos(f*x+e))*(cos(f*x+e)+1)^2/cos(f*x+e)^2/sin(f*x+e)^5/(b/cos(f*x+e))^(3/2)","C"
435,1,343,114,0.200000," ","int(csc(f*x+e)^4/(b*sec(f*x+e))^(3/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)-\cos \left(f x +e \right)\right)}{6 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{7} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/6/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-cos(f*x+e)^3-cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^7/(b/cos(f*x+e))^(3/2)","C"
436,1,493,140,0.240000," ","int(csc(f*x+e)^6/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+5 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-5 \left(\cos^{5}\left(f x +e \right)\right)+12 \left(\cos^{3}\left(f x +e \right)\right)+5 \cos \left(f x +e \right)\right)}{60 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{9} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/60/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(5*I*cos(f*x+e)^5*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*I*cos(f*x+e)^4*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+5*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-5*cos(f*x+e)^5+12*cos(f*x+e)^3+5*cos(f*x+e))/cos(f*x+e)^2/sin(f*x+e)^9/(b/cos(f*x+e))^(3/2)","C"
437,1,56,71,0.225000," ","int(sin(f*x+e)^7/(b*sec(f*x+e))^(5/2),x)","\frac{2 \left(385 \left(\cos^{6}\left(f x +e \right)\right)-1463 \left(\cos^{4}\left(f x +e \right)\right)+1995 \left(\cos^{2}\left(f x +e \right)\right)-1045\right) \cos \left(f x +e \right)}{7315 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"2/7315/f*(385*cos(f*x+e)^6-1463*cos(f*x+e)^4+1995*cos(f*x+e)^2-1045)*cos(f*x+e)/(b/cos(f*x+e))^(5/2)","A"
438,1,46,53,0.169000," ","int(sin(f*x+e)^5/(b*sec(f*x+e))^(5/2),x)","-\frac{2 \left(77 \left(\cos^{4}\left(f x +e \right)\right)-210 \left(\cos^{2}\left(f x +e \right)\right)+165\right) \cos \left(f x +e \right)}{1155 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/1155/f*(77*cos(f*x+e)^4-210*cos(f*x+e)^2+165)*cos(f*x+e)/(b/cos(f*x+e))^(5/2)","A"
439,1,36,35,0.150000," ","int(sin(f*x+e)^3/(b*sec(f*x+e))^(5/2),x)","\frac{2 \left(7 \left(\cos^{2}\left(f x +e \right)\right)-11\right) \cos \left(f x +e \right)}{77 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"2/77/f*(7*cos(f*x+e)^2-11)*cos(f*x+e)/(b/cos(f*x+e))^(5/2)","A"
440,1,17,16,0.024000," ","int(sin(f*x+e)/(b*sec(f*x+e))^(5/2),x)","-\frac{2 b}{7 f \left(b \sec \left(f x +e \right)\right)^{\frac{7}{2}}}"," ",0,"-2/7*b/f/(b*sec(f*x+e))^(7/2)","A"
441,1,377,65,0.185000," ","int(csc(f*x+e)/(b*sec(f*x+e))^(5/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(-3 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+4 \left(\cos^{2}\left(f x +e \right)\right)-3 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right)}{6 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)^{4} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"1/6/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(-3*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+4*cos(f*x+e)^2-3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))/cos(f*x+e)^3/sin(f*x+e)^4/(b/cos(f*x+e))^(5/2)","B"
442,1,437,73,0.186000," ","int(csc(f*x+e)^3/(b*sec(f*x+e))^(5/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right) \left(8 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+16 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+8 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+4 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-3 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)\right)}{8 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{4} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"-1/8/f*(-1+cos(f*x+e))*(8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+16*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-4*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))/cos(f*x+e)^2/sin(f*x+e)^4/(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
443,1,737,99,0.197000," ","int(csc(f*x+e)^5/(b*sec(f*x+e))^(5/2),x)","\frac{24 \left(\cos^{3}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+40 \left(\cos^{2}\left(f x +e \right)\right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-12 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-3 \left(\cos^{3}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)+8 \cos \left(f x +e \right) \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}+24 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-8 \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}}-12 \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+3 \cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)+3 \cos \left(f x +e \right) \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)-3 \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right)-3 \arctan \left(\frac{1}{2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}\right)}{64 f \cos \left(f x +e \right)^{2} \sin \left(f x +e \right)^{4} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}}"," ",0,"1/64/f*(24*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))+8*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+24*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^2*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-12*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*arctan(1/2/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)))/cos(f*x+e)^2/sin(f*x+e)^4/(b/cos(f*x+e))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)","B"
444,1,343,134,0.211000," ","int(sin(f*x+e)^4/(b*sec(f*x+e))^(5/2),x)","-\frac{2 \left(15 \left(\cos^{8}\left(f x +e \right)\right)-40 \left(\cos^{6}\left(f x +e \right)\right)+12 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+12 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+29 \left(\cos^{4}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)-12 \cos \left(f x +e \right)\right)}{195 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-2/195/f*(15*cos(f*x+e)^8-40*cos(f*x+e)^6+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+29*cos(f*x+e)^4+8*cos(f*x+e)^2-12*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)/(b/cos(f*x+e))^(5/2)","C"
445,1,333,110,0.184000," ","int(sin(f*x+e)^2/(b*sec(f*x+e))^(5/2),x)","\frac{\frac{4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)}{15}-\frac{4 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)}{15}+\frac{2 \left(\cos^{6}\left(f x +e \right)\right)}{9}+\frac{4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)}{15}-\frac{4 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)}{15}-\frac{14 \left(\cos^{4}\left(f x +e \right)\right)}{45}-\frac{8 \left(\cos^{2}\left(f x +e \right)\right)}{45}+\frac{4 \cos \left(f x +e \right)}{15}}{f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"2/45/f*(6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-6*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+5*cos(f*x+e)^6+6*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-7*cos(f*x+e)^4-4*cos(f*x+e)^2+6*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)/(b/cos(f*x+e))^(5/2)","C"
446,1,321,88,0.219000," ","int(1/(b*sec(f*x+e))^(5/2),x)","-\frac{2 \left(3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+\cos^{4}\left(f x +e \right)+2 \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right)\right)}{5 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}} \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"-2/5/f*(3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+cos(f*x+e)^4+2*cos(f*x+e)^2-3*cos(f*x+e))/(b/cos(f*x+e))^(5/2)/cos(f*x+e)^3/sin(f*x+e)","C"
447,1,312,88,0.218000," ","int(csc(f*x+e)^2/(b*sec(f*x+e))^(5/2),x)","\frac{3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+2 \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right)}{f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right) \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"1/f*(3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+2*cos(f*x+e)^2-3*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)/(b/cos(f*x+e))^(5/2)","C"
448,1,623,114,0.228000," ","int(csc(f*x+e)^4/(b*sec(f*x+e))^(5/2),x)","-\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(3 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \left(\cos^{3}\left(f x +e \right)\right)+2 \left(\cos^{2}\left(f x +e \right)\right)-3 \cos \left(f x +e \right)\right)}{6 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)^{7} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"-1/6/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(3*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*cos(f*x+e)^3+2*cos(f*x+e)^2-3*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)^7/(b/cos(f*x+e))^(5/2)","C"
449,1,923,140,0.251000," ","int(csc(f*x+e)^6/(b*sec(f*x+e))^(5/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(6 i \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \left(\cos^{5}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 i \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{5}\left(f x +e \right)\right)-3 i \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \sin \left(f x +e \right)-6 i \left(\cos^{3}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2 \left(\cos^{4}\left(f x +e \right)\right)-6 \left(\cos^{3}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right)}{20 f \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)^{9} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{5}{2}}}"," ",0,"1/20/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3*sin(f*x+e)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-6*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4*sin(f*x+e)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4*sin(f*x+e)-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*sin(f*x+e)-6*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^5*sin(f*x+e)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+3*cos(f*x+e)^5-3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^5*sin(f*x+e)-2*cos(f*x+e)^4-6*cos(f*x+e)^3-2*cos(f*x+e)^2+3*cos(f*x+e))/cos(f*x+e)^3/sin(f*x+e)^9/(b/cos(f*x+e))^(5/2)","C"
450,1,538,345,0.234000," ","int((a*sin(f*x+e))^(9/2)*(b*sec(f*x+e))^(1/2),x)","\frac{\left(8 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-21 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+21 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-22 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+22 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sqrt{2}}{64 f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/64/f*(8*cos(f*x+e)^4*2^(1/2)-21*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(f*x+e)^3*2^(1/2)+21*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-22*cos(f*x+e)^2*2^(1/2)+22*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(9/2)*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-1+cos(f*x+e))*2^(1/2)","C"
451,1,512,316,0.185000," ","int((a*sin(f*x+e))^(5/2)*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(-3 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+3 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-1/8/f*(-3*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+3*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-3*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(f*x+e)^2*2^(1/2)-2*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(5/2)*(b/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","C"
452,1,273,289,0.169000," ","int((a*sin(f*x+e))^(1/2)*(b*sec(f*x+e))^(1/2),x)","-\frac{\sqrt{a \sin \left(f x +e \right)}\, \sqrt{\frac{b}{\cos \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)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \sin \left(f x +e \right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/2/f*(a*sin(f*x+e))^(1/2)*(b/cos(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(I*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*sin(f*x+e)/(-1+cos(f*x+e))*2^(1/2)","C"
453,1,40,29,0.173000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(3/2),x)","-\frac{2 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}}{f \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-2/f*sin(f*x+e)*cos(f*x+e)*(b/cos(f*x+e))^(1/2)/(a*sin(f*x+e))^(3/2)","A"
454,1,52,59,0.180000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(7/2),x)","\frac{2 \left(4 \left(\cos^{2}\left(f x +e \right)\right)-5\right) \cos \left(f x +e \right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{5 f \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}}}"," ",0,"2/5/f*(4*cos(f*x+e)^2-5)*cos(f*x+e)*(b/cos(f*x+e))^(1/2)*sin(f*x+e)/(a*sin(f*x+e))^(7/2)","A"
455,1,62,88,0.197000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(11/2),x)","-\frac{2 \left(32 \left(\cos^{4}\left(f x +e \right)\right)-72 \left(\cos^{2}\left(f x +e \right)\right)+45\right) \cos \left(f x +e \right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right)}{45 f \left(a \sin \left(f x +e \right)\right)^{\frac{11}{2}}}"," ",0,"-2/45/f*(32*cos(f*x+e)^4-72*cos(f*x+e)^2+45)*cos(f*x+e)*(b/cos(f*x+e))^(1/2)*sin(f*x+e)/(a*sin(f*x+e))^(11/2)","A"
456,1,212,133,0.235000," ","int((a*sin(f*x+e))^(7/2)*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(5 \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)-2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+7 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-7 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sqrt{2}}{12 f \sin \left(f x +e \right)^{3} \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/12/f*(5*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))-2*cos(f*x+e)^4*2^(1/2)+2*cos(f*x+e)^3*2^(1/2)+7*cos(f*x+e)^2*2^(1/2)-7*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(7/2)*(b/cos(f*x+e))^(1/2)/sin(f*x+e)^3/(-1+cos(f*x+e))*2^(1/2)","A"
457,1,184,104,0.189000," ","int((a*sin(f*x+e))^(3/2)*(b*sec(f*x+e))^(1/2),x)","-\frac{\left(\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)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)}"," ",0,"-1/2/f*(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))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(3/2)*(b/cos(f*x+e))^(1/2)/(-1+cos(f*x+e))/sin(f*x+e)*2^(1/2)","A"
458,1,153,73,0.162000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\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) \sqrt{2}}{f \sqrt{a \sin \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/f*(b/cos(f*x+e))^(1/2)*sin(f*x+e)^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))/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*sin(f*x+e))^(1/2)/(-1+cos(f*x+e))*2^(1/2)","B"
459,1,279,106,0.183000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(5/2),x)","\frac{\left(2 \sin \left(f x +e \right) \cos \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)+2 \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)-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{3 f \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"1/3/f*(2*sin(f*x+e)*cos(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))+2*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))-cos(f*x+e)*2^(1/2))*(b/cos(f*x+e))^(1/2)*sin(f*x+e)/(a*sin(f*x+e))^(5/2)*2^(1/2)","B"
460,1,532,135,0.206000," ","int((b*sec(f*x+e))^(1/2)/(a*sin(f*x+e))^(9/2),x)","-\frac{\left(4 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\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)+4 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\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)-4 \sin \left(f x +e \right) \cos \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)-4 \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)-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+3 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}}{7 f \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}}}"," ",0,"-1/7/f*(4*sin(f*x+e)*cos(f*x+e)^3*((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))+4*sin(f*x+e)*cos(f*x+e)^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))/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))-4*sin(f*x+e)*cos(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))-4*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))-2*cos(f*x+e)^3*2^(1/2)+3*cos(f*x+e)*2^(1/2))*(b/cos(f*x+e))^(1/2)*sin(f*x+e)/(a*sin(f*x+e))^(9/2)*2^(1/2)","B"
461,1,524,120,0.159000," ","int(sin(f*x+e)^(9/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(12 \left(\cos^{6}\left(f x +e \right)\right) \sqrt{2}-38 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-21 \cos \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)+42 \cos \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)}}\, \EllipticE \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)-21 \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)+42 \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)}}\, \EllipticE \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)+47 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-21 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{120 f \cos \left(f x +e \right) \sqrt{\sin \left(f x +e \right)}\, \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-1/120/f*(12*cos(f*x+e)^6*2^(1/2)-38*cos(f*x+e)^4*2^(1/2)-21*cos(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))+42*cos(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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-21*((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))+42*((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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+47*cos(f*x+e)^2*2^(1/2)-21*cos(f*x+e)*2^(1/2))/cos(f*x+e)/sin(f*x+e)^(1/2)/(b/cos(f*x+e))^(1/2)*2^(1/2)","B"
462,1,511,96,0.177000," ","int(sin(f*x+e)^(5/2)/(b*sec(f*x+e))^(1/2),x)","\frac{\left(2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 \cos \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)-6 \cos \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)}}\, \EllipticE \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)+3 \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)-6 \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)}}\, \EllipticE \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)-5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+3 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{12 f \cos \left(f x +e \right) \sqrt{\sin \left(f x +e \right)}\, \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"1/12/f*(2*cos(f*x+e)^4*2^(1/2)+3*cos(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))-6*cos(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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*((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))-6*((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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-5*cos(f*x+e)^2*2^(1/2)+3*cos(f*x+e)*2^(1/2))/cos(f*x+e)/sin(f*x+e)^(1/2)/(b/cos(f*x+e))^(1/2)*2^(1/2)","B"
463,1,497,71,0.151000," ","int(sin(f*x+e)^(1/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(2 \cos \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)}}\, \EllipticE \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)-\cos \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)+2 \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)}}\, \EllipticE \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)-\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)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{2 f \cos \left(f x +e \right) \sqrt{\sin \left(f x +e \right)}\, \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-1/2/f*(2*cos(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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(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))+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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(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))/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))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))/cos(f*x+e)/sin(f*x+e)^(1/2)/(b/cos(f*x+e))^(1/2)*2^(1/2)","B"
464,1,484,96,0.151000," ","int(1/sin(f*x+e)^(3/2)/(b*sec(f*x+e))^(1/2),x)","\frac{\left(2 \cos \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)}}\, \EllipticE \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)-\cos \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)+2 \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)}}\, \EllipticE \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)-\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)-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{f \cos \left(f x +e \right) \sqrt{\sin \left(f x +e \right)}\, \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"1/f*(2*cos(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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(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))+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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(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))/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))-cos(f*x+e)*2^(1/2))/cos(f*x+e)/sin(f*x+e)^(1/2)/(b/cos(f*x+e))^(1/2)*2^(1/2)","B"
465,1,1030,120,0.177000," ","int(1/sin(f*x+e)^(7/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{16 \left(-1+\cos \left(f x +e \right)\right)^{4} \left(4 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \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) \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)}}-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{-1+\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)}}\, \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)+4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticE \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) \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)}}-2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{\frac{-1+\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)}}\, \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)-4 \cos \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)}}\, \EllipticE \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)+2 \cos \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)-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-4 \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)}}\, \EllipticE \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)+2 \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)+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+2 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{5 f \sin \left(f x +e \right)^{\frac{5}{2}} \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(\sin^{2}\left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right)^{3}}"," ",0,"-16/5/f*(-1+cos(f*x+e))^4*(4*cos(f*x+e)^3*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(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))/sin(f*x+e))^(1/2)-2*cos(f*x+e)^3*((-1+cos(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))/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))+4*cos(f*x+e)^2*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(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))/sin(f*x+e))^(1/2)-2*cos(f*x+e)^2*((-1+cos(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))/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))-4*cos(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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*cos(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))-2*cos(f*x+e)^3*2^(1/2)-4*((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)*EllipticE(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))+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))/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))+cos(f*x+e)^2*2^(1/2)+2*cos(f*x+e)*2^(1/2))/sin(f*x+e)^(5/2)/(b/cos(f*x+e))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))/(1-cos(f*x+e)+sin(f*x+e))/(sin(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)+1)^3*2^(1/2)","B"
466,1,646,281,0.146000," ","int(sin(f*x+e)^(3/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{\left(i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(f x +e \right)-i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sin \left(f x +e \right)-2 \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)+2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\right) \left(\sqrt{\sin}\left(f x +e \right)\right) \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right)}"," ",0,"-1/8/f*(I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*sin(f*x+e)-I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*sin(f*x+e)-2*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))+2*cos(f*x+e)^3*2^(1/2)-2*cos(f*x+e)^2*2^(1/2))*sin(f*x+e)^(1/2)/(-1+cos(f*x+e))/(b/cos(f*x+e))^(1/2)/cos(f*x+e)*2^(1/2)","C"
467,1,304,257,0.138000," ","int(1/sin(f*x+e)^(1/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{\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)}}\, \left(i \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \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)\right) \left(\sin^{\frac{3}{2}}\left(f x +e \right)\right) \sqrt{2}}{2 f \sqrt{\frac{b}{\cos \left(f x +e \right)}}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/2/f*((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)*(I*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2)))*sin(f*x+e)^(3/2)/(b/cos(f*x+e))^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))*2^(1/2)","C"
468,1,70,24,0.141000," ","int(1/sin(f*x+e)^(5/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{8 \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right)^{2}}{3 f \sin \left(f x +e \right)^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right)^{2} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-8/3/f*cos(f*x+e)*(-1+cos(f*x+e))^2/sin(f*x+e)^(3/2)/(sin(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)+1)^2/(b/cos(f*x+e))^(1/2)","B"
469,1,82,49,0.146000," ","int(1/sin(f*x+e)^(9/2)/(b*sec(f*x+e))^(1/2),x)","\frac{32 \cos \left(f x +e \right) \left(4 \left(\cos^{2}\left(f x +e \right)\right)-7\right) \left(-1+\cos \left(f x +e \right)\right)^{4}}{21 f \sin \left(f x +e \right)^{\frac{7}{2}} \left(\sin^{2}\left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right)^{4} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"32/21/f*cos(f*x+e)*(4*cos(f*x+e)^2-7)*(-1+cos(f*x+e))^4/sin(f*x+e)^(7/2)/(sin(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)+1)^4/(b/cos(f*x+e))^(1/2)","A"
470,1,92,73,0.185000," ","int(1/sin(f*x+e)^(13/2)/(b*sec(f*x+e))^(1/2),x)","-\frac{128 \cos \left(f x +e \right) \left(32 \left(\cos^{4}\left(f x +e \right)\right)-88 \left(\cos^{2}\left(f x +e \right)\right)+77\right) \left(-1+\cos \left(f x +e \right)\right)^{6}}{231 f \sin \left(f x +e \right)^{\frac{11}{2}} \left(\sin^{2}\left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right)^{6} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"-128/231/f*cos(f*x+e)*(32*cos(f*x+e)^4-88*cos(f*x+e)^2+77)*(-1+cos(f*x+e))^6/sin(f*x+e)^(11/2)/(sin(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)+1)^6/(b/cos(f*x+e))^(1/2)","A"
471,1,102,97,0.213000," ","int(1/sin(f*x+e)^(17/2)/(b*sec(f*x+e))^(1/2),x)","\frac{512 \cos \left(f x +e \right) \left(128 \left(\cos^{6}\left(f x +e \right)\right)-480 \left(\cos^{4}\left(f x +e \right)\right)+660 \left(\cos^{2}\left(f x +e \right)\right)-385\right) \left(-1+\cos \left(f x +e \right)\right)^{8}}{1155 f \sin \left(f x +e \right)^{\frac{15}{2}} \left(\sin^{2}\left(f x +e \right)+\cos^{2}\left(f x +e \right)-2 \cos \left(f x +e \right)+1\right)^{8} \sqrt{\frac{b}{\cos \left(f x +e \right)}}}"," ",0,"512/1155/f*cos(f*x+e)*(128*cos(f*x+e)^6-480*cos(f*x+e)^4+660*cos(f*x+e)^2-385)*(-1+cos(f*x+e))^8/sin(f*x+e)^(15/2)/(sin(f*x+e)^2+cos(f*x+e)^2-2*cos(f*x+e)+1)^8/(b/cos(f*x+e))^(1/2)","A"
472,1,572,380,0.214000," ","int((a*sin(f*x+e))^(9/2)/(b*sec(f*x+e))^(3/2),x)","\frac{\left(64 \left(\cos^{6}\left(f x +e \right)\right) \sqrt{2}-64 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{2}-120 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-21 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+120 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+21 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+21 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+42 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-42 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}} \sqrt{2}}{768 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/768/f*(64*cos(f*x+e)^6*2^(1/2)-64*cos(f*x+e)^5*2^(1/2)-120*cos(f*x+e)^4*2^(1/2)-21*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+120*cos(f*x+e)^3*2^(1/2)+21*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+21*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+42*cos(f*x+e)^2*2^(1/2)-42*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(9/2)/(-1+cos(f*x+e))/sin(f*x+e)^3/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)*2^(1/2)","C"
473,1,546,349,0.199000," ","int((a*sin(f*x+e))^(5/2)/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(8 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-8 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-3 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-3 \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+6 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{2}}{64 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/64/f*(8*cos(f*x+e)^4*2^(1/2)+3*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-8*cos(f*x+e)^3*2^(1/2)-3*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-3*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-6*cos(f*x+e)^2*2^(1/2)+6*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(5/2)/(-1+cos(f*x+e))/sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)*2^(1/2)","C"
474,1,516,320,0.214000," ","int((a*sin(f*x+e))^(1/2)/(b*sec(f*x+e))^(3/2),x)","\frac{\left(i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{a \sin \left(f x +e \right)}\, \sin \left(f x +e \right) \sqrt{2}}{8 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/8/f*(I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))-I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))+2*cos(f*x+e)^2*2^(1/2)-2*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(1/2)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)*2^(1/2)","C"
475,1,957,320,0.170000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(3/2),x)","-\frac{\left(i \cos \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \cos \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right)+i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\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)}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+2 \cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{2 f \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(I*cos(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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*cos(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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*cos(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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*cos(f*x+e)+I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*((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)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(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))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))+2*cos(f*x+e)*2^(1/2))*sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(3/2)*2^(1/2)","C"
476,1,40,29,0.143000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(7/2),x)","-\frac{2 \sin \left(f x +e \right) \cos \left(f x +e \right)}{5 f \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}}}"," ",0,"-2/5/f*sin(f*x+e)*cos(f*x+e)/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(7/2)","A"
477,1,246,171,0.211000," ","int((a*sin(f*x+e))^(7/2)/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(-12 \left(\cos^{6}\left(f x +e \right)\right) \sqrt{2}+12 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{2}+5 \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)+22 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-22 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-5 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+5 \cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{7}{2}} \sqrt{2}}{120 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{3} \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/120/f*(-12*cos(f*x+e)^6*2^(1/2)+12*cos(f*x+e)^5*2^(1/2)+5*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))+22*cos(f*x+e)^4*2^(1/2)-22*cos(f*x+e)^3*2^(1/2)-5*cos(f*x+e)^2*2^(1/2)+5*cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(7/2)/(-1+cos(f*x+e))/sin(f*x+e)^3/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)*2^(1/2)","A"
478,1,218,140,0.199000," ","int((a*sin(f*x+e))^(3/2)/(b*sec(f*x+e))^(3/2),x)","-\frac{\left(\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)+2 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-2 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}\right) \left(a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}}{12 f \left(-1+\cos \left(f x +e \right)\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/12/f*(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))+2*cos(f*x+e)^4*2^(1/2)-2*cos(f*x+e)^3*2^(1/2)-cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2))*(a*sin(f*x+e))^(3/2)/(-1+cos(f*x+e))/sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)*2^(1/2)","A"
479,1,190,107,0.168000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(1/2),x)","-\frac{\left(\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)-\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{a \sin \left(f x +e \right)}}"," ",0,"-1/2/f*(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))-cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2))*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(1/2)*2^(1/2)","A"
480,1,284,111,0.159000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(5/2),x)","-\frac{\left(\sin \left(f x +e \right) \cos \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)+\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)+\cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{3 f \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(a \sin \left(f x +e \right)\right)^{\frac{5}{2}}}"," ",0,"-1/3/f*(sin(f*x+e)*cos(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))+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))+cos(f*x+e)*2^(1/2))*sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(5/2)*2^(1/2)","B"
481,1,540,142,0.176000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(9/2),x)","\frac{\left(2 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\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)+2 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\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)-2 \sin \left(f x +e \right) \cos \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)-2 \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)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-2 \cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{21 f \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(a \sin \left(f x +e \right)\right)^{\frac{9}{2}}}"," ",0,"1/21/f*(2*sin(f*x+e)*cos(f*x+e)^3*((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))+2*sin(f*x+e)*cos(f*x+e)^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))/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))-2*sin(f*x+e)*cos(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))-2*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))-cos(f*x+e)^3*2^(1/2)-2*cos(f*x+e)*2^(1/2))*sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(9/2)*2^(1/2)","B"
482,1,793,173,0.218000," ","int(1/(b*sec(f*x+e))^(3/2)/(a*sin(f*x+e))^(13/2),x)","-\frac{\left(4 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\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)+4 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\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)-8 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\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)-8 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\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)+4 \sin \left(f x +e \right) \cos \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)-2 \left(\cos^{5}\left(f x +e \right)\right) \sqrt{2}+4 \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)+5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \cos \left(f x +e \right) \sqrt{2}\right) \sin \left(f x +e \right) \sqrt{2}}{77 f \cos \left(f x +e \right)^{2} \left(\frac{b}{\cos \left(f x +e \right)}\right)^{\frac{3}{2}} \left(a \sin \left(f x +e \right)\right)^{\frac{13}{2}}}"," ",0,"-1/77/f*(4*sin(f*x+e)*cos(f*x+e)^5*((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))+4*sin(f*x+e)*cos(f*x+e)^4*((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))-8*sin(f*x+e)*cos(f*x+e)^3*((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))-8*sin(f*x+e)*cos(f*x+e)^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))/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))+4*sin(f*x+e)*cos(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))-2*cos(f*x+e)^5*2^(1/2)+4*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))+5*cos(f*x+e)^3*2^(1/2)+4*cos(f*x+e)*2^(1/2))*sin(f*x+e)/cos(f*x+e)^2/(b/cos(f*x+e))^(3/2)/(a*sin(f*x+e))^(13/2)*2^(1/2)","B"
483,0,0,67,0.187000," ","int((d*sec(b*x+a))^(5/2)*(c*sin(b*x+a))^m,x)","\int \left(d \sec \left(b x +a \right)\right)^{\frac{5}{2}} \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((d*sec(b*x+a))^(5/2)*(c*sin(b*x+a))^m,x)","F"
484,0,0,67,0.148000," ","int((d*sec(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x)","\int \left(d \sec \left(b x +a \right)\right)^{\frac{3}{2}} \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((d*sec(b*x+a))^(3/2)*(c*sin(b*x+a))^m,x)","F"
485,0,0,69,0.158000," ","int((d*sec(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x)","\int \sqrt{d \sec \left(b x +a \right)}\, \left(c \sin \left(b x +a \right)\right)^{m}\, dx"," ",0,"int((d*sec(b*x+a))^(1/2)*(c*sin(b*x+a))^m,x)","F"
486,0,0,69,0.148000," ","int((c*sin(b*x+a))^m/(d*sec(b*x+a))^(1/2),x)","\int \frac{\left(c \sin \left(b x +a \right)\right)^{m}}{\sqrt{d \sec \left(b x +a \right)}}\, dx"," ",0,"int((c*sin(b*x+a))^m/(d*sec(b*x+a))^(1/2),x)","F"
487,0,0,69,0.137000," ","int((c*sin(b*x+a))^m/(d*sec(b*x+a))^(3/2),x)","\int \frac{\left(c \sin \left(b x +a \right)\right)^{m}}{\left(d \sec \left(b x +a \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*sin(b*x+a))^m/(d*sec(b*x+a))^(3/2),x)","F"
488,0,0,72,0.660000," ","int(sec(f*x+e)^n*sin(f*x+e)^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(\sin^{m}\left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^n*sin(f*x+e)^m,x)","F"
489,0,0,75,0.608000," ","int(sec(f*x+e)^n*(a*sin(f*x+e))^m,x)","\int \left(\sec^{n}\left(f x +e \right)\right) \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(sec(f*x+e)^n*(a*sin(f*x+e))^m,x)","F"
490,0,0,75,0.615000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^m,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(\sin^{m}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^n*sin(f*x+e)^m,x)","F"
491,0,0,78,0.642000," ","int((b*sec(f*x+e))^n*(a*sin(f*x+e))^m,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*sec(f*x+e))^n*(a*sin(f*x+e))^m,x)","F"
492,0,0,80,1.771000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^5,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(\sin^{5}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^n*sin(f*x+e)^5,x)","F"
493,1,1732,52,1.855000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^3,x)","-\frac{b^{n} 2^{n} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} \left({\mathrm e}^{i \left(f x +e \right)}\right)^{n} {\mathrm e}^{-\frac{i \left(\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i b \right)+\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i b \right)+6 f x +6 e \right)}{2}}}{8 \left(f n -3 f \right)}-\frac{\left({\mathrm e}^{i \left(f x +e \right)}\right)^{n} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} 2^{n} b^{n} {\mathrm e}^{\frac{i \left(-\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i b \right)-\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i b \right)+6 f x +6 e \right)}{2}}}{8 \left(f n -3 f \right)}+\frac{\left({\mathrm e}^{i \left(f x +e \right)}\right)^{n} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} 2^{n} b^{n} \left(n -9\right) {\mathrm e}^{-\frac{i \left(\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)-\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i b \right)+\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}-\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i b \right)+2 f x +2 e \right)}{2}}}{8 \left(-3+n \right) \left(-1+n \right) f}+\frac{\left({\mathrm e}^{i \left(f x +e \right)}\right)^{n} \left({\mathrm e}^{2 i \left(f x +e \right)}+1\right)^{-n} 2^{n} b^{n} \left(n -9\right) {\mathrm e}^{\frac{i \left(-\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)+\pi  n \,\mathrm{csgn}\left(\frac{i}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}+\pi  n \,\mathrm{csgn}\left(i {\mathrm e}^{i \left(f x +e \right)}\right) \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2}-\pi  n \,\mathrm{csgn}\left(\frac{i {\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right) \mathrm{csgn}\left(i b \right)-\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{3}+\pi  n \mathrm{csgn}\left(\frac{i b \,{\mathrm e}^{i \left(f x +e \right)}}{{\mathrm e}^{2 i \left(f x +e \right)}+1}\right)^{2} \mathrm{csgn}\left(i b \right)+2 f x +2 e \right)}{2}}}{8 \left(-3+n \right) \left(-1+n \right) f}"," ",0,"-1/8/(f*n-3*f)*b^n*2^n*(exp(2*I*(f*x+e))+1)^(-n)*exp(I*(f*x+e))^n*exp(-1/2*I*(Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))-Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b)+Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*b)+6*f*x+6*e))-1/8*exp(I*(f*x+e))^n*(exp(2*I*(f*x+e))+1)^(-n)*2^n*b^n/(f*n-3*f)*exp(1/2*I*(-Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))+Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b)-Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3+Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*b)+6*f*x+6*e))+1/8*exp(I*(f*x+e))^n*(exp(2*I*(f*x+e))+1)^(-n)*2^n*b^n/(-3+n)/(-1+n)/f*(n-9)*exp(-1/2*I*(Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))-Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b)+Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3-Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*b)+2*f*x+2*e))+1/8*exp(I*(f*x+e))^n*(exp(2*I*(f*x+e))+1)^(-n)*2^n*b^n/(-3+n)/(-1+n)/f*(n-9)*exp(1/2*I*(-Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))+Pi*n*csgn(I/(exp(2*I*(f*x+e))+1))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2+Pi*n*csgn(I*exp(I*(f*x+e)))*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3+Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2-Pi*n*csgn(I*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))*csgn(I*b)-Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^3+Pi*n*csgn(I*b*exp(I*(f*x+e))/(exp(2*I*(f*x+e))+1))^2*csgn(I*b)+2*f*x+2*e))","C"
494,1,120,25,0.039000," ","int((b*sec(f*x+e))^n*sin(f*x+e),x)","\frac{\frac{{\mathrm e}^{n \ln \left(\frac{b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{1-\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\right)}}{f \left(-1+n \right)}-\frac{\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) {\mathrm e}^{n \ln \left(\frac{b \left(1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{1-\left(\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\right)}}{f \left(-1+n \right)}}{1+\tan^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)}"," ",0,"(1/f/(-1+n)*exp(n*ln(b*(1+tan(1/2*f*x+1/2*e)^2)/(1-tan(1/2*f*x+1/2*e)^2)))-1/f/(-1+n)*tan(1/2*f*x+1/2*e)^2*exp(n*ln(b*(1+tan(1/2*f*x+1/2*e)^2)/(1-tan(1/2*f*x+1/2*e)^2))))/(1+tan(1/2*f*x+1/2*e)^2)","B"
495,0,0,47,0.564000," ","int(csc(f*x+e)*(b*sec(f*x+e))^n,x)","\int \csc \left(f x +e \right) \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)*(b*sec(f*x+e))^n,x)","F"
496,0,0,46,0.556000," ","int(csc(f*x+e)^3*(b*sec(f*x+e))^n,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)^3*(b*sec(f*x+e))^n,x)","F"
497,0,0,63,1.295000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^6,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(\sin^{6}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^n*sin(f*x+e)^6,x)","F"
498,0,0,63,1.062000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^4,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(\sin^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^n*sin(f*x+e)^4,x)","F"
499,0,0,63,1.335000," ","int((b*sec(f*x+e))^n*sin(f*x+e)^2,x)","\int \left(b \sec \left(f x +e \right)\right)^{n} \left(\sin^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((b*sec(f*x+e))^n*sin(f*x+e)^2,x)","F"
500,0,0,63,0.221000," ","int((b*sec(f*x+e))^n,x)","\int \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((b*sec(f*x+e))^n,x)","F"
501,0,0,63,0.441000," ","int(csc(f*x+e)^2*(b*sec(f*x+e))^n,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)^2*(b*sec(f*x+e))^n,x)","F"
502,0,0,63,0.306000," ","int(csc(f*x+e)^4*(b*sec(f*x+e))^n,x)","\int \left(\csc^{4}\left(f x +e \right)\right) \left(b \sec \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(csc(f*x+e)^4*(b*sec(f*x+e))^n,x)","F"
503,0,0,64,0.186000," ","int((b*sec(b*x+a))^n*(c*sin(b*x+a))^(3/2),x)","\int \left(b \sec \left(b x +a \right)\right)^{n} \left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((b*sec(b*x+a))^n*(c*sin(b*x+a))^(3/2),x)","F"
504,0,0,64,0.163000," ","int((b*sec(b*x+a))^n*(c*sin(b*x+a))^(1/2),x)","\int \left(b \sec \left(b x +a \right)\right)^{n} \sqrt{c \sin \left(b x +a \right)}\, dx"," ",0,"int((b*sec(b*x+a))^n*(c*sin(b*x+a))^(1/2),x)","F"
505,0,0,64,0.133000," ","int((b*sec(b*x+a))^n/(c*sin(b*x+a))^(1/2),x)","\int \frac{\left(b \sec \left(b x +a \right)\right)^{n}}{\sqrt{c \sin \left(b x +a \right)}}\, dx"," ",0,"int((b*sec(b*x+a))^n/(c*sin(b*x+a))^(1/2),x)","F"
506,0,0,66,0.126000," ","int((b*sec(b*x+a))^n/(c*sin(b*x+a))^(3/2),x)","\int \frac{\left(b \sec \left(b x +a \right)\right)^{n}}{\left(c \sin \left(b x +a \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*sec(b*x+a))^n/(c*sin(b*x+a))^(3/2),x)","F"
507,1,214,116,0.346000," ","int(sin(f*x+e)^4*(d*csc(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \left(-5 i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-8 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+8 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{21 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"1/21/f*sin(f*x+e)*(d/sin(f*x+e))^(1/2)*(-5*I*sin(f*x+e)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)+3*cos(f*x+e)^4*2^(1/2)-3*cos(f*x+e)^3*2^(1/2)-8*cos(f*x+e)^2*2^(1/2)+8*cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))*2^(1/2)","C"
508,1,538,95,0.277000," ","int(sin(f*x+e)^3*(d*csc(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \left(-6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}-6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-4 \cos \left(f x +e \right) \sqrt{2}+3 \sqrt{2}\right) \sqrt{2}}{5 f}"," ",0,"1/5/f*(d/sin(f*x+e))^(1/2)*(-6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^3*2^(1/2)-6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-4*cos(f*x+e)*2^(1/2)+3*2^(1/2))*2^(1/2)","C"
509,1,187,92,0.184000," ","int(sin(f*x+e)^2*(d*csc(f*x+e))^(1/2),x)","-\frac{\sin \left(f x +e \right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \left(i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/3/f*sin(f*x+e)*(d/sin(f*x+e))^(1/2)*(I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))*2^(1/2)","C"
510,1,525,70,0.160000," ","int(sin(f*x+e)*(d*csc(f*x+e))^(1/2),x)","-\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sqrt{2}}{f}"," ",0,"-1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2^(1/2))*(d/sin(f*x+e))^(1/2)*2^(1/2)","C"
511,1,165,69,0.130000," ","int((d*csc(f*x+e))^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos \left(f x +e \right)+1\right)^{2}}{f \sin \left(f x +e \right)^{2}}"," ",0,"-I/f*2^(1/2)*(d/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))/sin(f*x+e)^2*(cos(f*x+e)+1)^2","C"
512,1,514,92,0.158000," ","int(csc(f*x+e)*(d*csc(f*x+e))^(1/2),x)","\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sqrt{2}}{f}"," ",0,"1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-2^(1/2))*(d/sin(f*x+e))^(1/2)*2^(1/2)","C"
513,1,319,94,0.175000," ","int(csc(f*x+e)^2*(d*csc(f*x+e))^(1/2),x)","\frac{\sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{3 f \sin \left(f x +e \right)^{5}}"," ",0,"1/3/f*(d/sin(f*x+e))^(1/2)*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(I*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*sin(f*x+e)*cos(f*x+e)+I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*2^(1/2))/sin(f*x+e)^5*2^(1/2)","C"
514,1,1054,116,0.206000," ","int(csc(f*x+e)^3*(d*csc(f*x+e))^(1/2),x)","-\frac{\left(6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}+3 \sqrt{2}\right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sqrt{2}}{5 f \sin \left(f x +e \right)^{2}}"," ",0,"-1/5/f*(6*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2)+3*2^(1/2))*(d/sin(f*x+e))^(1/2)/sin(f*x+e)^2*2^(1/2)","C"
515,1,216,119,0.162000," ","int((d*csc(f*x+e))^(3/2)*sin(f*x+e)^5,x)","-\frac{\left(5 i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+8 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-8 \cos \left(f x +e \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{21 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/21/f*(5*I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^4*2^(1/2)+3*cos(f*x+e)^3*2^(1/2)+8*cos(f*x+e)^2*2^(1/2)-8*cos(f*x+e)*2^(1/2))*(d/sin(f*x+e))^(3/2)*sin(f*x+e)^2/(-1+cos(f*x+e))*2^(1/2)","C"
516,1,545,97,0.181000," ","int((d*csc(f*x+e))^(3/2)*sin(f*x+e)^4,x)","-\frac{\left(6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \cos \left(f x +e \right) \sqrt{2}-3 \sqrt{2}\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{2}}{5 f}"," ",0,"-1/5/f*(6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^3*2^(1/2)+4*cos(f*x+e)*2^(1/2)-3*2^(1/2))*(d/sin(f*x+e))^(3/2)*sin(f*x+e)*2^(1/2)","C"
517,1,189,95,0.152000," ","int((d*csc(f*x+e))^(3/2)*sin(f*x+e)^3,x)","-\frac{\left(i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right)}"," ",0,"-1/3/f*(I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))*(d/sin(f*x+e))^(3/2)*sin(f*x+e)^2/(-1+cos(f*x+e))*2^(1/2)","C"
518,1,531,72,0.150000," ","int((d*csc(f*x+e))^(3/2)*sin(f*x+e)^2,x)","-\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{2}}{f}"," ",0,"-1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2^(1/2))*(d/sin(f*x+e))^(3/2)*sin(f*x+e)*2^(1/2)","C"
519,1,165,70,0.171000," ","int((d*csc(f*x+e))^(3/2)*sin(f*x+e),x)","-\frac{i \sqrt{2}\, \left(\cos \left(f x +e \right)+1\right)^{2} \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}}}{f \sin \left(f x +e \right)}"," ",0,"-I/f*2^(1/2)*(cos(f*x+e)+1)^2*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(d/sin(f*x+e))^(3/2)/sin(f*x+e)","C"
520,1,520,95,0.138000," ","int((d*csc(f*x+e))^(3/2),x)","\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{2}}{f}"," ",0,"1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-2^(1/2))*(d/sin(f*x+e))^(3/2)*sin(f*x+e)*2^(1/2)","C"
521,1,319,92,0.145000," ","int(csc(f*x+e)*(d*csc(f*x+e))^(3/2),x)","\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}\right) \left(\cos \left(f x +e \right)+1\right)^{2} \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sqrt{2}}{3 f \sin \left(f x +e \right)^{4}}"," ",0,"1/3/f*(-1+cos(f*x+e))^2*(I*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*sin(f*x+e)*cos(f*x+e)+I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*2^(1/2))*(cos(f*x+e)+1)^2*(d/sin(f*x+e))^(3/2)/sin(f*x+e)^4*2^(1/2)","C"
522,1,1054,119,0.171000," ","int(csc(f*x+e)^2*(d*csc(f*x+e))^(3/2),x)","-\frac{\left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \left(6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}+3 \sqrt{2}\right) \sqrt{2}}{5 f \sin \left(f x +e \right)}"," ",0,"-1/5/f*(d/sin(f*x+e))^(3/2)*(6*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2)+3*2^(1/2))/sin(f*x+e)*2^(1/2)","C"
523,1,208,118,0.195000," ","int(sin(f*x+e)^3/(d*csc(f*x+e))^(1/2),x)","-\frac{\left(5 i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+8 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-8 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{21 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}}"," ",0,"-1/21/f*(5*I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^4*2^(1/2)+3*cos(f*x+e)^3*2^(1/2)+8*cos(f*x+e)^2*2^(1/2)-8*cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))/(d/sin(f*x+e))^(1/2)*2^(1/2)","C"
524,1,547,92,0.190000," ","int(sin(f*x+e)^2/(d*csc(f*x+e))^(1/2),x)","-\frac{\left(6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \cos \left(f x +e \right) \sqrt{2}-3 \sqrt{2}\right) \sqrt{2}}{5 f \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"-1/5/f*(6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^3*2^(1/2)+4*cos(f*x+e)*2^(1/2)-3*2^(1/2))/(d/sin(f*x+e))^(1/2)/sin(f*x+e)*2^(1/2)","C"
525,1,181,94,0.162000," ","int(sin(f*x+e)/(d*csc(f*x+e))^(1/2),x)","-\frac{\left(i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{d}{\sin \left(f x +e \right)}}}"," ",0,"-1/3/f*(I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))/(d/sin(f*x+e))^(1/2)*2^(1/2)","C"
526,1,533,69,0.154000," ","int(1/(d*csc(f*x+e))^(1/2),x)","-\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{f \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"-1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2^(1/2))/(d/sin(f*x+e))^(1/2)/sin(f*x+e)*2^(1/2)","C"
527,1,165,72,0.142000," ","int(csc(f*x+e)/(d*csc(f*x+e))^(1/2),x)","-\frac{i \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{2}}{f \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)^{3}}"," ",0,"-I/f*(-1+cos(f*x+e))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*(cos(f*x+e)+1)^2*2^(1/2)/(d/sin(f*x+e))^(1/2)/sin(f*x+e)^3","C"
528,1,522,94,0.161000," ","int(csc(f*x+e)^2/(d*csc(f*x+e))^(1/2),x)","\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\right) \sqrt{2}}{f \sqrt{\frac{d}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right)}"," ",0,"1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-2^(1/2))/(d/sin(f*x+e))^(1/2)/sin(f*x+e)*2^(1/2)","C"
529,1,318,97,0.175000," ","int(csc(f*x+e)^3/(d*csc(f*x+e))^(1/2),x)","-\frac{\left(-1+\cos \left(f x +e \right)\right)^{2} \left(-i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right) \cos \left(f x +e \right)-i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+\cos \left(f x +e \right) \sqrt{2}\right) \left(\cos \left(f x +e \right)+1\right)^{2} \sqrt{2}}{3 f \sin \left(f x +e \right)^{6} \sqrt{\frac{d}{\sin \left(f x +e \right)}}}"," ",0,"-1/3/f*(-1+cos(f*x+e))^2*(-I*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*sin(f*x+e)*cos(f*x+e)-I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2))*(cos(f*x+e)+1)^2/sin(f*x+e)^6/(d/sin(f*x+e))^(1/2)*2^(1/2)","C"
530,1,216,119,0.181000," ","int(sin(f*x+e)^2/(d*csc(f*x+e))^(3/2),x)","-\frac{\left(5 i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-3 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{2}+3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+8 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-8 \cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{21 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-1/21/f*(5*I*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^4*2^(1/2)+3*cos(f*x+e)^3*2^(1/2)+8*cos(f*x+e)^2*2^(1/2)-8*cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)*2^(1/2)","C"
531,1,547,94,0.171000," ","int(sin(f*x+e)/(d*csc(f*x+e))^(3/2),x)","-\frac{\left(6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}+4 \cos \left(f x +e \right) \sqrt{2}-3 \sqrt{2}\right) \sqrt{2}}{5 f \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{2}}"," ",0,"-1/5/f*(6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)^3*2^(1/2)+4*cos(f*x+e)*2^(1/2)-3*2^(1/2))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)^2*2^(1/2)","C"
532,1,189,97,0.137000," ","int(1/(d*csc(f*x+e))^(3/2),x)","-\frac{\left(i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}+\left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)}"," ",0,"-1/3/f*(I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)^2*2^(1/2)-cos(f*x+e)*2^(1/2))/(-1+cos(f*x+e))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)*2^(1/2)","C"
533,1,533,72,0.142000," ","int(csc(f*x+e)/(d*csc(f*x+e))^(3/2),x)","-\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+\cos \left(f x +e \right) \sqrt{2}-\sqrt{2}\right) \sqrt{2}}{f \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{2}}"," ",0,"-1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+cos(f*x+e)*2^(1/2)-2^(1/2))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)^2*2^(1/2)","C"
534,1,165,72,0.142000," ","int(csc(f*x+e)^2/(d*csc(f*x+e))^(3/2),x)","-\frac{i \sqrt{2}\, \left(\cos \left(f x +e \right)+1\right)^{2} \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right)}{f \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{4}}"," ",0,"-I/f*2^(1/2)*(cos(f*x+e)+1)^2*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)^4","C"
535,1,522,97,0.159000," ","int(csc(f*x+e)^3/(d*csc(f*x+e))^(3/2),x)","\frac{\left(2 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{2}\right) \sqrt{2}}{f \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{2}}"," ",0,"1/f*(2*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-2^(1/2))/(d/sin(f*x+e))^(3/2)/sin(f*x+e)^2*2^(1/2)","C"
536,1,319,97,0.171000," ","int(csc(f*x+e)^4/(d*csc(f*x+e))^(3/2),x)","\frac{\left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(i \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right) \cos \left(f x +e \right)+i \sin \left(f x +e \right) \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}-\cos \left(f x +e \right) \sqrt{2}\right) \sqrt{2}}{3 f \sin \left(f x +e \right)^{7} \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"1/3/f*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(I*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*sin(f*x+e)*cos(f*x+e)+I*sin(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-cos(f*x+e)*2^(1/2))/sin(f*x+e)^7/(d/sin(f*x+e))^(3/2)*2^(1/2)","C"
537,1,1054,121,0.182000," ","int(csc(f*x+e)^5/(d*csc(f*x+e))^(3/2),x)","-\frac{\left(6 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+6 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \cos \left(f x +e \right) \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)+3 \sqrt{-\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{i \cos \left(f x +e \right)-\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{\frac{i \cos \left(f x +e \right)+\sin \left(f x +e \right)-i}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right)-3 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}+\cos \left(f x +e \right) \sqrt{2}+3 \sqrt{2}\right) \sqrt{2}}{5 f \sin \left(f x +e \right)^{4} \left(\frac{d}{\sin \left(f x +e \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/5/f*(6*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+6*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*cos(f*x+e)*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-6*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticE(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))+3*(-I*(-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2)*(-(I*cos(f*x+e)-sin(f*x+e)-I)/sin(f*x+e))^(1/2)*EllipticF(((I*cos(f*x+e)+sin(f*x+e)-I)/sin(f*x+e))^(1/2),1/2*2^(1/2))-3*cos(f*x+e)^2*2^(1/2)+cos(f*x+e)*2^(1/2)+3*2^(1/2))/sin(f*x+e)^4/(d/sin(f*x+e))^(3/2)*2^(1/2)","C"
538,0,0,81,1.067000," ","int((b*csc(f*x+e))^n*(a*sin(f*x+e))^m,x)","\int \left(b \csc \left(f x +e \right)\right)^{n} \left(a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((b*csc(f*x+e))^n*(a*sin(f*x+e))^m,x)","F"