1,1,865,393,0.314000," ","int((d*cos(f*x+e))^(1/2)*(g*sin(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x)","-\frac{\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) a +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) b +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) a -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) b +\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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) a -\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) b +\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) a -\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) b -a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b -a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b \right) \sin \left(f x +e \right) \sqrt{d \cos \left(f x +e \right)}\, \sqrt{g \sin \left(f x +e \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)}}\, \sqrt{2}\, a}{f \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) b \left(\sqrt{-a^{2}+b^{2}}+a -b \right) \left(-a +b +\sqrt{-a^{2}+b^{2}}\right)}"," ",0,"-1/f*(-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))*a+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))*b+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))*a-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))*b+(-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))-(-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),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))*a-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))*b+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))*a-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))*b-a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b)*sin(f*x+e)*(d*cos(f*x+e))^(1/2)*(g*sin(f*x+e))^(1/2)*((-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)/cos(f*x+e)/(-1+cos(f*x+e))*2^(1/2)*a/b/((-a^2+b^2)^(1/2)+a-b)/(-a+b+(-a^2+b^2)^(1/2))","B"
2,1,608,173,0.258000," ","int((d*cos(f*x+e))^(1/2)/(a+b*cos(f*x+e))/(g*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{d \cos \left(f x +e \right)}\, \left(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) \sqrt{-a^{2}+b^{2}}+a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b -\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)-a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b -\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\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)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}\, a}{f \sqrt{g \sin \left(f x +e \right)}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \left(\sqrt{-a^{2}+b^{2}}+a -b \right) \left(-a +b +\sqrt{-a^{2}+b^{2}}\right)}"," ",0,"-1/f*(d*cos(f*x+e))^(1/2)*(2*EllipticF(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))-a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2)))*((-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)*sin(f*x+e)^2/(g*sin(f*x+e))^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))*2^(1/2)*a/(-a^2+b^2)^(1/2)/((-a^2+b^2)^(1/2)+a-b)/(-a+b+(-a^2+b^2)^(1/2))","B"
3,1,538,164,0.206000," ","int((g*sin(f*x+e))^(1/2)/(a+b*cos(f*x+e))/(d*cos(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(\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-a^{2}+b^{2}}\, \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right)-a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b -a \EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \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{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b \right) \sqrt{g \sin \left(f x +e \right)}\, \sin \left(f x +e \right) \sqrt{2}}{f \left(-1+\cos \left(f x +e \right)\right) \sqrt{d \cos \left(f x +e \right)}\, \left(-a +b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}+a -b \right)}"," ",0,"1/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)*((-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))-(-a^2+b^2)^(1/2)*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))-a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b-a*EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b)*(g*sin(f*x+e))^(1/2)*sin(f*x+e)/(-1+cos(f*x+e))/(d*cos(f*x+e))^(1/2)*2^(1/2)/(-a+b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)+a-b)","B"
4,1,607,257,0.216000," ","int(1/(a+b*cos(f*x+e))/(d*cos(f*x+e))^(1/2)/(g*sin(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(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) a \sqrt{-a^{2}+b^{2}}+\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a b -\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{2}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a -b}{a -b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) a b +\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b^{2}-\EllipticPi \left(\sqrt{\frac{1-\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a -b}{-a +b +\sqrt{-\left(a -b \right) \left(a +b \right)}}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}\right) \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{f \left(-1+\cos \left(f x +e \right)\right) \sqrt{g \sin \left(f x +e \right)}\, \sqrt{d \cos \left(f x +e \right)}\, \left(-a +b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}+a -b \right) \sqrt{-a^{2}+b^{2}}}"," ",0,"1/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)*(2*EllipticF(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*(-a^2+b^2)^(1/2)+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),(a-b)/(a-b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b*(-a^2+b^2)^(1/2)-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*a*b+EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b^2-EllipticPi(((1-cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2),-(a-b)/(-a+b+(-(a-b)*(a+b))^(1/2)),1/2*2^(1/2))*b*(-a^2+b^2)^(1/2))*sin(f*x+e)^2/(-1+cos(f*x+e))/(g*sin(f*x+e))^(1/2)/(d*cos(f*x+e))^(1/2)*2^(1/2)/(-a+b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)+a-b)/(-a^2+b^2)^(1/2)","B"