1,1,1181,286,0.342000," ","int(sin(x)^4/(a+b*sin(x)+c*sin(x)^2),x)","\frac{12 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{c^{3} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{16 a^{3} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{20 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{c^{3} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{12 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{c^{3} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{16 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{20 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{c^{3} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{\tan^{3}\left(\frac{x}{2}\right)}{c \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b}{c^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{c \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 b}{c^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a}{c^{2}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{c^{3}}+\frac{x}{2 c}"," ",0,"12/c^2*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b-4/c^3*a/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3-16/c*a^3/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))+20/c^2*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2-4/c^3*a/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4+12/c^2*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b-4/c^3*a/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3+16/c*a^3/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))-20/c^2*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2+4/c^3*a/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4+1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+2/c^2/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2*b-1/c/(tan(1/2*x)^2+1)^2*tan(1/2*x)+2/c^2/(tan(1/2*x)^2+1)^2*b-2/c^2*arctan(tan(1/2*x))*a+2/c^3*arctan(tan(1/2*x))*b^2+1/2*x/c","B"
2,1,890,260,0.289000," ","int(sin(x)^3/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{8 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{16 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{16 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3}}{c^{2} \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2}{c \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{2 b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{c^{2}}"," ",0,"-8/c*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)+4/c^2*a/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2-16/c*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b+4/c^2*a/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3-8/c*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)+4/c^2*a/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2+16/c*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b-4/c^2*a/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3-2/c/(tan(1/2*x)^2+1)-2/c^2*b*arctan(tan(1/2*x))","B"
3,1,638,220,0.279000," ","int(sin(x)^2/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{16 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{16 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c \left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{c}"," ",0,"-4*a/c/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)+16*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))-4*a/c/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2-4*a/c/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)-16*a^2/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))+4*a/c/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2+2/c*arctan(tan(1/2*x))","B"
4,1,216,192,0.276000," ","int(sin(x)/(a+b*sin(x)+c*sin(x)^2),x)","\frac{8 a \sqrt{-4 c a +b^{2}}\, \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a \sqrt{-4 c a +b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(8 c a -2 b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}"," ",0,"8*a*(-4*a*c+b^2)^(1/2)/(8*a*c-2*b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))+8*a*(-4*a*c+b^2)^(1/2)/(8*a*c-2*b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))","A"
5,1,610,187,0.281000," ","int(1/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}"," ",0,"-2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)-8*a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c+2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2-2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)+8*a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c-2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2","B"
6,1,849,210,0.355000," ","int(csc(x)/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{4 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c b}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c b}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-4/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*c+2/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2+8/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c*b-2/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3-4/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*c+2/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2-8/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c*b+2/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3+1/a*ln(tan(1/2*x))","B"
7,1,1087,238,0.373000," ","int(csc(x)^2/(a+b*sin(x)+c*sin(x)^2),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a}+\frac{6 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b c}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{10 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b c}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{10 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}"," ",0,"1/2/a*tan(1/2*x)+6/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c-2/a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3+8/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^2-10/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c+2/a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4+6/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c-2/a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3-8/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^2+10/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c-2/a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4-1/2/a/tan(1/2*x)-1/a^2*b*ln(tan(1/2*x))","B"
8,1,1369,289,0.391000," ","int(csc(x)^3/(a+b*sin(x)+c*sin(x)^2),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}-\frac{\tan \left(\frac{x}{2}\right) b}{2 a^{2}}+\frac{4 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, c^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2} c}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{4}}{a^{3} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{16 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \,c^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{12 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3} c}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{5}}{a^{3} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, c^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{2} c}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{4}}{a^{3} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{16 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \,c^{2}}{a \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{12 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{3} c}{a^{2} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{5}}{a^{3} \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) c}{a^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}+\frac{b}{2 a^{2} \tan \left(\frac{x}{2}\right)}"," ",0,"1/8/a*tan(1/2*x)^2-1/2/a^2*tan(1/2*x)*b+4/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*c^2-8/a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*c+2/a^3/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^4-16/a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*c^2+12/a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3*c-2/a^3/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^5+4/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*c^2-8/a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*c+2/a^3/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^4+16/a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*c^2-12/a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^3*c+2/a^3/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^5-1/8/a/tan(1/2*x)^2+1/2/a*ln(tan(1/2*x))-1/a^2*ln(tan(1/2*x))*c+1/a^3*ln(tan(1/2*x))*b^2+1/2*b/a^2/tan(1/2*x)","B"
9,1,143,70,0.289000," ","int(cos(x)^3/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{\sin \left(x \right)}{c}+\frac{b \ln \left(a +b \sin \left(x \right)+c \left(\sin^{2}\left(x \right)\right)\right)}{2 c^{2}}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a}{c \sqrt{4 c a -b^{2}}}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right)}{\sqrt{4 c a -b^{2}}}-\frac{\arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2}}{c^{2} \sqrt{4 c a -b^{2}}}"," ",0,"-sin(x)/c+1/2*b*ln(a+b*sin(x)+c*sin(x)^2)/c^2+2/c/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*a+2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))-1/c^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*b^2","B"
10,1,1246,196,0.345000," ","int(cos(x)^2/(a+b*sin(x)+c*sin(x)^2),x)","\frac{2 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b}{c \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b}{c \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b \sqrt{-4 c a +b^{2}}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right)}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{c \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2}}{\left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{c}"," ",0,"2*a/c/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b-2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)-8*a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))+2*a/c/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2-8*a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c+2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2+2*a/c/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b-2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b*(-4*a*c+b^2)^(1/2)+8*a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))-2*a/c/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2+8*a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c-2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2-2/c*arctan(tan(1/2*x))","B"
11,1,36,31,0.209000," ","int(cos(x)/(a+b*sin(x)+c*sin(x)^2),x)","\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right)}{\sqrt{4 c a -b^{2}}}"," ",0,"2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))","A"
12,1,224,118,0.291000," ","int(sec(x)/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{\ln \left(-1+\sin \left(x \right)\right)}{2 a +2 b +2 c}-\frac{b \ln \left(a +b \sin \left(x \right)+c \left(\sin^{2}\left(x \right)\right)\right)}{2 \left(a -b +c \right) \left(a +b +c \right)}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c a}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}-\frac{\arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2}}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \sqrt{4 c a -b^{2}}}+\frac{\ln \left(1+\sin \left(x \right)\right)}{2 a -2 b +2 c}"," ",0,"-1/(2*a+2*b+2*c)*ln(-1+sin(x))-1/2*b*ln(a+b*sin(x)+c*sin(x)^2)/(a-b+c)/(a+b+c)+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*c*a-1/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*b^2+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*c^2+1/(2*a-2*b+2*c)*ln(1+sin(x))","A"
13,1,1934,287,0.375000," ","int(sec(x)^2/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{6 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b c}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b \,c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a^{2} \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{10 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{8 a \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{3}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{-2 a \tan \left(\frac{x}{2}\right)+\sqrt{-4 c a +b^{2}}-b}{\sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}+2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{6 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b c}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b^{3}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) \sqrt{-4 c a +b^{2}}\, b \,c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{10 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{8 a \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) c^{3}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{4}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{x}{2}\right)+b +\sqrt{-4 c a +b^{2}}}{\sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}\right) b^{2} c^{2}}{\left(a -b +c \right) \left(a +b +c \right) \left(4 c a -b^{2}\right) \sqrt{4 c a -2 b^{2}-2 b \sqrt{-4 c a +b^{2}}+4 a^{2}}}-\frac{2}{\left(2 a +2 b +2 c \right) \left(\tan \left(\frac{x}{2}\right)-1\right)}-\frac{2}{\left(2 a -2 b +2 c \right) \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-6/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c^2-8/(a-b+c)/(a+b+c)*a^2/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^2+10/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c-8/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^3-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((-2*a*tan(1/2*x)+(-4*a*c+b^2)^(1/2)-b)/(4*c*a-2*b^2+2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c^2-6/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*c^2+8/(a-b+c)/(a+b+c)*a^2/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^2-10/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c+8/(a-b+c)/(a+b+c)*a/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*c^3+2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^4-2/(a-b+c)/(a+b+c)/(4*a*c-b^2)/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2)*arctan((2*a*tan(1/2*x)+b+(-4*a*c+b^2)^(1/2))/(4*c*a-2*b^2-2*b*(-4*a*c+b^2)^(1/2)+4*a^2)^(1/2))*b^2*c^2-2/(2*a+2*b+2*c)/(tan(1/2*x)-1)-2/(2*a-2*b+2*c)/(tan(1/2*x)+1)","B"
14,1,549,194,0.339000," ","int(sec(x)^3/(a+b*sin(x)+c*sin(x)^2),x)","-\frac{1}{\left(4 a +4 b +4 c \right) \left(-1+\sin \left(x \right)\right)}-\frac{\ln \left(-1+\sin \left(x \right)\right) a}{4 \left(a +b +c \right)^{2}}-\frac{\ln \left(-1+\sin \left(x \right)\right) b}{2 \left(a +b +c \right)^{2}}-\frac{3 \ln \left(-1+\sin \left(x \right)\right) c}{4 \left(a +b +c \right)^{2}}-\frac{c \ln \left(a +b \sin \left(x \right)+c \left(\sin^{2}\left(x \right)\right)\right) a b}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}+\frac{\ln \left(a +b \sin \left(x \right)+c \left(\sin^{2}\left(x \right)\right)\right) b^{3}}{2 \left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}-\frac{c^{2} \ln \left(a +b \sin \left(x \right)+c \left(\sin^{2}\left(x \right)\right)\right) b}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2}}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a^{2} c^{2}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{4 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a \,b^{2} c}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{4 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) a \,c^{3}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{\arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{4}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) b^{2} c^{2}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}+\frac{2 \arctan \left(\frac{b +2 c \sin \left(x \right)}{\sqrt{4 c a -b^{2}}}\right) c^{4}}{\left(a -b +c \right)^{2} \left(a +b +c \right)^{2} \sqrt{4 c a -b^{2}}}-\frac{1}{\left(4 a -4 b +4 c \right) \left(1+\sin \left(x \right)\right)}+\frac{\ln \left(1+\sin \left(x \right)\right) a}{4 \left(a -b +c \right)^{2}}-\frac{\ln \left(1+\sin \left(x \right)\right) b}{2 \left(a -b +c \right)^{2}}+\frac{3 \ln \left(1+\sin \left(x \right)\right) c}{4 \left(a -b +c \right)^{2}}"," ",0,"-1/(4*a+4*b+4*c)/(-1+sin(x))-1/4/(a+b+c)^2*ln(-1+sin(x))*a-1/2/(a+b+c)^2*ln(-1+sin(x))*b-3/4/(a+b+c)^2*ln(-1+sin(x))*c-1/(a-b+c)^2/(a+b+c)^2*c*ln(a+b*sin(x)+c*sin(x)^2)*a*b+1/2/(a-b+c)^2/(a+b+c)^2*ln(a+b*sin(x)+c*sin(x)^2)*b^3-1/(a-b+c)^2/(a+b+c)^2*c^2*ln(a+b*sin(x)+c*sin(x)^2)*b+2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*a^2*c^2-4/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*a*b^2*c+4/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*a*c^3+1/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*b^4-2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*b^2*c^2+2/(a-b+c)^2/(a+b+c)^2/(4*a*c-b^2)^(1/2)*arctan((b+2*c*sin(x))/(4*a*c-b^2)^(1/2))*c^4-1/(4*a-4*b+4*c)/(1+sin(x))+1/4/(a-b+c)^2*ln(1+sin(x))*a-1/2/(a-b+c)^2*ln(1+sin(x))*b+3/4/(a-b+c)^2*ln(1+sin(x))*c","B"
15,1,16,17,0.200000," ","int(cos(x)/(-6+sin(x)+sin(x)^2),x)","-\frac{\ln \left(3+\sin \left(x \right)\right)}{5}+\frac{\ln \left(\sin \left(x \right)-2\right)}{5}"," ",0,"-1/5*ln(3+sin(x))+1/5*ln(sin(x)-2)","A"
16,1,14,17,0.209000," ","int(cos(x)/(2-3*sin(x)+sin(x)^2),x)","-\ln \left(-1+\sin \left(x \right)\right)+\ln \left(\sin \left(x \right)-2\right)"," ",0,"-ln(-1+sin(x))+ln(sin(x)-2)","A"
17,1,16,17,0.218000," ","int(cos(x)/(-5+4*sin(x)+sin(x)^2),x)","\frac{\ln \left(-1+\sin \left(x \right)\right)}{6}-\frac{\ln \left(5+\sin \left(x \right)\right)}{6}"," ",0,"1/6*ln(-1+sin(x))-1/6*ln(5+sin(x))","A"
18,1,6,5,0.215000," ","int(cos(x)/(10-6*sin(x)+sin(x)^2),x)","\arctan \left(-3+\sin \left(x \right)\right)"," ",0,"arctan(-3+sin(x))","A"
19,1,6,5,0.202000," ","int(cos(x)/(2+2*sin(x)+sin(x)^2),x)","\arctan \left(1+\sin \left(x \right)\right)"," ",0,"arctan(1+sin(x))","A"