1,1,260,166,0.009000," ","int((d*x^2+c)/(b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, d \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/8*c*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))+1/4*c*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*c*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8*d/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))+1/4*d/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*d/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
2,1,260,166,0.003000," ","int((-d*x^2+c)/(b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, d \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8/(a/b)^(1/4)*2^(1/2)/b*d*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/(a/b)^(1/4)*2^(1/2)/b*d*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4/(a/b)^(1/4)*2^(1/2)/b*d*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
3,1,122,58,0.005000," ","int((d*x^2+c)/(-b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{d \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/4*c*(a/b)^(1/4)/a*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*c*(a/b)^(1/4)/a*arctan(x/(a/b)^(1/4))-1/2*d/b/(a/b)^(1/4)*arctan(x/(a/b)^(1/4))+1/4*d/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
4,1,122,58,0.003000," ","int((-d*x^2+c)/(-b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}+\frac{d \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/4*(a/b)^(1/4)/a*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*(a/b)^(1/4)/a*c*arctan(1/(a/b)^(1/4)*x)+1/2/(a/b)^(1/4)/b*d*arctan(1/(a/b)^(1/4)*x)-1/4/(a/b)^(1/4)/b*d*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
5,1,122,27,0.006000," ","int((3*x^2+2)/(9*x^4+4),x)","\frac{\sqrt{6}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{6}\, \sqrt{2}\, x}{2}-1\right)}{12}+\frac{\sqrt{6}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{6}\, \sqrt{2}\, x}{2}+1\right)}{12}+\frac{\sqrt{6}\, \sqrt{2}\, \ln \left(\frac{x^{2}-\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}{x^{2}+\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}\right)}{48}+\frac{\sqrt{6}\, \sqrt{2}\, \ln \left(\frac{x^{2}+\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}{x^{2}-\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}\right)}{48}"," ",0,"1/12*6^(1/2)*2^(1/2)*arctan(1/2*6^(1/2)*x*2^(1/2)-1)+1/48*6^(1/2)*2^(1/2)*ln((x^2+1/3*6^(1/2)*x*2^(1/2)+2/3)/(x^2-1/3*6^(1/2)*x*2^(1/2)+2/3))+1/12*6^(1/2)*2^(1/2)*arctan(1/2*6^(1/2)*x*2^(1/2)+1)+1/48*6^(1/2)*2^(1/2)*ln((x^2-1/3*6^(1/2)*x*2^(1/2)+2/3)/(x^2+1/3*6^(1/2)*x*2^(1/2)+2/3))","B"
6,1,82,39,0.003000," ","int((-3*x^2+2)/(9*x^4+4),x)","-\frac{\sqrt{6}\, \sqrt{2}\, \ln \left(\frac{x^{2}-\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}{x^{2}+\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}\right)}{48}+\frac{\sqrt{6}\, \sqrt{2}\, \ln \left(\frac{x^{2}+\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}{x^{2}-\frac{\sqrt{6}\, \sqrt{2}\, x}{3}+\frac{2}{3}}\right)}{48}"," ",0,"1/48*6^(1/2)*2^(1/2)*ln((x^2+1/3*6^(1/2)*2^(1/2)*x+2/3)/(x^2-1/3*6^(1/2)*2^(1/2)*x+2/3))-1/48*6^(1/2)*2^(1/2)*ln((x^2-1/3*6^(1/2)*2^(1/2)*x+2/3)/(x^2+1/3*6^(1/2)*2^(1/2)*x+2/3))","B"
7,1,13,12,0.002000," ","int((3*x^2+2)/(-9*x^4+4),x)","\frac{\sqrt{6}\, \arctanh \left(\frac{\sqrt{6}\, x}{2}\right)}{6}"," ",0,"1/6*arctanh(1/2*6^(1/2)*x)*6^(1/2)","A"
8,1,13,12,0.003000," ","int((-3*x^2+2)/(-9*x^4+4),x)","\frac{\sqrt{6}\, \arctan \left(\frac{\sqrt{6}\, x}{2}\right)}{6}"," ",0,"1/6*arctan(1/2*6^(1/2)*x)*6^(1/2)","A"
9,1,254,51,0.005000," ","int((b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \sqrt{a}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \sqrt{a}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \sqrt{a}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"1/8/a^(1/2)*b^(1/2)*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/a^(1/2)*b^(1/2)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/a^(1/2)*b^(1/2)*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","B"
10,1,254,70,0.004000," ","int((-b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \sqrt{a}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \sqrt{a}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{b}\, \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \sqrt{a}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}}}"," ",0,"1/8*(a/b)^(1/4)*2^(1/2)/a^(1/2)*b^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*(a/b)^(1/4)*2^(1/2)/a^(1/2)*b^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a^(1/2)*b^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","B"
11,1,290,51,0.010000," ","int((e*x^2+d)/(e^2*x^4+d^2),x)","\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d}+\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d}+\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}{x^{2}-\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}\right)}{8 d}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}{x^{2}+\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}\right)}{8 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}"," ",0,"1/8/d*(d^2/e^2)^(1/4)*2^(1/2)*ln((x^2+(d^2/e^2)^(1/4)*x*2^(1/2)+(d^2/e^2)^(1/2))/(x^2-(d^2/e^2)^(1/4)*x*2^(1/2)+(d^2/e^2)^(1/2)))+1/4/d*(d^2/e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x+1)+1/4/d*(d^2/e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x-1)+1/8/e/(d^2/e^2)^(1/4)*2^(1/2)*ln((x^2-(d^2/e^2)^(1/4)*x*2^(1/2)+(d^2/e^2)^(1/2))/(x^2+(d^2/e^2)^(1/4)*x*2^(1/2)+(d^2/e^2)^(1/2)))+1/4/e/(d^2/e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x+1)+1/4/e/(d^2/e^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x-1)","B"
12,1,290,62,0.004000," ","int((-e*x^2+d)/(e^2*x^4+d^2),x)","\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d}+\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d}+\frac{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}{x^{2}-\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}\right)}{8 d}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}-\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}{x^{2}+\left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{d^{2}}{e^{2}}}}\right)}{8 \left(\frac{d^{2}}{e^{2}}\right)^{\frac{1}{4}} e}"," ",0,"1/8*(d^2/e^2)^(1/4)*2^(1/2)/d*ln((x^2+(d^2/e^2)^(1/4)*2^(1/2)*x+(d^2/e^2)^(1/2))/(x^2-(d^2/e^2)^(1/4)*2^(1/2)*x+(d^2/e^2)^(1/2)))+1/4*(d^2/e^2)^(1/4)*2^(1/2)/d*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x+1)+1/4*(d^2/e^2)^(1/4)*2^(1/2)/d*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x-1)-1/8/(d^2/e^2)^(1/4)*2^(1/2)/e*ln((x^2-(d^2/e^2)^(1/4)*2^(1/2)*x+(d^2/e^2)^(1/2))/(x^2+(d^2/e^2)^(1/4)*2^(1/2)*x+(d^2/e^2)^(1/2)))-1/4/(d^2/e^2)^(1/4)*2^(1/2)/e*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x+1)-1/4/(d^2/e^2)^(1/4)*2^(1/2)/e*arctan(2^(1/2)/(d^2/e^2)^(1/4)*x-1)","B"
13,1,18,9,0.006000," ","int((2*x^2+5)/(x^4-1),x)","-\frac{3 \arctan \left(x \right)}{2}-\frac{7 \ln \left(x +1\right)}{4}+\frac{7 \ln \left(x -1\right)}{4}"," ",0,"7/4*ln(x-1)-7/4*ln(x+1)-3/2*arctan(x)","A"
14,1,100,12,0.017000," ","int((b*x^2+1)/(-b^2*x^4+1)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+1}\, \sqrt{b \,x^{2}+1}\, \EllipticF \left(\sqrt{b}\, x , i\right)}{\sqrt{-b^{2} x^{4}+1}\, \sqrt{b}}-\frac{\sqrt{-b \,x^{2}+1}\, \sqrt{b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{b}\, x , i\right)+\EllipticF \left(\sqrt{b}\, x , i\right)\right)}{\sqrt{-b^{2} x^{4}+1}\, \sqrt{b}}"," ",0,"-1/b^(1/2)*(-b*x^2+1)^(1/2)*(b*x^2+1)^(1/2)/(-b^2*x^4+1)^(1/2)*(EllipticF(b^(1/2)*x,I)-EllipticE(b^(1/2)*x,I))+1/b^(1/2)*(-b*x^2+1)^(1/2)*(b*x^2+1)^(1/2)/(-b^2*x^4+1)^(1/2)*EllipticF(b^(1/2)*x,I)","B"
15,1,99,27,0.007000," ","int((-b*x^2+1)/(-b^2*x^4+1)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+1}\, \sqrt{b \,x^{2}+1}\, \EllipticF \left(\sqrt{b}\, x , i\right)}{\sqrt{-b^{2} x^{4}+1}\, \sqrt{b}}+\frac{\sqrt{-b \,x^{2}+1}\, \sqrt{b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{b}\, x , i\right)+\EllipticF \left(\sqrt{b}\, x , i\right)\right)}{\sqrt{-b^{2} x^{4}+1}\, \sqrt{b}}"," ",0,"1/b^(1/2)*(-b*x^2+1)^(1/2)*(b*x^2+1)^(1/2)/(-b^2*x^4+1)^(1/2)*(EllipticF(b^(1/2)*x,I)-EllipticE(b^(1/2)*x,I))+1/b^(1/2)*(-b*x^2+1)^(1/2)*(b*x^2+1)^(1/2)/(-b^2*x^4+1)^(1/2)*EllipticF(b^(1/2)*x,I)","B"
16,1,107,35,0.013000," ","int((b*x^2+1)/(b^2*x^4-1)^(1/2),x)","\frac{\sqrt{b \,x^{2}+1}\, \sqrt{-b \,x^{2}+1}\, \EllipticF \left(\sqrt{-b}\, x , i\right)}{\sqrt{-b}\, \sqrt{b^{2} x^{4}-1}}+\frac{\sqrt{b \,x^{2}+1}\, \sqrt{-b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-b}\, x , i\right)+\EllipticF \left(\sqrt{-b}\, x , i\right)\right)}{\sqrt{-b}\, \sqrt{b^{2} x^{4}-1}}"," ",0,"1/(-b)^(1/2)*(b*x^2+1)^(1/2)*(-b*x^2+1)^(1/2)/(b^2*x^4-1)^(1/2)*(EllipticF(x*(-b)^(1/2),I)-EllipticE(x*(-b)^(1/2),I))+1/(-b)^(1/2)*(b*x^2+1)^(1/2)*(-b*x^2+1)^(1/2)/(b^2*x^4-1)^(1/2)*EllipticF(x*(-b)^(1/2),I)","B"
17,1,108,73,0.006000," ","int((-b*x^2+1)/(b^2*x^4-1)^(1/2),x)","\frac{\sqrt{b \,x^{2}+1}\, \sqrt{-b \,x^{2}+1}\, \EllipticF \left(\sqrt{-b}\, x , i\right)}{\sqrt{-b}\, \sqrt{b^{2} x^{4}-1}}-\frac{\sqrt{b \,x^{2}+1}\, \sqrt{-b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-b}\, x , i\right)+\EllipticF \left(\sqrt{-b}\, x , i\right)\right)}{\sqrt{-b}\, \sqrt{b^{2} x^{4}-1}}"," ",0,"-1/(-b)^(1/2)*(b*x^2+1)^(1/2)*(-b*x^2+1)^(1/2)/(b^2*x^4-1)^(1/2)*(EllipticF((-b)^(1/2)*x,I)-EllipticE((-b)^(1/2)*x,I))+1/(-b)^(1/2)*(b*x^2+1)^(1/2)*(-b*x^2+1)^(1/2)/(b^2*x^4-1)^(1/2)*EllipticF((-b)^(1/2)*x,I)","A"
18,1,120,106,0.013000," ","int((-b*x^2+1)/(b^2*x^4+1)^(1/2),x)","\frac{\sqrt{-i b \,x^{2}+1}\, \sqrt{i b \,x^{2}+1}\, \EllipticF \left(\sqrt{i b}\, x , i\right)}{\sqrt{i b}\, \sqrt{b^{2} x^{4}+1}}-\frac{i \sqrt{-i b \,x^{2}+1}\, \sqrt{i b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{i b}\, x , i\right)+\EllipticF \left(\sqrt{i b}\, x , i\right)\right)}{\sqrt{i b}\, \sqrt{b^{2} x^{4}+1}}"," ",0,"-I/(I*b)^(1/2)*(1-I*b*x^2)^(1/2)*(1+I*b*x^2)^(1/2)/(b^2*x^4+1)^(1/2)*(EllipticF(x*(I*b)^(1/2),I)-EllipticE(x*(I*b)^(1/2),I))+1/(I*b)^(1/2)*(1-I*b*x^2)^(1/2)*(1+I*b*x^2)^(1/2)/(b^2*x^4+1)^(1/2)*EllipticF(x*(I*b)^(1/2),I)","C"
19,1,120,188,0.004000," ","int((b*x^2+1)/(b^2*x^4+1)^(1/2),x)","\frac{\sqrt{-i b \,x^{2}+1}\, \sqrt{i b \,x^{2}+1}\, \EllipticF \left(\sqrt{i b}\, x , i\right)}{\sqrt{i b}\, \sqrt{b^{2} x^{4}+1}}+\frac{i \sqrt{-i b \,x^{2}+1}\, \sqrt{i b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{i b}\, x , i\right)+\EllipticF \left(\sqrt{i b}\, x , i\right)\right)}{\sqrt{i b}\, \sqrt{b^{2} x^{4}+1}}"," ",0,"I/(I*b)^(1/2)*(-I*b*x^2+1)^(1/2)*(I*b*x^2+1)^(1/2)/(b^2*x^4+1)^(1/2)*(EllipticF((I*b)^(1/2)*x,I)-EllipticE((I*b)^(1/2)*x,I))+1/(I*b)^(1/2)*(-I*b*x^2+1)^(1/2)*(I*b*x^2+1)^(1/2)/(b^2*x^4+1)^(1/2)*EllipticF((I*b)^(1/2)*x,I)","C"
20,1,122,107,0.012000," ","int((-b*x^2+1)/(-b^2*x^4-1)^(1/2),x)","\frac{\sqrt{i b \,x^{2}+1}\, \sqrt{-i b \,x^{2}+1}\, \EllipticF \left(\sqrt{-i b}\, x , i\right)}{\sqrt{-i b}\, \sqrt{-b^{2} x^{4}-1}}+\frac{i \sqrt{i b \,x^{2}+1}\, \sqrt{-i b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-i b}\, x , i\right)+\EllipticF \left(\sqrt{-i b}\, x , i\right)\right)}{\sqrt{-i b}\, \sqrt{-b^{2} x^{4}-1}}"," ",0,"I/(-I*b)^(1/2)*(I*b*x^2+1)^(1/2)*(-I*b*x^2+1)^(1/2)/(-b^2*x^4-1)^(1/2)*(EllipticF(x*(-I*b)^(1/2),I)-EllipticE(x*(-I*b)^(1/2),I))+1/(-I*b)^(1/2)*(I*b*x^2+1)^(1/2)*(-I*b*x^2+1)^(1/2)/(-b^2*x^4-1)^(1/2)*EllipticF(x*(-I*b)^(1/2),I)","C"
21,1,122,192,0.004000," ","int((b*x^2+1)/(-b^2*x^4-1)^(1/2),x)","\frac{\sqrt{i b \,x^{2}+1}\, \sqrt{-i b \,x^{2}+1}\, \EllipticF \left(\sqrt{-i b}\, x , i\right)}{\sqrt{-i b}\, \sqrt{-b^{2} x^{4}-1}}-\frac{i \sqrt{i b \,x^{2}+1}\, \sqrt{-i b \,x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-i b}\, x , i\right)+\EllipticF \left(\sqrt{-i b}\, x , i\right)\right)}{\sqrt{-i b}\, \sqrt{-b^{2} x^{4}-1}}"," ",0,"-I/(-I*b)^(1/2)*(I*b*x^2+1)^(1/2)*(-I*b*x^2+1)^(1/2)/(-b^2*x^4-1)^(1/2)*(EllipticF((-I*b)^(1/2)*x,I)-EllipticE((-I*b)^(1/2)*x,I))+1/(-I*b)^(1/2)*(I*b*x^2+1)^(1/2)*(-I*b*x^2+1)^(1/2)/(-b^2*x^4-1)^(1/2)*EllipticF((-I*b)^(1/2)*x,I)","C"
22,1,15,10,0.031000," ","int((c^2*x^2+1)^(1/2)/(-c^2*x^2+1)^(1/2),x)","\frac{\EllipticE \left(c x \,\mathrm{csgn}\left(c \right), i\right) \mathrm{csgn}\left(c \right)}{c}"," ",0,"EllipticE(x*csgn(c)*c,I)*csgn(c)/c","C"
23,1,118,10,0.014000," ","int((c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c^{2} x^{2}+1}\, \EllipticF \left(\sqrt{c^{2}}\, x , i\right)}{\sqrt{c^{2}}\, \sqrt{-c^{4} x^{4}+1}}-\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c^{2} x^{2}+1}\, \left(-\EllipticE \left(\sqrt{c^{2}}\, x , i\right)+\EllipticF \left(\sqrt{c^{2}}\, x , i\right)\right)}{\sqrt{c^{2}}\, \sqrt{-c^{4} x^{4}+1}}"," ",0,"1/(c^2)^(1/2)*(-c^2*x^2+1)^(1/2)*(c^2*x^2+1)^(1/2)/(-c^4*x^4+1)^(1/2)*EllipticF(x*(c^2)^(1/2),I)-1/(c^2)^(1/2)*(-c^2*x^2+1)^(1/2)*(c^2*x^2+1)^(1/2)/(-c^4*x^4+1)^(1/2)*(EllipticF(x*(c^2)^(1/2),I)-EllipticE(x*(c^2)^(1/2),I))","B"
24,1,28,23,0.015000," ","int((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x)","\frac{\left(-\EllipticE \left(c x \,\mathrm{csgn}\left(c \right), i\right)+2 \EllipticF \left(c x \,\mathrm{csgn}\left(c \right), i\right)\right) \mathrm{csgn}\left(c \right)}{c}"," ",0,"(2*EllipticF(c*x*csgn(c),I)-EllipticE(c*x*csgn(c),I))*csgn(c)/c","C"
25,1,117,23,0.008000," ","int((-c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x)","\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c^{2} x^{2}+1}\, \EllipticF \left(\sqrt{c^{2}}\, x , i\right)}{\sqrt{c^{2}}\, \sqrt{-c^{4} x^{4}+1}}+\frac{\sqrt{-c^{2} x^{2}+1}\, \sqrt{c^{2} x^{2}+1}\, \left(-\EllipticE \left(\sqrt{c^{2}}\, x , i\right)+\EllipticF \left(\sqrt{c^{2}}\, x , i\right)\right)}{\sqrt{c^{2}}\, \sqrt{-c^{4} x^{4}+1}}"," ",0,"1/(c^2)^(1/2)*(-c^2*x^2+1)^(1/2)*(c^2*x^2+1)^(1/2)/(-c^4*x^4+1)^(1/2)*EllipticF((c^2)^(1/2)*x,I)+1/(c^2)^(1/2)*(-c^2*x^2+1)^(1/2)*(c^2*x^2+1)^(1/2)/(-c^4*x^4+1)^(1/2)*(EllipticF((c^2)^(1/2)*x,I)-EllipticE((c^2)^(1/2)*x,I))","B"
26,1,71,70,0.039000," ","int((e*x^2+d)/(e^2*x^4+b*x^2+d^2),x)","-\frac{\arctan \left(\frac{-2 e x +\sqrt{2 d e -b}}{\sqrt{2 d e +b}}\right)}{\sqrt{2 d e +b}}+\frac{\arctan \left(\frac{2 e x +\sqrt{2 d e -b}}{\sqrt{2 d e +b}}\right)}{\sqrt{2 d e +b}}"," ",0,"-arctan((-2*e*x+(2*d*e-b)^(1/2))/(2*d*e+b)^(1/2))/(2*d*e+b)^(1/2)+arctan((2*e*x+(2*d*e-b)^(1/2))/(2*d*e+b)^(1/2))/(2*d*e+b)^(1/2)","A"
27,1,71,70,0.037000," ","int((e*x^2+d)/(e^2*x^4+f*x^2+d^2),x)","-\frac{\arctan \left(\frac{-2 e x +\sqrt{2 d e -f}}{\sqrt{2 d e +f}}\right)}{\sqrt{2 d e +f}}+\frac{\arctan \left(\frac{2 e x +\sqrt{2 d e -f}}{\sqrt{2 d e +f}}\right)}{\sqrt{2 d e +f}}"," ",0,"-arctan((-2*e*x+(2*d*e-f)^(1/2))/(2*d*e+f)^(1/2))/(2*d*e+f)^(1/2)+arctan((2*e*x+(2*d*e-f)^(1/2))/(2*d*e+f)^(1/2))/(2*d*e+f)^(1/2)","A"
28,1,75,66,0.034000," ","int((e*x^2+d)/(e^2*x^4-b*x^2+d^2),x)","-\frac{\arctan \left(\frac{-2 e x +\sqrt{2 d e +b}}{\sqrt{2 d e -b}}\right)}{\sqrt{2 d e -b}}+\frac{\arctan \left(\frac{2 e x +\sqrt{2 d e +b}}{\sqrt{2 d e -b}}\right)}{\sqrt{2 d e -b}}"," ",0,"-1/(2*d*e-b)^(1/2)*arctan((-2*e*x+(2*d*e+b)^(1/2))/(2*d*e-b)^(1/2))+1/(2*d*e-b)^(1/2)*arctan((2*e*x+(2*d*e+b)^(1/2))/(2*d*e-b)^(1/2))","A"
29,1,75,74,0.032000," ","int((e*x^2+d)/(e^2*x^4-f*x^2+d^2),x)","-\frac{\arctan \left(\frac{-2 e x +\sqrt{2 d e +f}}{\sqrt{2 d e -f}}\right)}{\sqrt{2 d e -f}}+\frac{\arctan \left(\frac{2 e x +\sqrt{2 d e +f}}{\sqrt{2 d e -f}}\right)}{\sqrt{2 d e -f}}"," ",0,"-arctan((-2*e*x+(2*d*e+f)^(1/2))/(2*d*e-f)^(1/2))/(2*d*e-f)^(1/2)+arctan((2*e*x+(2*d*e+f)^(1/2))/(2*d*e-f)^(1/2))/(2*d*e-f)^(1/2)","A"
30,1,88,66,0.023000," ","int((-e*x^2+d)/(e^2*x^4+b*x^2+d^2),x)","-\frac{\sqrt{2 d e -b}\, \ln \left(e \,x^{2}+d +\sqrt{2 d e -b}\, x \right)}{-4 d e +2 b}+\frac{\sqrt{2 d e -b}\, \ln \left(-e \,x^{2}-d +\sqrt{2 d e -b}\, x \right)}{-4 d e +2 b}"," ",0,"1/(-4*d*e+2*b)*(2*d*e-b)^(1/2)*ln(-e*x^2+x*(2*d*e-b)^(1/2)-d)-1/(-4*d*e+2*b)*(2*d*e-b)^(1/2)*ln(d+e*x^2+x*(2*d*e-b)^(1/2))","A"
31,1,69,66,0.025000," ","int((-e*x^2+d)/(e^2*x^4+f*x^2+d^2),x)","\frac{\ln \left(e \,x^{2}+d +\sqrt{2 d e -f}\, x \right)}{2 \sqrt{2 d e -f}}-\frac{\ln \left(-e \,x^{2}-d +\sqrt{2 d e -f}\, x \right)}{2 \sqrt{2 d e -f}}"," ",0,"1/2*ln(d+e*x^2+x*(2*d*e-f)^(1/2))/(2*d*e-f)^(1/2)-1/2/(2*d*e-f)^(1/2)*ln(-e*x^2+x*(2*d*e-f)^(1/2)-d)","A"
32,1,61,58,0.023000," ","int((-e*x^2+d)/(e^2*x^4-b*x^2+d^2),x)","\frac{\ln \left(e \,x^{2}+d +\sqrt{2 d e +b}\, x \right)}{2 \sqrt{2 d e +b}}-\frac{\ln \left(-e \,x^{2}-d +\sqrt{2 d e +b}\, x \right)}{2 \sqrt{2 d e +b}}"," ",0,"-1/2/(2*d*e+b)^(1/2)*ln(-e*x^2+x*(2*d*e+b)^(1/2)-d)+1/2*ln(d+e*x^2+x*(2*d*e+b)^(1/2))/(2*d*e+b)^(1/2)","A"
33,1,61,58,0.024000," ","int((-e*x^2+d)/(e^2*x^4-f*x^2+d^2),x)","\frac{\ln \left(e \,x^{2}+d +\sqrt{2 d e +f}\, x \right)}{2 \sqrt{2 d e +f}}-\frac{\ln \left(-e \,x^{2}-d +\sqrt{2 d e +f}\, x \right)}{2 \sqrt{2 d e +f}}"," ",0,"1/2*ln(d+e*x^2+x*(2*d*e+f)^(1/2))/(2*d*e+f)^(1/2)-1/2/(2*d*e+f)^(1/2)*ln(-e*x^2+x*(2*d*e+f)^(1/2)-d)","A"
34,1,582,102,0.081000," ","int((-e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x)","-\frac{\sqrt{2}\, b \,e^{4} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b \,e^{4} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e^{2} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}"," ",0,"-1/2*e^4/(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2)*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctanh(c*e*x*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))*b-e^3*c/(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2)*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctanh(c*e*x*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))*d+1/2*e^2*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctanh(c*e*x*2^(1/2)/((-e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))-1/2*e^4/(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2)*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctan(c*e*x*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))*b-e^3*c/(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2)*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctan(c*e*x*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))*d-1/2*e^2*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2)*arctan(c*e*x*2^(1/2)/((e^2*b+(e^2*(b*e-2*c*d)*(b*e+2*c*d))^(1/2))*c)^(1/2))","B"
35,1,582,102,0.027000," ","int((e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x)","\frac{\sqrt{2}\, b \,e^{4} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{4} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, e^{2} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}"," ",0,"1/2*e^4/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)*b-e^3*c/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)*d-1/2*e^2*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)+1/2/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*b*e^4*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)-1/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*d*e^3*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)+1/2*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*e^2*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)","B"
36,1,582,102,0.013000," ","int((e*x^2+d)/(b*x^2+c*(d^2/e^2+x^4)),x)","\frac{\sqrt{2}\, b \,e^{4} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{4} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, c d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\, \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}-\frac{\sqrt{2}\, e^{2} \arctanh \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(-b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, c e x}{\sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}\right)}{2 \sqrt{\left(b \,e^{2}+\sqrt{\left(b e -2 c d \right) \left(b e +2 c d \right) e^{2}}\right) c}}"," ",0,"1/2*e^4/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)*b-e^3*c/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)*d-1/2*e^2*2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)+1/2/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*b*e^4*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)-1/((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2)*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*d*e^3*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)+1/2*2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*e^2*arctan(2^(1/2)/((b*e^2+((b*e-2*c*d)*(b*e+2*c*d)*e^2)^(1/2))*c)^(1/2)*c*e*x)","B"
37,1,26,25,0.012000," ","int((-b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x)","-\frac{\ln \left(b \,x^{2}+a -x \right)}{2}+\frac{\ln \left(b \,x^{2}+a +x \right)}{2}"," ",0,"-1/2*ln(b*x^2+a-x)+1/2*ln(b*x^2+a+x)","A"
38,1,52,52,0.007000," ","int((b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x)","\frac{\arctan \left(\frac{2 b x -1}{\sqrt{4 a b -1}}\right)}{\sqrt{4 a b -1}}+\frac{\arctan \left(\frac{2 b x +1}{\sqrt{4 a b -1}}\right)}{\sqrt{4 a b -1}}"," ",0,"1/(4*a*b-1)^(1/2)*arctan((2*b*x-1)/(4*a*b-1)^(1/2))+1/(4*a*b-1)^(1/2)*arctan((2*b*x+1)/(4*a*b-1)^(1/2))","A"
39,1,277,50,0.045000," ","int((2*x^2+1)/(4*x^4+b*x^2+1),x)","-\frac{b \arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{b \arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{4 \arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{\arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{4 \arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{\arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}"," ",0,"4/((b-4)*(4+b))^(1/2)/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))+1/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))-1/((b-4)*(4+b))^(1/2)/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))*b-4/((b-4)*(4+b))^(1/2)/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))+1/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))+1/((b-4)*(4+b))^(1/2)/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2)*arctan(4*x/(2*((b-4)*(4+b))^(1/2)+2*b)^(1/2))*b","B"
40,1,277,54,0.032000," ","int((2*x^2+1)/(4*x^4-b*x^2+1),x)","\frac{b \arctan \left(\frac{4 x}{\sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{b \arctan \left(\frac{4 x}{\sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{4 \arctan \left(\frac{4 x}{\sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{\arctan \left(\frac{4 x}{\sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{-2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{4 \arctan \left(\frac{4 x}{\sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{\arctan \left(\frac{4 x}{\sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{-2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}"," ",0,"-4/((b-4)*(b+4))^(1/2)/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))+1/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))-1/((b-4)*(b+4))^(1/2)/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))*b+4/((b-4)*(b+4))^(1/2)/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))+1/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))+1/((b-4)*(b+4))^(1/2)/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2)*arctan(4*x/(-2*((b-4)*(b+4))^(1/2)-2*b)^(1/2))*b","B"
41,1,136,45,0.052000," ","int((2*x^2+1)/(4*x^4+6*x^2+1),x)","-\frac{2 \sqrt{5}\, \arctan \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}-2 \sqrt{2}\right)}+\frac{2 \arctan \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{2 \sqrt{10}-2 \sqrt{2}}+\frac{2 \sqrt{5}\, \arctan \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}+2 \sqrt{2}\right)}+\frac{2 \arctan \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{2 \sqrt{10}+2 \sqrt{2}}"," ",0,"2/5*5^(1/2)/(2*10^(1/2)+2*2^(1/2))*arctan(8*x/(2*10^(1/2)+2*2^(1/2)))+2/(2*10^(1/2)+2*2^(1/2))*arctan(8*x/(2*10^(1/2)+2*2^(1/2)))-2/5*5^(1/2)/(2*10^(1/2)-2*2^(1/2))*arctan(8*x/(2*10^(1/2)-2*2^(1/2)))+2/(2*10^(1/2)-2*2^(1/2))*arctan(8*x/(2*10^(1/2)-2*2^(1/2)))","B"
42,1,12,11,0.009000," ","int((2*x^2+1)/(4*x^4+5*x^2+1),x)","\frac{\arctan \left(x \right)}{3}+\frac{\arctan \left(2 x \right)}{3}"," ",0,"1/3*arctan(x)+1/3*arctan(2*x)","A"
43,1,12,11,0.002000," ","int((2*x^2+1)/(4*x^4+4*x^2+1),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x \right)}{2}"," ",0,"1/2*arctan(2^(1/2)*x)*2^(1/2)","A"
44,1,34,33,0.008000," ","int((2*x^2+1)/(4*x^4+3*x^2+1),x)","\frac{\sqrt{7}\, \arctan \left(\frac{\left(4 x +1\right) \sqrt{7}}{7}\right)}{7}+\frac{\sqrt{7}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{7}}{7}\right)}{7}"," ",0,"1/7*7^(1/2)*arctan(1/7*(4*x-1)*7^(1/2))+1/7*arctan(1/7*(1+4*x)*7^(1/2))*7^(1/2)","A"
45,1,40,39,0.033000," ","int((2*x^2+1)/(4*x^4+2*x^2+1),x)","\frac{\sqrt{6}\, \arctan \left(\frac{\left(4 x -\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}+\frac{\sqrt{6}\, \arctan \left(\frac{\left(4 x +\sqrt{2}\right) \sqrt{6}}{6}\right)}{6}"," ",0,"1/6*6^(1/2)*arctan(1/6*(4*x+2^(1/2))*6^(1/2))+1/6*6^(1/2)*arctan(1/6*(4*x-2^(1/2))*6^(1/2))","A"
46,1,40,37,0.032000," ","int((2*x^2+1)/(4*x^4+x^2+1),x)","\frac{\sqrt{5}\, \arctan \left(\frac{\left(4 x -\sqrt{3}\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctan \left(\frac{\left(4 x +\sqrt{3}\right) \sqrt{5}}{5}\right)}{5}"," ",0,"1/5*arctan(1/5*(4*x+3^(1/2))*5^(1/2))*5^(1/2)+1/5*5^(1/2)*arctan(1/5*(4*x-3^(1/2))*5^(1/2))","A"
47,1,18,17,0.006000," ","int((2*x^2+1)/(4*x^4+1),x)","\frac{\arctan \left(2 x +1\right)}{2}+\frac{\arctan \left(2 x -1\right)}{2}"," ",0,"1/2*arctan(2*x-1)+1/2*arctan(2*x+1)","A"
48,1,40,37,0.033000," ","int((2*x^2+1)/(4*x^4-x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(4 x -\sqrt{5}\right) \sqrt{3}}{3}\right)}{3}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(4 x +\sqrt{5}\right) \sqrt{3}}{3}\right)}{3}"," ",0,"1/3*arctan(1/3*(4*x+5^(1/2))*3^(1/2))*3^(1/2)+1/3*3^(1/2)*arctan(1/3*(4*x-5^(1/2))*3^(1/2))","A"
49,1,40,35,0.036000," ","int((2*x^2+1)/(4*x^4-2*x^2+1),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\left(4 x -\sqrt{6}\right) \sqrt{2}}{2}\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(4 x +\sqrt{6}\right) \sqrt{2}}{2}\right)}{2}"," ",0,"1/2*2^(1/2)*arctan(1/2*(4*x+6^(1/2))*2^(1/2))+1/2*2^(1/2)*arctan(1/2*(4*x-6^(1/2))*2^(1/2))","A"
50,1,20,19,0.035000," ","int((2*x^2+1)/(4*x^4-3*x^2+1),x)","\arctan \left(4 x -\sqrt{7}\right)+\arctan \left(4 x +\sqrt{7}\right)"," ",0,"arctan(4*x-7^(1/2))+arctan(4*x+7^(1/2))","A"
51,1,11,11,0.006000," ","int((2*x^2+1)/(4*x^4-4*x^2+1),x)","-\frac{x}{2 \left(x^{2}-\frac{1}{2}\right)}"," ",0,"-1/2*x/(x^2-1/2)","A"
52,1,30,31,0.009000," ","int((2*x^2+1)/(4*x^4-5*x^2+1),x)","-\frac{\ln \left(x +1\right)}{2}+\frac{\ln \left(2 x +1\right)}{2}+\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(2 x -1\right)}{2}"," ",0,"-1/2*ln(2*x-1)+1/2*ln(2*x+1)-1/2*ln(x+1)+1/2*ln(x-1)","A"
53,1,82,35,0.043000," ","int((2*x^2+1)/(4*x^4-6*x^2+1),x)","-\frac{2 \left(-5+\sqrt{5}\right) \sqrt{5}\, \arctanh \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}-2 \sqrt{2}\right)}-\frac{2 \left(5+\sqrt{5}\right) \sqrt{5}\, \arctanh \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}+2 \sqrt{2}\right)}"," ",0,"-2/5*(-5+5^(1/2))*5^(1/2)/(2*10^(1/2)-2*2^(1/2))*arctanh(8/(2*10^(1/2)-2*2^(1/2))*x)-2/5*(5+5^(1/2))*5^(1/2)/(2*10^(1/2)+2*2^(1/2))*arctanh(8/(2*10^(1/2)+2*2^(1/2))*x)","B"
54,1,279,54,0.019000," ","int((-2*x^2+1)/(4*x^4+b*x^2+1),x)","\frac{b \arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{b \arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}+\frac{4 \arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{\arctan \left(\frac{4 x}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{4 \arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{\left(b -4\right) \left(b +4\right)}\, \sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}-\frac{\arctan \left(\frac{4 x}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -4\right) \left(b +4\right)}}}"," ",0,"4/((b-4)*(b+4))^(1/2)/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*arctan(4/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*x)-1/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*arctan(4/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*x)+1/((b-4)*(b+4))^(1/2)/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*b*arctan(4/(2*b-2*((b-4)*(b+4))^(1/2))^(1/2)*x)-4/((b-4)*(b+4))^(1/2)/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*arctan(4/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*x)-1/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*arctan(4/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*x)-1/((b-4)*(b+4))^(1/2)/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*b*arctan(4/(2*b+2*((b-4)*(b+4))^(1/2))^(1/2)*x)","B"
55,1,136,45,0.017000," ","int((-2*x^2+1)/(4*x^4+6*x^2+1),x)","\frac{2 \sqrt{5}\, \arctan \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{2 \sqrt{10}-2 \sqrt{2}}-\frac{2 \arctan \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{2 \sqrt{10}-2 \sqrt{2}}-\frac{2 \sqrt{5}\, \arctan \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{2 \sqrt{10}+2 \sqrt{2}}-\frac{2 \arctan \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{2 \sqrt{10}+2 \sqrt{2}}"," ",0,"-2*5^(1/2)/(2*10^(1/2)+2*2^(1/2))*arctan(8/(2*10^(1/2)+2*2^(1/2))*x)-2/(2*10^(1/2)+2*2^(1/2))*arctan(8/(2*10^(1/2)+2*2^(1/2))*x)+2*5^(1/2)/(2*10^(1/2)-2*2^(1/2))*arctan(8/(2*10^(1/2)-2*2^(1/2))*x)-2/(2*10^(1/2)-2*2^(1/2))*arctan(8/(2*10^(1/2)-2*2^(1/2))*x)","B"
56,1,10,9,0.007000," ","int((-2*x^2+1)/(4*x^4+5*x^2+1),x)","-\arctan \left(x \right)+\arctan \left(2 x \right)"," ",0,"-arctan(x)+arctan(2*x)","A"
57,1,11,11,0.008000," ","int((-2*x^2+1)/(4*x^4+4*x^2+1),x)","\frac{x}{2 x^{2}+1}"," ",0,"1/2*x/(x^2+1/2)","A"
58,1,26,25,0.004000," ","int((-2*x^2+1)/(4*x^4+3*x^2+1),x)","-\frac{\ln \left(2 x^{2}-x +1\right)}{2}+\frac{\ln \left(2 x^{2}+x +1\right)}{2}"," ",0,"-1/2*ln(2*x^2-x+1)+1/2*ln(2*x^2+x+1)","A"
59,1,39,38,0.010000," ","int((-2*x^2+1)/(4*x^4+2*x^2+1),x)","-\frac{\sqrt{2}\, \ln \left(2 x^{2}-\sqrt{2}\, x +1\right)}{4}+\frac{\sqrt{2}\, \ln \left(2 x^{2}+\sqrt{2}\, x +1\right)}{4}"," ",0,"-1/4*ln(1+2*x^2-2^(1/2)*x)*2^(1/2)+1/4*ln(1+2*x^2+2^(1/2)*x)*2^(1/2)","A"
60,1,39,38,0.011000," ","int((-2*x^2+1)/(4*x^4+x^2+1),x)","-\frac{\sqrt{3}\, \ln \left(2 x^{2}-\sqrt{3}\, x +1\right)}{6}+\frac{\sqrt{3}\, \ln \left(2 x^{2}+\sqrt{3}\, x +1\right)}{6}"," ",0,"-1/6*ln(1+2*x^2-3^(1/2)*x)*3^(1/2)+1/6*ln(1+2*x^2+3^(1/2)*x)*3^(1/2)","A"
61,1,28,27,0.004000," ","int((-2*x^2+1)/(4*x^4+1),x)","-\frac{\ln \left(2 x^{2}-2 x +1\right)}{4}+\frac{\ln \left(2 x^{2}+2 x +1\right)}{4}"," ",0,"-1/4*ln(2*x^2-2*x+1)+1/4*ln(2*x^2+2*x+1)","A"
62,1,39,38,0.011000," ","int((-2*x^2+1)/(4*x^4-x^2+1),x)","-\frac{\sqrt{5}\, \ln \left(2 x^{2}-\sqrt{5}\, x +1\right)}{10}+\frac{\sqrt{5}\, \ln \left(2 x^{2}+\sqrt{5}\, x +1\right)}{10}"," ",0,"-1/10*ln(1+2*x^2-5^(1/2)*x)*5^(1/2)+1/10*ln(1+2*x^2+5^(1/2)*x)*5^(1/2)","A"
63,1,39,38,0.010000," ","int((-2*x^2+1)/(4*x^4-2*x^2+1),x)","-\frac{\sqrt{6}\, \ln \left(2 x^{2}-\sqrt{6}\, x +1\right)}{12}+\frac{\sqrt{6}\, \ln \left(2 x^{2}+\sqrt{6}\, x +1\right)}{12}"," ",0,"-1/12*ln(1+2*x^2-6^(1/2)*x)*6^(1/2)+1/12*ln(1+2*x^2+6^(1/2)*x)*6^(1/2)","A"
64,1,39,38,0.010000," ","int((-2*x^2+1)/(4*x^4-3*x^2+1),x)","-\frac{\sqrt{7}\, \ln \left(2 x^{2}-\sqrt{7}\, x +1\right)}{14}+\frac{\sqrt{7}\, \ln \left(2 x^{2}+\sqrt{7}\, x +1\right)}{14}"," ",0,"-1/14*ln(1+2*x^2-x*7^(1/2))*7^(1/2)+1/14*ln(1+2*x^2+x*7^(1/2))*7^(1/2)","A"
65,1,12,11,0.002000," ","int((-2*x^2+1)/(4*x^4-4*x^2+1),x)","\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, x \right)}{2}"," ",0,"1/2*arctanh(2^(1/2)*x)*2^(1/2)","A"
66,1,30,31,0.009000," ","int((-2*x^2+1)/(4*x^4-5*x^2+1),x)","\frac{\ln \left(x +1\right)}{6}+\frac{\ln \left(2 x +1\right)}{6}-\frac{\ln \left(x -1\right)}{6}-\frac{\ln \left(2 x -1\right)}{6}"," ",0,"-1/6*ln(2*x-1)+1/6*ln(2*x+1)+1/6*ln(x+1)-1/6*ln(x-1)","A"
67,1,82,39,0.017000," ","int((-2*x^2+1)/(4*x^4-6*x^2+1),x)","\frac{2 \left(\sqrt{5}-1\right) \sqrt{5}\, \arctanh \left(\frac{8 x}{2 \sqrt{10}-2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}-2 \sqrt{2}\right)}+\frac{2 \left(\sqrt{5}+1\right) \sqrt{5}\, \arctanh \left(\frac{8 x}{2 \sqrt{10}+2 \sqrt{2}}\right)}{5 \left(2 \sqrt{10}+2 \sqrt{2}\right)}"," ",0,"2/5*(5^(1/2)-1)*5^(1/2)/(2*10^(1/2)-2*2^(1/2))*arctanh(8/(2*10^(1/2)-2*2^(1/2))*x)+2/5*(5^(1/2)+1)*5^(1/2)/(2*10^(1/2)+2*2^(1/2))*arctanh(8/(2*10^(1/2)+2*2^(1/2))*x)","B"
68,1,277,50,0.043000," ","int((x^2+1)/(x^4+b*x^2+1),x)","-\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{2 \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{2 \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}"," ",0,"-2/((b-2)*(2+b))^(1/2)/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))+1/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))+1/((b-2)*(2+b))^(1/2)/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))*b+2/((b-2)*(2+b))^(1/2)/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))+1/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))-1/((b-2)*(2+b))^(1/2)/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2)*arctan(2*x/(-2*((b-2)*(2+b))^(1/2)+2*b)^(1/2))*b","B"
69,1,136,38,0.050000," ","int((x^2+1)/(x^4+5*x^2+1),x)","-\frac{2 \sqrt{21}\, \arctan \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{7 \left(2 \sqrt{7}-2 \sqrt{3}\right)}+\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{2 \sqrt{7}-2 \sqrt{3}}+\frac{2 \sqrt{21}\, \arctan \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{7 \left(2 \sqrt{7}+2 \sqrt{3}\right)}+\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{2 \sqrt{7}+2 \sqrt{3}}"," ",0,"-2/7*21^(1/2)/(2*7^(1/2)-2*3^(1/2))*arctan(4*x/(2*7^(1/2)-2*3^(1/2)))+2/(2*7^(1/2)-2*3^(1/2))*arctan(4*x/(2*7^(1/2)-2*3^(1/2)))+2/7*21^(1/2)/(2*7^(1/2)+2*3^(1/2))*arctan(4*x/(2*7^(1/2)+2*3^(1/2)))+2/(2*7^(1/2)+2*3^(1/2))*arctan(4*x/(2*7^(1/2)+2*3^(1/2)))","B"
70,1,110,43,0.048000," ","int((x^2+1)/(x^4+4*x^2+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{3 \left(\sqrt{6}-\sqrt{2}\right)}+\frac{\arctan \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{\sqrt{6}-\sqrt{2}}+\frac{\sqrt{3}\, \arctan \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{3 \sqrt{6}+3 \sqrt{2}}+\frac{\arctan \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{\sqrt{6}+\sqrt{2}}"," ",0,"1/3*3^(1/2)/(6^(1/2)+2^(1/2))*arctan(2*x/(6^(1/2)+2^(1/2)))+1/(6^(1/2)+2^(1/2))*arctan(2*x/(6^(1/2)+2^(1/2)))-1/3*3^(1/2)/(6^(1/2)-2^(1/2))*arctan(2*x/(6^(1/2)-2^(1/2)))+1/(6^(1/2)-2^(1/2))*arctan(2*x/(6^(1/2)-2^(1/2)))","B"
71,1,104,34,0.043000," ","int((x^2+1)/(x^4+3*x^2+1),x)","-\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{5 \left(2 \sqrt{5}-2\right)}+\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{2 \sqrt{5}-2}+\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{5 \left(2 \sqrt{5}+2\right)}+\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{2 \sqrt{5}+2}"," ",0,"2/5*5^(1/2)/(2*5^(1/2)+2)*arctan(4*x/(2*5^(1/2)+2))+2/(2*5^(1/2)+2)*arctan(4*x/(2*5^(1/2)+2))-2/5*5^(1/2)/(2*5^(1/2)-2)*arctan(4*x/(2*5^(1/2)-2))+2/(2*5^(1/2)-2)*arctan(4*x/(2*5^(1/2)-2))","B"
72,1,3,2,0.002000," ","int((x^2+1)/(x^4+2*x^2+1),x)","\arctan \left(x \right)"," ",0,"arctan(x)","A"
73,1,34,33,0.006000," ","int((x^2+1)/(x^4+x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}"," ",0,"1/3*arctan(1/3*(2*x+1)*3^(1/2))*3^(1/2)+1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
74,1,88,27,0.004000," ","int((x^2+1)/(x^4+1),x)","\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{2}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{8}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{8}"," ",0,"1/2*arctan(-1+2^(1/2)*x)*2^(1/2)+1/8*2^(1/2)*ln((1+x^2+2^(1/2)*x)/(1+x^2-2^(1/2)*x))+1/2*arctan(1+2^(1/2)*x)*2^(1/2)+1/8*2^(1/2)*ln((1+x^2-2^(1/2)*x)/(1+x^2+2^(1/2)*x))","B"
75,1,20,19,0.019000," ","int((x^2+1)/(x^4-x^2+1),x)","\arctan \left(2 x -\sqrt{3}\right)+\arctan \left(2 x +\sqrt{3}\right)"," ",0,"arctan(2*x-3^(1/2))+arctan(2*x+3^(1/2))","A"
76,1,16,11,0.005000," ","int((x^2+1)/(x^4-2*x^2+1),x)","-\frac{1}{2 \left(x +1\right)}-\frac{1}{2 \left(x -1\right)}"," ",0,"-1/2/(x+1)-1/2/(x-1)","A"
77,1,22,49,0.006000," ","int((x^2+1)/(x^4-3*x^2+1),x)","\frac{\ln \left(x^{2}-x -1\right)}{2}-\frac{\ln \left(x^{2}+x -1\right)}{2}"," ",0,"-1/2*ln(x^2+x-1)+1/2*ln(x^2-x-1)","A"
78,1,70,33,0.040000," ","int((x^2+1)/(x^4-4*x^2+1),x)","-\frac{\left(-3+\sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{3 \left(\sqrt{6}-\sqrt{2}\right)}-\frac{\left(\sqrt{3}+3\right) \sqrt{3}\, \arctanh \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{3 \left(\sqrt{6}+\sqrt{2}\right)}"," ",0,"-1/3*(-3+3^(1/2))*3^(1/2)/(6^(1/2)-2^(1/2))*arctanh(2/(6^(1/2)-2^(1/2))*x)-1/3*(3^(1/2)+3)*3^(1/2)/(6^(1/2)+2^(1/2))*arctanh(2/(6^(1/2)+2^(1/2))*x)","B"
79,1,82,37,0.036000," ","int((x^2+1)/(x^4-5*x^2+1),x)","-\frac{2 \sqrt{21}\, \left(-7+\sqrt{21}\right) \arctanh \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{21 \left(2 \sqrt{7}-2 \sqrt{3}\right)}-\frac{2 \left(7+\sqrt{21}\right) \sqrt{21}\, \arctanh \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{21 \left(2 \sqrt{7}+2 \sqrt{3}\right)}"," ",0,"-2/21*(7+21^(1/2))*21^(1/2)/(2*7^(1/2)+2*3^(1/2))*arctanh(4/(2*7^(1/2)+2*3^(1/2))*x)-2/21*21^(1/2)*(-7+21^(1/2))/(2*7^(1/2)-2*3^(1/2))*arctanh(4/(2*7^(1/2)-2*3^(1/2))*x)","B"
80,1,279,50,0.018000," ","int((-x^2+1)/(x^4+b*x^2+1),x)","\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{2 \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{2 \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}"," ",0,"-2/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)-1/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)-1/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)+2/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)-1/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)+1/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)","B"
81,1,136,38,0.017000," ","int((-x^2+1)/(x^4+5*x^2+1),x)","\frac{2 \sqrt{21}\, \arctan \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{3 \left(2 \sqrt{7}-2 \sqrt{3}\right)}-\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{2 \sqrt{7}-2 \sqrt{3}}-\frac{2 \sqrt{21}\, \arctan \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{3 \left(2 \sqrt{7}+2 \sqrt{3}\right)}-\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{2 \sqrt{7}+2 \sqrt{3}}"," ",0,"2/3*21^(1/2)/(2*7^(1/2)-2*3^(1/2))*arctan(4/(2*7^(1/2)-2*3^(1/2))*x)-2/(2*7^(1/2)-2*3^(1/2))*arctan(4/(2*7^(1/2)-2*3^(1/2))*x)-2/3*21^(1/2)/(2*7^(1/2)+2*3^(1/2))*arctan(4/(2*7^(1/2)+2*3^(1/2))*x)-2/(2*7^(1/2)+2*3^(1/2))*arctan(4/(2*7^(1/2)+2*3^(1/2))*x)","B"
82,1,111,43,0.017000," ","int((-x^2+1)/(x^4+4*x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{\sqrt{6}-\sqrt{2}}-\frac{\arctan \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{\sqrt{6}-\sqrt{2}}-\frac{\sqrt{3}\, \arctan \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{\sqrt{6}+\sqrt{2}}-\frac{\arctan \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{\sqrt{6}+\sqrt{2}}"," ",0,"-3^(1/2)/(6^(1/2)+2^(1/2))*arctan(2/(6^(1/2)+2^(1/2))*x)-1/(6^(1/2)+2^(1/2))*arctan(2/(6^(1/2)+2^(1/2))*x)+3^(1/2)/(6^(1/2)-2^(1/2))*arctan(2/(6^(1/2)-2^(1/2))*x)-1/(6^(1/2)-2^(1/2))*arctan(2/(6^(1/2)-2^(1/2))*x)","B"
83,1,104,26,0.018000," ","int((-x^2+1)/(x^4+3*x^2+1),x)","\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{2 \sqrt{5}-2}-\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{2 \sqrt{5}-2}-\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{2 \sqrt{5}+2}-\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{2 \sqrt{5}+2}"," ",0,"-2*5^(1/2)/(2*5^(1/2)+2)*arctan(4/(2*5^(1/2)+2)*x)-2/(2*5^(1/2)+2)*arctan(4/(2*5^(1/2)+2)*x)+2*5^(1/2)/(2*5^(1/2)-2)*arctan(4/(2*5^(1/2)-2)*x)-2/(2*5^(1/2)-2)*arctan(4/(2*5^(1/2)-2)*x)","B"
84,1,10,9,0.007000," ","int((-x^2+1)/(x^4+2*x^2+1),x)","\frac{x}{x^{2}+1}"," ",0,"1/(x^2+1)*x","A"
85,1,22,21,0.004000," ","int((-x^2+1)/(x^4+x^2+1),x)","-\frac{\ln \left(x^{2}-x +1\right)}{2}+\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"-1/2*ln(x^2-x+1)+1/2*ln(x^2+x+1)","A"
86,1,62,34,0.003000," ","int((-x^2+1)/(x^4+1),x)","-\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{8}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{8}"," ",0,"1/8*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))-1/8*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))","A"
87,1,35,34,0.012000," ","int((-x^2+1)/(x^4-x^2+1),x)","-\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{6}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{6}"," ",0,"-1/6*3^(1/2)*ln(x^2-3^(1/2)*x+1)+1/6*3^(1/2)*ln(x^2+3^(1/2)*x+1)","A"
88,1,3,2,0.001000," ","int((-x^2+1)/(x^4-2*x^2+1),x)","\arctanh \left(x \right)"," ",0,"arctanh(x)","A"
89,1,34,33,0.004000," ","int((-x^2+1)/(x^4-3*x^2+1),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x +1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x -1\right) \sqrt{5}}{5}\right)}{5}"," ",0,"1/5*arctanh(1/5*(2*x+1)*5^(1/2))*5^(1/2)+1/5*5^(1/2)*arctanh(1/5*(2*x-1)*5^(1/2))","A"
90,1,70,38,0.018000," ","int((-x^2+1)/(x^4-4*x^2+1),x)","\frac{\left(\sqrt{3}-1\right) \sqrt{3}\, \arctanh \left(\frac{2 x}{\sqrt{6}-\sqrt{2}}\right)}{3 \sqrt{6}-3 \sqrt{2}}+\frac{\left(1+\sqrt{3}\right) \sqrt{3}\, \arctanh \left(\frac{2 x}{\sqrt{6}+\sqrt{2}}\right)}{3 \sqrt{6}+3 \sqrt{2}}"," ",0,"1/3*(3^(1/2)-1)*3^(1/2)/(6^(1/2)-2^(1/2))*arctanh(2/(6^(1/2)-2^(1/2))*x)+1/3*(1+3^(1/2))*3^(1/2)/(6^(1/2)+2^(1/2))*arctanh(2/(6^(1/2)+2^(1/2))*x)","A"
91,1,82,37,0.018000," ","int((-x^2+1)/(x^4-5*x^2+1),x)","\frac{2 \left(-3+\sqrt{21}\right) \sqrt{21}\, \arctanh \left(\frac{4 x}{2 \sqrt{7}-2 \sqrt{3}}\right)}{21 \left(2 \sqrt{7}-2 \sqrt{3}\right)}+\frac{2 \left(3+\sqrt{21}\right) \sqrt{21}\, \arctanh \left(\frac{4 x}{2 \sqrt{7}+2 \sqrt{3}}\right)}{21 \left(2 \sqrt{7}+2 \sqrt{3}\right)}"," ",0,"2/21*(3+21^(1/2))*21^(1/2)/(2*7^(1/2)+2*3^(1/2))*arctanh(4/(2*7^(1/2)+2*3^(1/2))*x)+2/21*(-3+21^(1/2))*21^(1/2)/(2*7^(1/2)-2*3^(1/2))*arctanh(4/(2*7^(1/2)-2*3^(1/2))*x)","B"
92,1,34,33,0.008000," ","int((-3*x^2-1)/(9*x^4+2*x^2+1),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 x -2\right) \sqrt{2}}{4}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 x +2\right) \sqrt{2}}{4}\right)}{4}"," ",0,"-1/4*2^(1/2)*arctan(1/4*(6*x+2)*2^(1/2))-1/4*2^(1/2)*arctan(1/4*(6*x-2)*2^(1/2))","A"
93,1,34,33,0.004000," ","int((3*x^2+1)/(-9*x^4-2*x^2-1),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 x -2\right) \sqrt{2}}{4}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 x +2\right) \sqrt{2}}{4}\right)}{4}"," ",0,"-1/4*2^(1/2)*arctan(1/4*(6*x-2)*2^(1/2))-1/4*2^(1/2)*arctan(1/4*(6*x+2)*2^(1/2))","A"
94,1,28,17,0.009000," ","int((2*x^2+3)/(x^4-2*x^2+1),x)","\frac{\ln \left(x +1\right)}{4}-\frac{\ln \left(x -1\right)}{4}-\frac{5}{4 \left(x +1\right)}-\frac{5}{4 \left(x -1\right)}"," ",0,"-5/4/(x+1)+1/4*ln(x+1)-5/4/(x-1)-1/4*ln(x-1)","A"
95,1,26,17,0.006000," ","int((3*x^2+2)/(3*x^4-8*x^2+5),x)","-\frac{7 \sqrt{15}\, \arctanh \left(\frac{\sqrt{15}\, x}{5}\right)}{10}+\frac{5 \ln \left(x +1\right)}{4}-\frac{5 \ln \left(x -1\right)}{4}"," ",0,"-7/10*arctanh(1/5*x*15^(1/2))*15^(1/2)+5/4*ln(x+1)-5/4*ln(x-1)","A"
96,1,56,27,0.008000," ","int((e*x^2+d)/(3*x^4-8*x^2+5),x)","-\frac{\sqrt{15}\, d \arctanh \left(\frac{\sqrt{15}\, x}{5}\right)}{10}+\frac{d \ln \left(x +1\right)}{4}-\frac{d \ln \left(x -1\right)}{4}-\frac{\sqrt{15}\, e \arctanh \left(\frac{\sqrt{15}\, x}{5}\right)}{6}+\frac{e \ln \left(x +1\right)}{4}-\frac{e \ln \left(x -1\right)}{4}"," ",0,"-1/10*15^(1/2)*arctanh(1/5*15^(1/2)*x)*d-1/6*15^(1/2)*arctanh(1/5*15^(1/2)*x)*e+1/4*ln(x+1)*d+1/4*ln(x+1)*e-1/4*ln(x-1)*d-1/4*ln(x-1)*e","B"
97,1,104,45,0.025000," ","int((x^2+3)/(x^4+3*x^2+1),x)","\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{2 \sqrt{5}-2}+\frac{6 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}-2}\right)}{5 \left(2 \sqrt{5}-2\right)}+\frac{2 \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{2 \sqrt{5}+2}-\frac{6 \sqrt{5}\, \arctan \left(\frac{4 x}{2 \sqrt{5}+2}\right)}{5 \left(2 \sqrt{5}+2\right)}"," ",0,"2/(2*5^(1/2)+2)*arctan(4/(2*5^(1/2)+2)*x)-6/5*5^(1/2)/(2*5^(1/2)+2)*arctan(4/(2*5^(1/2)+2)*x)+2/(2*5^(1/2)-2)*arctan(4/(2*5^(1/2)-2)*x)+6/5*5^(1/2)/(2*5^(1/2)-2)*arctan(4/(2*5^(1/2)-2)*x)","B"
98,1,114,69,0.005000," ","int((b*x^2+a)/(x^4+x^2+1),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, a \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{a \ln \left(x^{2}-x +1\right)}{4}+\frac{a \ln \left(x^{2}+x +1\right)}{4}+\frac{\sqrt{3}\, b \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, b \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{b \ln \left(x^{2}-x +1\right)}{4}-\frac{b \ln \left(x^{2}+x +1\right)}{4}"," ",0,"1/4*ln(x^2+x+1)*a-1/4*ln(x^2+x+1)*b+1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))*a+1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))*b-1/4*ln(x^2-x+1)*a+1/4*ln(x^2-x+1)*b+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))*a+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))*b","A"
99,1,168,103,0.014000," ","int((b*x^2+a)/(x^4+x^2+1)^2,x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{9}+\frac{\sqrt{3}\, a \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{9}-\frac{a \ln \left(x^{2}-x +1\right)}{4}+\frac{a \ln \left(x^{2}+x +1\right)}{4}+\frac{\sqrt{3}\, b \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{36}+\frac{\sqrt{3}\, b \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{36}+\frac{b \ln \left(x^{2}-x +1\right)}{8}-\frac{b \ln \left(x^{2}+x +1\right)}{8}+\frac{-\frac{2 a}{3}+\frac{b}{3}+\left(-\frac{a}{3}+\frac{2 b}{3}\right) x}{4 x^{2}+4 x +4}-\frac{-\frac{2 a}{3}+\frac{b}{3}+\left(\frac{a}{3}-\frac{2 b}{3}\right) x}{4 \left(x^{2}-x +1\right)}"," ",0,"1/4*((-1/3*a+2/3*b)*x-2/3*a+1/3*b)/(x^2+x+1)+1/4*a*ln(x^2+x+1)-1/8*b*ln(x^2+x+1)+1/9*3^(1/2)*a*arctan(1/3*(2*x+1)*3^(1/2))+1/36*3^(1/2)*b*arctan(1/3*(2*x+1)*3^(1/2))-1/4*((1/3*a-2/3*b)*x-2/3*a+1/3*b)/(x^2-x+1)-1/4*a*ln(x^2-x+1)+1/8*b*ln(x^2-x+1)+1/9*3^(1/2)*a*arctan(1/3*(2*x-1)*3^(1/2))+1/36*3^(1/2)*b*arctan(1/3*(2*x-1)*3^(1/2))","A"
100,1,710,162,0.099000," ","int((b*x^2+a)/(x^4+x^2+2),x)","-\frac{\left(-1+2 \sqrt{2}\right) \sqrt{2}\, a \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{28 \sqrt{1+2 \sqrt{2}}}-\frac{\left(-1+2 \sqrt{2}\right) a \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{7 \sqrt{1+2 \sqrt{2}}}+\frac{\sqrt{2}\, a \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{2 \sqrt{1+2 \sqrt{2}}}-\frac{\left(-1+2 \sqrt{2}\right) \sqrt{2}\, a \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{28 \sqrt{1+2 \sqrt{2}}}-\frac{\left(-1+2 \sqrt{2}\right) a \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{7 \sqrt{1+2 \sqrt{2}}}+\frac{\sqrt{2}\, a \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{2 \sqrt{1+2 \sqrt{2}}}-\frac{\sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, a \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{56}-\frac{\sqrt{-1+2 \sqrt{2}}\, a \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{14}+\frac{\sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, a \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{56}+\frac{\sqrt{-1+2 \sqrt{2}}\, a \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{14}+\frac{\left(-1+2 \sqrt{2}\right) \sqrt{2}\, b \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{7 \sqrt{1+2 \sqrt{2}}}+\frac{\left(-1+2 \sqrt{2}\right) b \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{14 \sqrt{1+2 \sqrt{2}}}+\frac{\left(-1+2 \sqrt{2}\right) \sqrt{2}\, b \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{7 \sqrt{1+2 \sqrt{2}}}+\frac{\left(-1+2 \sqrt{2}\right) b \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{14 \sqrt{1+2 \sqrt{2}}}+\frac{\sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, b \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{14}+\frac{\sqrt{-1+2 \sqrt{2}}\, b \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{28}-\frac{\sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, b \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{14}-\frac{\sqrt{-1+2 \sqrt{2}}\, b \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{28}"," ",0,"1/56*ln(x^2+2^(1/2)+x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*a-1/14*ln(x^2+2^(1/2)+x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*b+1/14*ln(x^2+2^(1/2)+x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*a-1/28*ln(x^2+2^(1/2)+x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*b-1/28/(1+2*2^(1/2))^(1/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*2^(1/2)*a+1/7/(1+2*2^(1/2))^(1/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*2^(1/2)*b-1/7/(1+2*2^(1/2))^(1/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*a+1/14/(1+2*2^(1/2))^(1/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*b+1/2/(1+2*2^(1/2))^(1/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*2^(1/2)*a-1/56*ln(x^2+2^(1/2)-x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*a+1/14*ln(x^2+2^(1/2)-x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*b-1/14*ln(x^2+2^(1/2)-x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*a+1/28*ln(x^2+2^(1/2)-x*(-1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))^(1/2)*b-1/28/(1+2*2^(1/2))^(1/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*2^(1/2)*a+1/7/(1+2*2^(1/2))^(1/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*2^(1/2)*b-1/7/(1+2*2^(1/2))^(1/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*a+1/14/(1+2*2^(1/2))^(1/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*(-1+2*2^(1/2))*b+1/2/(1+2*2^(1/2))^(1/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*2^(1/2)*a","B"
101,1,756,235,0.313000," ","int((b*x^2+a)/(x^4+x^2+2)^2,x)","\frac{\sqrt{2}\, a \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{16 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}+\frac{3 a \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{8 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}+\frac{\sqrt{2}\, a \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{16 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}+\frac{3 a \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{8 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}-\frac{107 \sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, a \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{1568 \left(1+2 \sqrt{2}\right)}-\frac{53 \sqrt{-1+2 \sqrt{2}}\, a \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{784 \left(1+2 \sqrt{2}\right)}+\frac{107 \sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, a \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{1568 \left(1+2 \sqrt{2}\right)}+\frac{53 \sqrt{-1+2 \sqrt{2}}\, a \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{784 \left(1+2 \sqrt{2}\right)}+\frac{\sqrt{2}\, b \arctan \left(\frac{2 x -\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{8 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}+\frac{\sqrt{2}\, b \arctan \left(\frac{2 x +\sqrt{-1+2 \sqrt{2}}}{\sqrt{1+2 \sqrt{2}}}\right)}{8 \left(1+2 \sqrt{2}\right)^{\frac{3}{2}}}+\frac{25 \sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, b \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{784 \left(1+2 \sqrt{2}\right)}+\frac{11 \sqrt{-1+2 \sqrt{2}}\, b \ln \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{196 \left(1+2 \sqrt{2}\right)}-\frac{25 \sqrt{-1+2 \sqrt{2}}\, \sqrt{2}\, b \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{784 \left(1+2 \sqrt{2}\right)}-\frac{11 \sqrt{-1+2 \sqrt{2}}\, b \ln \left(x^{2}+\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}{196 \left(1+2 \sqrt{2}\right)}+\frac{\frac{\left(-14 a -28 \sqrt{2}\, a +112 \sqrt{2}\, b +56 b \right) x}{1+2 \sqrt{2}}+\frac{\sqrt{-1+2 \sqrt{2}}\, \left(-70 a -42 \sqrt{2}\, a +56 \sqrt{2}\, b +28 b \right)}{1+2 \sqrt{2}}}{784 x^{2}+784 \sqrt{-1+2 \sqrt{2}}\, x +784 \sqrt{2}}-\frac{-\frac{\left(-14 a -28 \sqrt{2}\, a +112 \sqrt{2}\, b +56 b \right) x}{1+2 \sqrt{2}}+\frac{\sqrt{-1+2 \sqrt{2}}\, \left(-70 a -42 \sqrt{2}\, a +56 \sqrt{2}\, b +28 b \right)}{1+2 \sqrt{2}}}{784 \left(x^{2}-\sqrt{-1+2 \sqrt{2}}\, x +\sqrt{2}\right)}"," ",0,"1/784*((-14*a-28*2^(1/2)*a+112*b*2^(1/2)+56*b)/(1+2*2^(1/2))*x+1/(1+2*2^(1/2))*(-1+2*2^(1/2))^(1/2)*(-70*a-42*2^(1/2)*a+56*b*2^(1/2)+28*b))/(x^2+(-1+2*2^(1/2))^(1/2)*x+2^(1/2))+107/1568/(1+2*2^(1/2))*ln(x^2+(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*a-25/784/(1+2*2^(1/2))*ln(x^2+(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*b+53/784/(1+2*2^(1/2))*ln(x^2+(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*a-11/196/(1+2*2^(1/2))*ln(x^2+(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*b+1/16/(1+2*2^(1/2))^(3/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*2^(1/2)*a+3/8/(1+2*2^(1/2))^(3/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*a+1/8/(1+2*2^(1/2))^(3/2)*arctan((2*x+(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*b*2^(1/2)-1/784*(-(-14*a-28*2^(1/2)*a+112*b*2^(1/2)+56*b)/(1+2*2^(1/2))*x+1/(1+2*2^(1/2))*(-1+2*2^(1/2))^(1/2)*(-70*a-42*2^(1/2)*a+56*b*2^(1/2)+28*b))/(x^2-(-1+2*2^(1/2))^(1/2)*x+2^(1/2))-107/1568/(1+2*2^(1/2))*ln(x^2-(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*a+25/784/(1+2*2^(1/2))*ln(x^2-(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*2^(1/2)*b-53/784/(1+2*2^(1/2))*ln(x^2-(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*a+11/196/(1+2*2^(1/2))*ln(x^2-(-1+2*2^(1/2))^(1/2)*x+2^(1/2))*(-1+2*2^(1/2))^(1/2)*b+1/16/(1+2*2^(1/2))^(3/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*2^(1/2)*a+3/8/(1+2*2^(1/2))^(3/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*a+1/8/(1+2*2^(1/2))^(3/2)*arctan((2*x-(-1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2))*b*2^(1/2)","B"
102,1,199,116,0.089000," ","int((-x^2+2^(1/2))/(1+x^4-x^2*2^(1/2)),x)","\frac{\sqrt{2}\, \arctan \left(\frac{2 x -\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}-\frac{\arctan \left(\frac{2 x -\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 x +\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}-\frac{\arctan \left(\frac{2 x +\sqrt{2+\sqrt{2}}}{\sqrt{2-\sqrt{2}}}\right)}{2 \sqrt{2-\sqrt{2}}}-\frac{\sqrt{2}\, \sqrt{2+\sqrt{2}}\, \ln \left(x^{2}-\sqrt{2+\sqrt{2}}\, x +1\right)}{8}+\frac{\sqrt{2}\, \sqrt{2+\sqrt{2}}\, \ln \left(x^{2}+\sqrt{2+\sqrt{2}}\, x +1\right)}{8}"," ",0,"1/8*2^(1/2)*(2+2^(1/2))^(1/2)*ln(1+x^2+x*(2+2^(1/2))^(1/2))+1/2/(2-2^(1/2))^(1/2)*arctan((2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))*2^(1/2)-1/2/(2-2^(1/2))^(1/2)*arctan((2*x+(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))-1/8*2^(1/2)*(2+2^(1/2))^(1/2)*ln(1+x^2-x*(2+2^(1/2))^(1/2))+1/2/(2-2^(1/2))^(1/2)*arctan((2*x-(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))*2^(1/2)-1/2/(2-2^(1/2))^(1/2)*arctan((2*x-(2+2^(1/2))^(1/2))/(2-2^(1/2))^(1/2))","A"
103,1,199,124,0.088000," ","int((x^2+2^(1/2))/(1+x^4+x^2*2^(1/2)),x)","\frac{\arctan \left(\frac{2 x -\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 x -\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}+\frac{\arctan \left(\frac{2 x +\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 x +\sqrt{2-\sqrt{2}}}{\sqrt{2+\sqrt{2}}}\right)}{2 \sqrt{2+\sqrt{2}}}-\frac{\sqrt{2}\, \sqrt{2-\sqrt{2}}\, \ln \left(x^{2}-\sqrt{2-\sqrt{2}}\, x +1\right)}{8}+\frac{\sqrt{2}\, \sqrt{2-\sqrt{2}}\, \ln \left(x^{2}+\sqrt{2-\sqrt{2}}\, x +1\right)}{8}"," ",0,"1/8*2^(1/2)*(2-2^(1/2))^(1/2)*ln(1+x^2+x*(2-2^(1/2))^(1/2))+1/2/(2+2^(1/2))^(1/2)*arctan((2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))+1/2/(2+2^(1/2))^(1/2)*arctan((2*x+(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))*2^(1/2)-1/8*2^(1/2)*(2-2^(1/2))^(1/2)*ln(1+x^2-x*(2-2^(1/2))^(1/2))+1/2/(2+2^(1/2))^(1/2)*arctan((2*x-(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))+1/2/(2+2^(1/2))^(1/2)*arctan((2*x-(2-2^(1/2))^(1/2))/(2+2^(1/2))^(1/2))*2^(1/2)","A"
104,1,285,124,0.023000," ","int((-x^2+2^(1/2))/(x^4+b*x^2+1),x)","\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{2 \sqrt{2}\, \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{2 \sqrt{2}\, \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}"," ",0,"-1/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)-1/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)-2/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)*2^(1/2)-1/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)+1/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)+2/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)*2^(1/2)","B"
105,1,283,124,0.019000," ","int((x^2+2^(1/2))/(x^4+b*x^2+1),x)","-\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{b \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{2 \sqrt{2}\, \arctan \left(\frac{2 x}{\sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b -2 \sqrt{\left(b -2\right) \left(b +2\right)}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}-\frac{2 \sqrt{2}\, \arctan \left(\frac{2 x}{\sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}\right)}{\sqrt{\left(b -2\right) \left(b +2\right)}\, \sqrt{2 b +2 \sqrt{\left(b -2\right) \left(b +2\right)}}}"," ",0,"1/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)+1/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)-2/((b-2)*(b+2))^(1/2)/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*2^(1/2)*arctan(2/(2*b+2*((b-2)*(b+2))^(1/2))^(1/2)*x)+1/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)-1/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*b*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)+2/((b-2)*(b+2))^(1/2)/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*2^(1/2)*arctan(2/(2*b-2*((b-2)*(b+2))^(1/2))^(1/2)*x)","B"
106,1,92,80,0.037000," ","int((-x^2+2*a)/(x^4-a*x^2+a^2),x)","\frac{\arctan \left(\frac{2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\arctan \left(\frac{-2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 \sqrt{a}}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, \sqrt{a}\, x +a \right)}{4 \sqrt{a}}-\frac{\sqrt{3}\, \ln \left(-x^{2}+\sqrt{3}\, \sqrt{a}\, x -a \right)}{4 \sqrt{a}}"," ",0,"-1/4/a^(1/2)*3^(1/2)*ln(x*3^(1/2)*a^(1/2)-x^2-a)-1/2/a^(1/2)*arctan((3^(1/2)*a^(1/2)-2*x)/a^(1/2))+1/4*ln(a+x^2+x*3^(1/2)*a^(1/2))*3^(1/2)/a^(1/2)+1/2/a^(1/2)*arctan((2*x+3^(1/2)*a^(1/2))/a^(1/2))","A"
107,1,96,84,0.048000," ","int((-x^2+2*a^(1/2))/(a+x^4-a^(1/2)*x^2),x)","\frac{\arctan \left(\frac{2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{1}{4}}}-\frac{\arctan \left(\frac{-2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{1}{4}}}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x +\sqrt{a}\right)}{4 a^{\frac{1}{4}}}-\frac{\sqrt{3}\, \ln \left(-x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x -\sqrt{a}\right)}{4 a^{\frac{1}{4}}}"," ",0,"1/4*ln(x^2+a^(1/4)*x*3^(1/2)+a^(1/2))*3^(1/2)/a^(1/4)+1/2/a^(1/4)*arctan((2*x+3^(1/2)*a^(1/4))/a^(1/4))-1/4/a^(1/4)*3^(1/2)*ln(a^(1/4)*x*3^(1/2)-x^2-a^(1/2))-1/2/a^(1/4)*arctan((3^(1/2)*a^(1/4)-2*x)/a^(1/4))","A"
108,1,89,86,0.026000," ","int((2*b^(2/3)+x^2)/(b^(4/3)+b^(2/3)*x^2+x^4),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -b^{\frac{1}{3}}\right) \sqrt{3}}{3 b^{\frac{1}{3}}}\right)}{2 b^{\frac{1}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +b^{\frac{1}{3}}\right) \sqrt{3}}{3 b^{\frac{1}{3}}}\right)}{2 b^{\frac{1}{3}}}-\frac{\ln \left(x^{2}-b^{\frac{1}{3}} x +b^{\frac{2}{3}}\right)}{4 b^{\frac{1}{3}}}+\frac{\ln \left(x^{2}+b^{\frac{1}{3}} x +b^{\frac{2}{3}}\right)}{4 b^{\frac{1}{3}}}"," ",0,"-1/4*ln(b^(2/3)-b^(1/3)*x+x^2)/b^(1/3)+1/2*3^(1/2)/b^(1/3)*arctan(1/3*(-b^(1/3)+2*x)*3^(1/2)/b^(1/3))+1/4*ln(b^(2/3)+b^(1/3)*x+x^2)/b^(1/3)+1/2*arctan(1/3*(b^(1/3)+2*x)/b^(1/3)*3^(1/2))*3^(1/2)/b^(1/3)","A"
109,1,190,102,0.026000," ","int((B*x^2+A)/(x^4-a*x^2+a^2),x)","\frac{B \arctan \left(\frac{2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{B \arctan \left(\frac{-2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{3}\, B \ln \left(x^{2}+\sqrt{3}\, \sqrt{a}\, x +a \right)}{12 \sqrt{a}}+\frac{\sqrt{3}\, B \ln \left(-x^{2}+\sqrt{3}\, \sqrt{a}\, x -a \right)}{12 \sqrt{a}}+\frac{A \arctan \left(\frac{2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 a^{\frac{3}{2}}}-\frac{A \arctan \left(\frac{-2 x +\sqrt{3}\, \sqrt{a}}{\sqrt{a}}\right)}{2 a^{\frac{3}{2}}}+\frac{\sqrt{3}\, A \ln \left(x^{2}+\sqrt{3}\, \sqrt{a}\, x +a \right)}{12 a^{\frac{3}{2}}}-\frac{\sqrt{3}\, A \ln \left(-x^{2}+\sqrt{3}\, \sqrt{a}\, x -a \right)}{12 a^{\frac{3}{2}}}"," ",0,"1/12/a^(1/2)*ln(-x^2+3^(1/2)*a^(1/2)*x-a)*B*3^(1/2)-1/12/a^(3/2)*ln(-x^2+3^(1/2)*a^(1/2)*x-a)*A*3^(1/2)-1/2/a^(1/2)*arctan((-2*x+3^(1/2)*a^(1/2))/a^(1/2))*B-1/2/a^(3/2)*arctan((-2*x+3^(1/2)*a^(1/2))/a^(1/2))*A-1/12/a^(1/2)*ln(x^2+3^(1/2)*a^(1/2)*x+a)*B*3^(1/2)+1/12/a^(3/2)*ln(x^2+3^(1/2)*a^(1/2)*x+a)*A*3^(1/2)+1/2/a^(1/2)*arctan((2*x+3^(1/2)*a^(1/2))/a^(1/2))*B+1/2/a^(3/2)*arctan((2*x+3^(1/2)*a^(1/2))/a^(1/2))*A","A"
110,1,198,114,0.041000," ","int((B*x^2+A)/(a+x^4-a^(1/2)*x^2),x)","\frac{B \arctan \left(\frac{2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{1}{4}}}-\frac{B \arctan \left(\frac{-2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{1}{4}}}-\frac{\sqrt{3}\, B \ln \left(x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a^{\frac{1}{4}}}+\frac{\sqrt{3}\, B \ln \left(-x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a^{\frac{1}{4}}}+\frac{A \arctan \left(\frac{2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{3}{4}}}-\frac{A \arctan \left(\frac{-2 x +\sqrt{3}\, a^{\frac{1}{4}}}{a^{\frac{1}{4}}}\right)}{2 a^{\frac{3}{4}}}+\frac{\sqrt{3}\, A \ln \left(x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a^{\frac{3}{4}}}-\frac{\sqrt{3}\, A \ln \left(-x^{2}+\sqrt{3}\, a^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a^{\frac{3}{4}}}"," ",0,"1/12/a^(3/4)*ln(x^2+3^(1/2)*a^(1/4)*x+a^(1/2))*A*3^(1/2)-1/12/a^(1/4)*ln(x^2+3^(1/2)*a^(1/4)*x+a^(1/2))*B*3^(1/2)+1/2/a^(3/4)*arctan((2*x+3^(1/2)*a^(1/4))/a^(1/4))*A+1/2/a^(1/4)*arctan((2*x+3^(1/2)*a^(1/4))/a^(1/4))*B-1/12/a^(3/4)*ln(-x^2+3^(1/2)*a^(1/4)*x-a^(1/2))*A*3^(1/2)+1/12/a^(1/4)*ln(-x^2+3^(1/2)*a^(1/4)*x-a^(1/2))*B*3^(1/2)-1/2/a^(3/4)*arctan((-2*x+3^(1/2)*a^(1/4))/a^(1/4))*A-1/2/a^(1/4)*arctan((-2*x+3^(1/2)*a^(1/4))/a^(1/4))*B","A"
111,1,404,286,0.064000," ","int((B*x^2+A)/(a+c*x^4-x^2*(a*c)^(1/2)),x)","-\frac{A \arctan \left(\frac{-2 \sqrt{c}\, x +\sqrt{3}\, \left(a c \right)^{\frac{1}{4}}}{\sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}}\right)}{2 \sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}\, \sqrt{a}}+\frac{A \arctan \left(\frac{2 \sqrt{c}\, x +\sqrt{3}\, \left(a c \right)^{\frac{1}{4}}}{\sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}}\right)}{2 \sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}\, \sqrt{a}}-\frac{B \arctan \left(\frac{-2 \sqrt{c}\, x +\sqrt{3}\, \left(a c \right)^{\frac{1}{4}}}{\sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}}\right)}{2 \sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}\, \sqrt{c}}+\frac{B \arctan \left(\frac{2 \sqrt{c}\, x +\sqrt{3}\, \left(a c \right)^{\frac{1}{4}}}{\sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}}\right)}{2 \sqrt{4 \sqrt{a}\, \sqrt{c}-3 \sqrt{a c}}\, \sqrt{c}}+\frac{\sqrt{3}\, \left(a c \right)^{\frac{3}{4}} A \ln \left(\sqrt{c}\, x^{2}+\sqrt{3}\, \left(a c \right)^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a^{\frac{3}{2}} c}-\frac{\sqrt{3}\, \left(a c \right)^{\frac{3}{4}} A \ln \left(-\sqrt{c}\, x^{2}+\sqrt{3}\, \left(a c \right)^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a^{\frac{3}{2}} c}-\frac{\sqrt{3}\, \left(a c \right)^{\frac{3}{4}} B \ln \left(\sqrt{c}\, x^{2}+\sqrt{3}\, \left(a c \right)^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a \,c^{\frac{3}{2}}}+\frac{\sqrt{3}\, \left(a c \right)^{\frac{3}{4}} B \ln \left(-\sqrt{c}\, x^{2}+\sqrt{3}\, \left(a c \right)^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a \,c^{\frac{3}{2}}}"," ",0,"1/12/a/c^(3/2)*ln(x*3^(1/2)*(a*c)^(1/4)-c^(1/2)*x^2-a^(1/2))*B*3^(1/2)*(a*c)^(3/4)-1/12/a^(3/2)/c*ln(x*3^(1/2)*(a*c)^(1/4)-c^(1/2)*x^2-a^(1/2))*A*3^(1/2)*(a*c)^(3/4)-1/2/a^(1/2)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2)*arctan((3^(1/2)*(a*c)^(1/4)-2*c^(1/2)*x)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2))*A-1/2/c^(1/2)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2)*arctan((3^(1/2)*(a*c)^(1/4)-2*c^(1/2)*x)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2))*B-1/12/a/c^(3/2)*ln(c^(1/2)*x^2+x*3^(1/2)*(a*c)^(1/4)+a^(1/2))*B*3^(1/2)*(a*c)^(3/4)+1/12/a^(3/2)/c*ln(c^(1/2)*x^2+x*3^(1/2)*(a*c)^(1/4)+a^(1/2))*A*3^(1/2)*(a*c)^(3/4)+1/2/a^(1/2)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2)*arctan((2*c^(1/2)*x+3^(1/2)*(a*c)^(1/4))/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2))*A+1/2/c^(1/2)/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2)*arctan((2*c^(1/2)*x+3^(1/2)*(a*c)^(1/4))/(4*a^(1/2)*c^(1/2)-3*(a*c)^(1/2))^(1/2))*B","A"
112,1,320,160,0.071000," ","int((B*x^2+A)/(a+c*x^4-x^2*a^(1/2)*c^(1/2)),x)","\frac{A \arctan \left(\frac{2 \sqrt{c}\, x +\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}}}{\sqrt{\sqrt{a}\, \sqrt{c}}}\right)}{2 \sqrt{\sqrt{a}\, \sqrt{c}}\, \sqrt{a}}-\frac{A \arctan \left(\frac{-2 \sqrt{c}\, x +\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}}}{\sqrt{\sqrt{a}\, \sqrt{c}}}\right)}{2 \sqrt{\sqrt{a}\, \sqrt{c}}\, \sqrt{a}}+\frac{B \arctan \left(\frac{2 \sqrt{c}\, x +\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}}}{\sqrt{\sqrt{a}\, \sqrt{c}}}\right)}{2 \sqrt{\sqrt{a}\, \sqrt{c}}\, \sqrt{c}}-\frac{B \arctan \left(\frac{-2 \sqrt{c}\, x +\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}}}{\sqrt{\sqrt{a}\, \sqrt{c}}}\right)}{2 \sqrt{\sqrt{a}\, \sqrt{c}}\, \sqrt{c}}+\frac{\sqrt{3}\, A \ln \left(\sqrt{c}\, x^{2}+\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a^{\frac{3}{4}} c^{\frac{1}{4}}}-\frac{\sqrt{3}\, A \ln \left(-\sqrt{c}\, x^{2}+\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a^{\frac{3}{4}} c^{\frac{1}{4}}}-\frac{\sqrt{3}\, B \ln \left(\sqrt{c}\, x^{2}+\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}} x +\sqrt{a}\right)}{12 a^{\frac{1}{4}} c^{\frac{3}{4}}}+\frac{\sqrt{3}\, B \ln \left(-\sqrt{c}\, x^{2}+\sqrt{3}\, a^{\frac{1}{4}} c^{\frac{1}{4}} x -\sqrt{a}\right)}{12 a^{\frac{1}{4}} c^{\frac{3}{4}}}"," ",0,"-1/12/c^(1/4)/a^(3/4)*ln(a^(1/4)*c^(1/4)*x*3^(1/2)-c^(1/2)*x^2-a^(1/2))*A*3^(1/2)+1/12/c^(3/4)/a^(1/4)*ln(a^(1/4)*c^(1/4)*x*3^(1/2)-c^(1/2)*x^2-a^(1/2))*B*3^(1/2)-1/2/a^(1/2)/(a^(1/2)*c^(1/2))^(1/2)*arctan((3^(1/2)*c^(1/4)*a^(1/4)-2*c^(1/2)*x)/(a^(1/2)*c^(1/2))^(1/2))*A-1/2/c^(1/2)/(a^(1/2)*c^(1/2))^(1/2)*arctan((3^(1/2)*c^(1/4)*a^(1/4)-2*c^(1/2)*x)/(a^(1/2)*c^(1/2))^(1/2))*B+1/12/c^(1/4)/a^(3/4)*ln(a^(1/4)*c^(1/4)*x*3^(1/2)+a^(1/2)+c^(1/2)*x^2)*A*3^(1/2)-1/12/c^(3/4)/a^(1/4)*ln(a^(1/4)*c^(1/4)*x*3^(1/2)+a^(1/2)+c^(1/2)*x^2)*B*3^(1/2)+1/2/a^(1/2)/(a^(1/2)*c^(1/2))^(1/2)*arctan((2*c^(1/2)*x+3^(1/2)*c^(1/4)*a^(1/4))/(a^(1/2)*c^(1/2))^(1/2))*A+1/2/c^(1/2)/(a^(1/2)*c^(1/2))^(1/2)*arctan((2*c^(1/2)*x+3^(1/2)*c^(1/4)*a^(1/4))/(a^(1/2)*c^(1/2))^(1/2))*B","A"
113,1,200,74,0.110000," ","int((-x^2+3)/(-x^4+x^2+3)^(1/2),x)","\frac{18 \sqrt{-\left(-\frac{1}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{3}}{6}+\frac{i \sqrt{39}}{6}\right)}{\sqrt{-6+6 \sqrt{13}}\, \sqrt{-x^{4}+x^{2}+3}}+\frac{36 \sqrt{-\left(-\frac{1}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{3}}{6}+\frac{i \sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{3}}{6}+\frac{i \sqrt{39}}{6}\right)\right)}{\sqrt{-6+6 \sqrt{13}}\, \sqrt{-x^{4}+x^{2}+3}\, \left(1+\sqrt{13}\right)}"," ",0,"36/(-6+6*13^(1/2))^(1/2)*(1-(-1/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(-1/6-1/6*13^(1/2))*x^2)^(1/2)/(-x^4+x^2+3)^(1/2)/(1+13^(1/2))*(EllipticF(1/6*x*(-6+6*13^(1/2))^(1/2),1/6*I*3^(1/2)+1/6*I*39^(1/2))-EllipticE(1/6*x*(-6+6*13^(1/2))^(1/2),1/6*I*3^(1/2)+1/6*I*39^(1/2)))+18/(-6+6*13^(1/2))^(1/2)*(1-(-1/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(-1/6-1/6*13^(1/2))*x^2)^(1/2)/(-x^4+x^2+3)^(1/2)*EllipticF(1/6*x*(-6+6*13^(1/2))^(1/2),1/6*I*3^(1/2)+1/6*I*39^(1/2))","B"
114,1,113,31,0.016000," ","int((-x^2+3)/(-x^4+2*x^2+3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{-3 x^{2}+9}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3}\, x}{3}, i \sqrt{3}\right)}{\sqrt{-x^{4}+2 x^{2}+3}}+\frac{\sqrt{3}\, \sqrt{-3 x^{2}+9}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{3}\, x}{3}, i \sqrt{3}\right)+\EllipticF \left(\frac{\sqrt{3}\, x}{3}, i \sqrt{3}\right)\right)}{3 \sqrt{-x^{4}+2 x^{2}+3}}"," ",0,"1/3*3^(1/2)*(-3*x^2+9)^(1/2)*(x^2+1)^(1/2)/(-x^4+2*x^2+3)^(1/2)*(EllipticF(1/3*3^(1/2)*x,I*3^(1/2))-EllipticE(1/3*3^(1/2)*x,I*3^(1/2)))+3^(1/2)*(-3*x^2+9)^(1/2)*(x^2+1)^(1/2)/(-x^4+2*x^2+3)^(1/2)*EllipticF(1/3*3^(1/2)*x,I*3^(1/2))","B"
115,1,204,74,0.099000," ","int((-x^2+3)/(-x^4+3*x^2+3)^(1/2),x)","\frac{18 \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{3}}{2}+\frac{i \sqrt{7}}{2}\right)}{\sqrt{-18+6 \sqrt{21}}\, \sqrt{-x^{4}+3 x^{2}+3}}+\frac{36 \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{3}}{2}+\frac{i \sqrt{7}}{2}\right)+\EllipticF \left(\frac{\sqrt{-18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{3}}{2}+\frac{i \sqrt{7}}{2}\right)\right)}{\sqrt{-18+6 \sqrt{21}}\, \sqrt{-x^{4}+3 x^{2}+3}\, \left(3+\sqrt{21}\right)}"," ",0,"36/(-18+6*21^(1/2))^(1/2)*(1-(-1/2+1/6*21^(1/2))*x^2)^(1/2)*(1-(-1/2-1/6*21^(1/2))*x^2)^(1/2)/(-x^4+3*x^2+3)^(1/2)/(3+21^(1/2))*(EllipticF(1/6*x*(-18+6*21^(1/2))^(1/2),1/2*I*3^(1/2)+1/2*I*7^(1/2))-EllipticE(1/6*x*(-18+6*21^(1/2))^(1/2),1/2*I*3^(1/2)+1/2*I*7^(1/2)))+18/(-18+6*21^(1/2))^(1/2)*(1-(-1/2+1/6*21^(1/2))*x^2)^(1/2)*(1-(-1/2-1/6*21^(1/2))*x^2)^(1/2)/(-x^4+3*x^2+3)^(1/2)*EllipticF(1/6*x*(-18+6*21^(1/2))^(1/2),1/2*I*3^(1/2)+1/2*I*7^(1/2))","B"
116,1,204,74,0.100000," ","int((-x^2+3)/(-x^4-x^2+3)^(1/2),x)","\frac{18 \sqrt{-\left(\frac{1}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{39}}{6}-\frac{i \sqrt{3}}{6}\right)}{\sqrt{6+6 \sqrt{13}}\, \sqrt{-x^{4}-x^{2}+3}}+\frac{36 \sqrt{-\left(\frac{1}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{39}}{6}-\frac{i \sqrt{3}}{6}\right)+\EllipticF \left(\frac{\sqrt{6+6 \sqrt{13}}\, x}{6}, \frac{i \sqrt{39}}{6}-\frac{i \sqrt{3}}{6}\right)\right)}{\sqrt{6+6 \sqrt{13}}\, \sqrt{-x^{4}-x^{2}+3}\, \left(-1+\sqrt{13}\right)}"," ",0,"36/(6+6*13^(1/2))^(1/2)*(1-(1/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(1/6-1/6*13^(1/2))*x^2)^(1/2)/(-x^4-x^2+3)^(1/2)/(-1+13^(1/2))*(EllipticF(1/6*x*(6+6*13^(1/2))^(1/2),1/6*I*39^(1/2)-1/6*I*3^(1/2))-EllipticE(1/6*x*(6+6*13^(1/2))^(1/2),1/6*I*39^(1/2)-1/6*I*3^(1/2)))+18/(6+6*13^(1/2))^(1/2)*(1-(1/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(1/6-1/6*13^(1/2))*x^2)^(1/2)/(-x^4-x^2+3)^(1/2)*EllipticF(1/6*x*(6+6*13^(1/2))^(1/2),1/6*I*39^(1/2)-1/6*I*3^(1/2))","B"
117,1,95,27,0.010000," ","int((-x^2+3)/(-x^4-2*x^2+3)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)}{\sqrt{-x^{4}-2 x^{2}+3}}+\frac{\sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \left(-\EllipticE \left(x , \frac{i \sqrt{3}}{3}\right)+\EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)\right)}{\sqrt{-x^{4}-2 x^{2}+3}}"," ",0,"(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*(EllipticF(x,1/3*I*3^(1/2))-EllipticE(x,1/3*I*3^(1/2)))+(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*EllipticF(x,1/3*I*3^(1/2))","B"
118,1,204,74,0.094000," ","int((-x^2+3)/(-x^4-3*x^2+3)^(1/2),x)","\frac{18 \sqrt{-\left(\frac{1}{2}+\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}-\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{7}}{2}-\frac{i \sqrt{3}}{2}\right)}{\sqrt{18+6 \sqrt{21}}\, \sqrt{-x^{4}-3 x^{2}+3}}+\frac{36 \sqrt{-\left(\frac{1}{2}+\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}-\frac{\sqrt{21}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{7}}{2}-\frac{i \sqrt{3}}{2}\right)+\EllipticF \left(\frac{\sqrt{18+6 \sqrt{21}}\, x}{6}, \frac{i \sqrt{7}}{2}-\frac{i \sqrt{3}}{2}\right)\right)}{\sqrt{18+6 \sqrt{21}}\, \sqrt{-x^{4}-3 x^{2}+3}\, \left(-3+\sqrt{21}\right)}"," ",0,"36/(18+6*21^(1/2))^(1/2)*(1-(1/2+1/6*21^(1/2))*x^2)^(1/2)*(1-(1/2-1/6*21^(1/2))*x^2)^(1/2)/(-x^4-3*x^2+3)^(1/2)/(-3+21^(1/2))*(EllipticF(1/6*x*(18+6*21^(1/2))^(1/2),1/2*I*7^(1/2)-1/2*I*3^(1/2))-EllipticE(1/6*x*(18+6*21^(1/2))^(1/2),1/2*I*7^(1/2)-1/2*I*3^(1/2)))+18/(18+6*21^(1/2))^(1/2)*(1-(1/2+1/6*21^(1/2))*x^2)^(1/2)*(1-(1/2-1/6*21^(1/2))*x^2)^(1/2)/(-x^4-3*x^2+3)^(1/2)*EllipticF(1/6*x*(18+6*21^(1/2))^(1/2),1/2*I*7^(1/2)-1/2*I*3^(1/2))","B"
119,1,515,294,0.050000," ","int((2*c*x^2-(-4*a*c+b^2)^(1/2)+b)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a c}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}"," ",0,"-c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))-1/4*(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/4*b*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
120,1,97,94,0.002000," ","int((e*x^2+d)^4*(c*x^4+a),x)","\frac{c \,e^{4} x^{13}}{13}+\frac{4 c d \,e^{3} x^{11}}{11}+\frac{\left(e^{4} a +6 d^{2} e^{2} c \right) x^{9}}{9}+\frac{4 a \,d^{3} e \,x^{3}}{3}+\frac{\left(4 d \,e^{3} a +4 d^{3} e c \right) x^{7}}{7}+a \,d^{4} x +\frac{\left(6 d^{2} e^{2} a +d^{4} c \right) x^{5}}{5}"," ",0,"1/13*c*e^4*x^13+4/11*c*d*e^3*x^11+1/9*(a*e^4+6*c*d^2*e^2)*x^9+1/7*(4*a*d*e^3+4*c*d^3*e)*x^7+1/5*(6*a*d^2*e^2+c*d^4)*x^5+4/3*a*d^3*e*x^3+a*d^4*x","A"
121,1,72,71,0.002000," ","int((e*x^2+d)^3*(c*x^4+a),x)","\frac{c \,e^{3} x^{11}}{11}+\frac{c d \,e^{2} x^{9}}{3}+a \,d^{2} e \,x^{3}+\frac{\left(a \,e^{3}+3 c \,d^{2} e \right) x^{7}}{7}+a \,d^{3} x +\frac{\left(3 d \,e^{2} a +d^{3} c \right) x^{5}}{5}"," ",0,"1/11*c*e^3*x^11+1/3*c*d*e^2*x^9+1/7*(a*e^3+3*c*d^2*e)*x^7+1/5*(3*a*d*e^2+c*d^3)*x^5+a*d^2*e*x^3+a*d^3*x","A"
122,1,49,48,0.000000," ","int((e*x^2+d)^2*(c*x^4+a),x)","\frac{c \,e^{2} x^{9}}{9}+\frac{2 c d e \,x^{7}}{7}+\frac{2 a d e \,x^{3}}{3}+\frac{\left(a \,e^{2}+c \,d^{2}\right) x^{5}}{5}+a \,d^{2} x"," ",0,"a*d^2*x+2/3*a*d*e*x^3+1/5*(a*e^2+c*d^2)*x^5+2/7*c*d*e*x^7+1/9*c*e^2*x^9","A"
123,1,27,26,0.001000," ","int((e*x^2+d)*(c*x^4+a),x)","\frac{1}{7} c e \,x^{7}+\frac{1}{5} c d \,x^{5}+\frac{1}{3} a e \,x^{3}+a d x"," ",0,"a*d*x+1/3*a*e*x^3+1/5*c*d*x^5+1/7*c*e*x^7","A"
124,1,57,45,0.008000," ","int((c*x^4+a)/(e*x^2+d),x)","\frac{c \,x^{3}}{3 e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}-\frac{c d x}{e^{2}}"," ",0,"1/3*c*x^3/e-c*d*x/e^2+1/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))*a+1/e^2/(d*e)^(1/2)*arctan(x*e/(d*e)^(1/2))*c*d^2","A"
125,1,82,62,0.011000," ","int((c*x^4+a)/(e*x^2+d)^2,x)","\frac{a x}{2 \left(e \,x^{2}+d \right) d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}+\frac{c d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}+\frac{c x}{e^{2}}"," ",0,"c*x/e^2+1/2/d*x/(e*x^2+d)*a+1/2/e^2*d*x/(e*x^2+d)*c+1/2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-3/2/e^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
126,1,99,79,0.009000," ","int((c*x^4+a)/(e*x^2+d)^3,x)","\frac{3 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{3 c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}+\frac{\frac{\left(3 a \,e^{2}-5 c \,d^{2}\right) x^{3}}{8 d^{2} e}+\frac{\left(5 a \,e^{2}-3 c \,d^{2}\right) x}{8 d \,e^{2}}}{\left(e \,x^{2}+d \right)^{2}}"," ",0,"(1/8*(3*a*e^2-5*c*d^2)/d^2/e*x^3+1/8*(5*a*e^2-3*c*d^2)/d/e^2*x)/(e*x^2+d)^2+3/8/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+3/8/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
127,1,122,107,0.009000," ","int((c*x^4+a)/(e*x^2+d)^4,x)","\frac{5 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{3}}+\frac{c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d \,e^{2}}+\frac{\frac{\left(5 a \,e^{2}+c \,d^{2}\right) x^{5}}{16 d^{3}}+\frac{\left(5 a \,e^{2}-c \,d^{2}\right) x^{3}}{6 d^{2} e}+\frac{\left(11 a \,e^{2}-c \,d^{2}\right) x}{16 d \,e^{2}}}{\left(e \,x^{2}+d \right)^{3}}"," ",0,"(1/16*(5*a*e^2+c*d^2)/d^3*x^5+1/6*(5*a*e^2-c*d^2)/d^2/e*x^3+1/16*(11*a*e^2-c*d^2)/d/e^2*x)/(e*x^2+d)^3+5/16/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+1/16/d/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
128,1,130,121,0.002000," ","int((e*x^2+d)^3*(c*x^4+a)^2,x)","\frac{c^{2} e^{3} x^{15}}{15}+\frac{3 c^{2} d \,e^{2} x^{13}}{13}+\frac{\left(2 e^{3} a c +3 d^{2} e \,c^{2}\right) x^{11}}{11}+\frac{\left(6 a c d \,e^{2}+c^{2} d^{3}\right) x^{9}}{9}+a^{2} d^{2} e \,x^{3}+\frac{\left(e^{3} a^{2}+6 d^{2} e a c \right) x^{7}}{7}+a^{2} d^{3} x +\frac{\left(3 d \,e^{2} a^{2}+2 d^{3} a c \right) x^{5}}{5}"," ",0,"1/15*c^2*e^3*x^15+3/13*c^2*d*e^2*x^13+1/11*(2*a*c*e^3+3*c^2*d^2*e)*x^11+1/9*(6*a*c*d*e^2+c^2*d^3)*x^9+1/7*(a^2*e^3+6*a*c*d^2*e)*x^7+1/5*(3*a^2*d*e^2+2*a*c*d^3)*x^5+a^2*d^2*e*x^3+a^2*d^3*x","A"
129,1,90,85,0.002000," ","int((e*x^2+d)^2*(c*x^4+a)^2,x)","\frac{c^{2} e^{2} x^{13}}{13}+\frac{2 c^{2} d e \,x^{11}}{11}+\frac{4 a c d e \,x^{7}}{7}+\frac{\left(2 e^{2} a c +c^{2} d^{2}\right) x^{9}}{9}+\frac{2 a^{2} d e \,x^{3}}{3}+a^{2} d^{2} x +\frac{\left(e^{2} a^{2}+2 d^{2} a c \right) x^{5}}{5}"," ",0,"1/13*c^2*e^2*x^13+2/11*c^2*d*e*x^11+1/9*(2*a*c*e^2+c^2*d^2)*x^9+4/7*a*c*d*e*x^7+1/5*(a^2*e^2+2*a*c*d^2)*x^5+2/3*a^2*d*e*x^3+a^2*d^2*x","A"
130,1,51,50,0.002000," ","int((e*x^2+d)*(c*x^4+a)^2,x)","\frac{1}{11} c^{2} e \,x^{11}+\frac{1}{9} c^{2} d \,x^{9}+\frac{2}{7} a c e \,x^{7}+\frac{2}{5} a c d \,x^{5}+\frac{1}{3} a^{2} e \,x^{3}+a^{2} d x"," ",0,"a^2*d*x+1/3*a^2*e*x^3+2/5*a*c*d*x^5+2/7*a*c*e*x^7+1/9*c^2*d*x^9+1/11*c^2*e*x^11","A"
131,1,22,21,0.000000," ","int((c*x^4+a)^2,x)","\frac{1}{9} c^{2} x^{9}+\frac{2}{5} a c \,x^{5}+a^{2} x"," ",0,"a^2*x+2/5*a*c*x^5+1/9*c^2*x^9","A"
132,1,136,94,0.005000," ","int((c*x^4+a)^2/(e*x^2+d),x)","\frac{c^{2} x^{7}}{7 e}-\frac{c^{2} d \,x^{5}}{5 e^{2}}+\frac{2 a c \,x^{3}}{3 e}+\frac{c^{2} d^{2} x^{3}}{3 e^{3}}+\frac{a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}+\frac{2 a c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}+\frac{c^{2} d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{4}}-\frac{2 a c d x}{e^{2}}-\frac{c^{2} d^{3} x}{e^{4}}"," ",0,"1/7*c^2*x^7/e-1/5*c^2*d*x^5/e^2+2/3*c/e*x^3*a+1/3*c^2/e^3*x^3*d^2-2*c/e^2*d*a*x-c^2/e^4*d^3*x+1/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a^2+2/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*c*d^2+1/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2*d^4","A"
133,1,170,115,0.011000," ","int((c*x^4+a)^2/(e*x^2+d)^2,x)","\frac{c^{2} x^{5}}{5 e^{2}}-\frac{2 c^{2} d \,x^{3}}{3 e^{3}}+\frac{a^{2} x}{2 \left(e \,x^{2}+d \right) d}+\frac{a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}+\frac{a c d x}{\left(e \,x^{2}+d \right) e^{2}}-\frac{3 a c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}+\frac{c^{2} d^{3} x}{2 \left(e \,x^{2}+d \right) e^{4}}-\frac{7 c^{2} d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{4}}+\frac{2 a c x}{e^{2}}+\frac{3 c^{2} d^{2} x}{e^{4}}"," ",0,"1/5*c^2*x^5/e^2-2/3*c^2*d*x^3/e^3+2*c/e^2*a*x+3*c^2/e^4*d^2*x+1/2/d*x/(e*x^2+d)*a^2+1/e^2*d*x/(e*x^2+d)*a*c+1/2/e^4*d^3*x/(e*x^2+d)*c^2+1/2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a^2-3/e^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*c-7/2/e^4*d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2","A"
134,1,211,139,0.011000," ","int((c*x^4+a)^2/(e*x^2+d)^3,x)","\frac{3 a^{2} e \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}-\frac{5 a c \,x^{3}}{4 \left(e \,x^{2}+d \right)^{2} e}-\frac{13 c^{2} d^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}+\frac{5 a^{2} x}{8 \left(e \,x^{2}+d \right)^{2} d}-\frac{3 a c d x}{4 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{11 c^{2} d^{3} x}{8 \left(e \,x^{2}+d \right)^{2} e^{4}}+\frac{c^{2} x^{3}}{3 e^{3}}+\frac{3 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{3 a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{4 \sqrt{d e}\, e^{2}}+\frac{35 c^{2} d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{4}}-\frac{3 c^{2} d x}{e^{4}}"," ",0,"1/3*c^2*x^3/e^3-3*c^2*d*x/e^4+3/8*e/(e*x^2+d)^2/d^2*x^3*a^2-5/4/e/(e*x^2+d)^2*x^3*a*c-13/8/e^3/(e*x^2+d)^2*d^2*x^3*c^2+5/8/(e*x^2+d)^2/d*x*a^2-3/4/e^2/(e*x^2+d)^2*d*x*a*c-11/8/e^4/(e*x^2+d)^2*d^3*x*c^2+3/8/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a^2+3/4/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*c+35/8/e^4*d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2","A"
135,1,262,168,0.014000," ","int((c*x^4+a)^2/(e*x^2+d)^4,x)","\frac{5 a^{2} e^{2} x^{5}}{16 \left(e \,x^{2}+d \right)^{3} d^{3}}+\frac{a c \,x^{5}}{8 \left(e \,x^{2}+d \right)^{3} d}+\frac{29 c^{2} d \,x^{5}}{16 \left(e \,x^{2}+d \right)^{3} e^{2}}+\frac{5 a^{2} e \,x^{3}}{6 \left(e \,x^{2}+d \right)^{3} d^{2}}-\frac{a c \,x^{3}}{3 \left(e \,x^{2}+d \right)^{3} e}+\frac{17 c^{2} d^{2} x^{3}}{6 \left(e \,x^{2}+d \right)^{3} e^{3}}+\frac{11 a^{2} x}{16 \left(e \,x^{2}+d \right)^{3} d}-\frac{a c d x}{8 \left(e \,x^{2}+d \right)^{3} e^{2}}+\frac{19 c^{2} d^{3} x}{16 \left(e \,x^{2}+d \right)^{3} e^{4}}+\frac{5 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{3}}+\frac{a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d \,e^{2}}-\frac{35 c^{2} d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, e^{4}}+\frac{c^{2} x}{e^{4}}"," ",0,"c^2*x/e^4+5/16*e^2/(e*x^2+d)^3/d^3*x^5*a^2+1/8/(e*x^2+d)^3/d*x^5*a*c+29/16/e^2/(e*x^2+d)^3*d*x^5*c^2+5/6*e/(e*x^2+d)^3/d^2*x^3*a^2-1/3/e/(e*x^2+d)^3*x^3*a*c+17/6/e^3/(e*x^2+d)^3*d^2*x^3*c^2+11/16/(e*x^2+d)^3/d*x*a^2-1/8/e^2/(e*x^2+d)^3*d*x*a*c+19/16/e^4/(e*x^2+d)^3*d^3*x*c^2+5/16/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a^2+1/8/e^2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*c-35/16/e^4*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2","A"
136,1,231,205,0.012000," ","int((c*x^4+a)^2/(e*x^2+d)^5,x)","\frac{35 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{128 \sqrt{d e}\, d^{4}}+\frac{3 a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{64 \sqrt{d e}\, d^{2} e^{2}}+\frac{35 c^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{128 \sqrt{d e}\, e^{4}}+\frac{\frac{\left(35 a^{2} e^{4}+6 a c \,d^{2} e^{2}-93 c^{2} d^{4}\right) x^{7}}{128 d^{4} e}+\frac{\left(385 a^{2} e^{4}+66 a c \,d^{2} e^{2}-511 c^{2} d^{4}\right) x^{5}}{384 d^{3} e^{2}}+\frac{\left(511 a^{2} e^{4}-66 a c \,d^{2} e^{2}-385 c^{2} d^{4}\right) x^{3}}{384 d^{2} e^{3}}+\frac{\left(93 a^{2} e^{4}-6 a c \,d^{2} e^{2}-35 c^{2} d^{4}\right) x}{128 d \,e^{4}}}{\left(e \,x^{2}+d \right)^{4}}"," ",0,"(1/128*(35*a^2*e^4+6*a*c*d^2*e^2-93*c^2*d^4)/d^4/e*x^7+1/384*(385*a^2*e^4+66*a*c*d^2*e^2-511*c^2*d^4)/d^3/e^2*x^5+1/384*(511*a^2*e^4-66*a*c*d^2*e^2-385*c^2*d^4)/d^2/e^3*x^3+1/128*(93*a^2*e^4-6*a*c*d^2*e^2-35*c^2*d^4)/d/e^4*x)/(e*x^2+d)^4+35/128/d^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a^2+3/64/d^2/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*c+35/128/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2","A"
137,1,741,352,0.011000," ","int((e*x^2+d)^4/(c*x^4+a),x)","\frac{e^{4} x^{5}}{5 c}+\frac{4 d \,e^{3} x^{3}}{3 c}-\frac{\sqrt{2}\, a d \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a d \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a d \,e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{2 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{a \,e^{4} x}{c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a}+\frac{\sqrt{2}\, d^{3} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{\left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, d^{3} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{\left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, d^{3} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{2 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{6 d^{2} e^{2} x}{c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{2 c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{2 c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{4 c}"," ",0,"1/5*e^4*x^5/c+4/3*d*e^3*x^3/c-e^4/c^2*a*x+6*e^2/c*d^2*x+1/4/c^2*(a/c)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^4-3/2/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^4+1/8/c^2*(a/c)^(1/4)*a*2^(1/2)*ln((x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))*e^4-3/4/c*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))*d^2*e^2+1/8*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))*d^4+1/4/c^2*(a/c)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^4-3/2/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^4-1/2/c^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))*a*d*e^3+1/2/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))*d^3*e-1/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*a*d*e^3+1/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3*e-1/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*a*d*e^3+1/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3*e","B"
138,1,572,287,0.004000," ","int((e*x^2+d)^3/(c*x^4+a),x)","\frac{e^{3} x^{3}}{3 c}-\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a \,e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a}+\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{3 \sqrt{2}\, d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{3 d \,e^{2} x}{c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 c}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 c}"," ",0,"1/3*e^3*x^3/c+3*d*e^2*x/c-3/4/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3-3/8/c*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2+1/8*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3-3/4/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-1/8/c^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*a*e^3+3/8/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e-1/4/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*a*e^3+3/4/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e-1/4/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*a*e^3+3/4/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e","A"
139,1,412,216,0.004000," ","int((e*x^2+d)^2/(c*x^4+a),x)","\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a}+\frac{\sqrt{2}\, d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, d e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{e^{2} x}{c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 c}"," ",0,"e^2*x/c-1/4/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2-1/8/c*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^2+1/8*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2-1/4/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^2+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2+1/4/c*d*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/2/c*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/2/c*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
140,1,260,166,0.003000," ","int((e*x^2+d)/(c*x^4+a),x)","\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(\frac{a}{c}\right)^{\frac{1}{4}} c}"," ",0,"1/8*d*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/8*e/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*e/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*e/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
141,1,128,120,0.003000," ","int(1/(c*x^4+a),x)","\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a}"," ",0,"1/8*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
142,1,363,247,0.007000," ","int(1/(e*x^2+d)/(c*x^4+a),x)","\frac{e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}"," ",0,"e^2/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/8*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/8/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
143,1,650,352,0.012000," ","int(1/(e*x^2+d)^2/(c*x^4+a),x)","\frac{a \,e^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d}+\frac{a \,e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}\, d}+\frac{c d \,e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right)}+\frac{5 c d \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{\sqrt{2}\, c d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, c d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, c d e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/2*e^4/(a*e^2+c*d^2)^2/d*x/(e*x^2+d)*a+1/2*e^2/(a*e^2+c*d^2)^2*d*x/(e*x^2+d)*c+1/2*e^4/(a*e^2+c*d^2)^2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+5/2*e^2/(a*e^2+c*d^2)^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c-1/8*c/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^2+1/8*c^2/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2-1/4*c/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^2+1/4*c^2/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2-1/4*c/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^2+1/4*c^2/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2-1/4*c/(a*e^2+c*d^2)^2*d*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/2*c/(a*e^2+c*d^2)^2*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/2*c/(a*e^2+c*d^2)^2*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
144,1,624,280,0.011000," ","int((e*x^2+d)^3/(c*x^4+a)^2,x)","\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{3 \sqrt{2}\, d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a^{2}}+\frac{3 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{-\frac{\left(a \,e^{2}-3 c \,d^{2}\right) e \,x^{3}}{4 a c}-\frac{\left(3 a \,e^{2}-c \,d^{2}\right) d x}{4 a c}}{c \,x^{4}+a}"," ",0,"(-1/4*e*(a*e^2-3*c*d^2)/a/c*x^3-1/4*d*(3*a*e^2-c*d^2)/a/c*x)/(c*x^4+a)+3/32/a/c*d*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^2+3/32/a^2*d^3*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+3/16/a/c*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^2+3/16/a^2*d^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+3/16/a/c*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^2+3/16/a^2*d^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+3/32/c^2*e^3/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+3/32/a/c*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2+3/16/c^2*e^3/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+3/16/a/c*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2+3/16/c^2*e^3/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+3/16/a/c*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2","B"
145,1,464,264,0.009000," ","int((e*x^2+d)^2/(c*x^4+a)^2,x)","\frac{\sqrt{2}\, d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{\sqrt{2}\, d e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{\sqrt{2}\, d e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a^{2}}+\frac{\frac{d e \,x^{3}}{2 a}-\frac{\left(a \,e^{2}-c \,d^{2}\right) x}{4 a c}}{c \,x^{4}+a}"," ",0,"(1/2*d*e/a*x^3-1/4*(a*e^2-c*d^2)/a/c*x)/(c*x^4+a)+1/16/a/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^2+3/16/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2+1/32/a/c*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^2+3/32/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2+1/16/a/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^2+3/16/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2+1/16/a/c*d*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/8/a/c*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/8/a/c*d*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
146,1,303,192,0.006000," ","int((e*x^2+d)/(c*x^4+a)^2,x)","\frac{e \,x^{3}}{4 \left(c \,x^{4}+a \right) a}+\frac{d x}{4 \left(c \,x^{4}+a \right) a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(\frac{a}{c}\right)^{\frac{1}{4}} a c}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a^{2}}"," ",0,"1/4*d*x/a/(c*x^4+a)+3/32*d/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+3/16*d/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+3/16*d/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/4*e*x^3/a/(c*x^4+a)+1/32*e/a/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/16*e/a/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/16*e/a/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
147,1,143,135,0.005000," ","int(1/(c*x^4+a)^2,x)","\frac{x}{4 \left(c \,x^{4}+a \right) a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 a^{2}}"," ",0,"1/4*x/a/(c*x^4+a)+3/32/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+3/16/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+3/16/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)","A"
148,1,873,517,0.017000," ","int(1/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{c^{2} d^{2} e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c \,e^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c^{2} d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c d \,e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}-\frac{\sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c \,d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{5 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}"," ",0,"e^4/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)-1/4/(a*e^2+c*d^2)^2*c/(c*x^4+a)*e^3*x^3-1/4/(a*e^2+c*d^2)^2*c^2/(c*x^4+a)*e/a*x^3*d^2+1/4/(a*e^2+c*d^2)^2*c/(c*x^4+a)*d*x*e^2+1/4/(a*e^2+c*d^2)^2*c^2/(c*x^4+a)*d^3/a*x+7/16/(a*e^2+c*d^2)^2*c/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2+3/16/(a*e^2+c*d^2)^2*c^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3+7/32/(a*e^2+c*d^2)^2*c/a*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2+3/32/(a*e^2+c*d^2)^2*c^2/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3+7/16/(a*e^2+c*d^2)^2*c/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2+3/16/(a*e^2+c*d^2)^2*c^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-5/32/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3-1/32/(a*e^2+c*d^2)^2*c/a/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e-5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3-1/16/(a*e^2+c*d^2)^2*c/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e-5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3-1/16/(a*e^2+c*d^2)^2*c/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e","A"
149,1,1169,680,0.020000," ","int(1/(e*x^2+d)^2/(c*x^4+a)^2,x)","-\frac{c^{3} d^{3} e \,x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{4}+a \right) a}-\frac{c^{2} d \,e^{3} x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{4}+a \right)}-\frac{a c \,e^{4} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{4}+a \right)}+\frac{a \,e^{6} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(e \,x^{2}+d \right) d}+\frac{a \,e^{6} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{d e}\, d}+\frac{c^{3} d^{4} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(c \,x^{4}+a \right) a}+\frac{c d \,e^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(e \,x^{2}+d \right)}+\frac{9 c d \,e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{d e}}-\frac{\sqrt{2}\, c^{2} d^{3} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c^{2} d^{3} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c^{2} d^{3} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{3} a^{2}}-\frac{9 \sqrt{2}\, c d \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{9 \sqrt{2}\, c d \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{9 \sqrt{2}\, c d \,e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{3}}"," ",0,"1/2*e^6/(a*e^2+c*d^2)^3/d*x/(e*x^2+d)*a+1/2*e^4/(a*e^2+c*d^2)^3*d*x/(e*x^2+d)*c+1/2*e^6/(a*e^2+c*d^2)^3/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+9/2*e^4/(a*e^2+c*d^2)^3*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c-1/2*c^2/(a*e^2+c*d^2)^3/(c*x^4+a)*d*e^3*x^3-1/2*c^3/(a*e^2+c*d^2)^3/(c*x^4+a)*d^3*e/a*x^3-1/4*c/(a*e^2+c*d^2)^3/(c*x^4+a)*a*x*e^4+1/4*c^3/(a*e^2+c*d^2)^3/(c*x^4+a)/a*x*d^4-7/16*c/(a*e^2+c*d^2)^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^4+3/4*c^2/(a*e^2+c*d^2)^3/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e^2+3/16*c^3/(a*e^2+c*d^2)^3/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^4-7/16*c/(a*e^2+c*d^2)^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^4+3/4*c^2/(a*e^2+c*d^2)^3/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e^2+3/16*c^3/(a*e^2+c*d^2)^3/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^4-7/32*c/(a*e^2+c*d^2)^3*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^4+3/8*c^2/(a*e^2+c*d^2)^3/a*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e^2+3/32*c^3/(a*e^2+c*d^2)^3/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^4-9/16*c/(a*e^2+c*d^2)^3/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^3-1/16*c^2/(a*e^2+c*d^2)^3/a/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3*e-9/8*c/(a*e^2+c*d^2)^3/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^3-1/8*c^2/(a*e^2+c*d^2)^3/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3*e-9/8*c/(a*e^2+c*d^2)^3/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^3-1/8*c^2/(a*e^2+c*d^2)^3/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3*e","A"
150,1,506,380,0.017000," ","int((e*x^2+d)^4/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{4} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{4 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d^{3} e}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+6 \left(-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}+\frac{\sqrt{c \,x^{4}+a}\, x}{3 c}\right) d^{2} e^{2}+4 \left(\frac{\sqrt{c \,x^{4}+a}\, x^{3}}{5 c}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) a^{\frac{3}{2}}}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right) d \,e^{3}+\left(\frac{\sqrt{c \,x^{4}+a}\, x^{5}}{7 c}+\frac{5 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{2}}-\frac{5 \sqrt{c \,x^{4}+a}\, a x}{21 c^{2}}\right) e^{4}"," ",0,"e^4*(1/7/c*x^5*(c*x^4+a)^(1/2)-5/21*a/c^2*x*(c*x^4+a)^(1/2)+5/21*a^2/c^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+4*d*e^3*(1/5/c*x^3*(c*x^4+a)^(1/2)-3/5*I*a^(3/2)/c^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+6*d^2*e^2*(1/3*(c*x^4+a)^(1/2)/c*x-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+4*I*d^3*e*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+d^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
151,1,388,328,0.010000," ","int((e*x^2+d)^3/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d^{2} e}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+3 \left(-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}+\frac{\sqrt{c \,x^{4}+a}\, x}{3 c}\right) d \,e^{2}+\left(\frac{\sqrt{c \,x^{4}+a}\, x^{3}}{5 c}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) a^{\frac{3}{2}}}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right) e^{3}"," ",0,"e^3*(1/5*(c*x^4+a)^(1/2)/c*x^3-3/5*I*a^(3/2)/c^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+3*d*e^2*(1/3*(c*x^4+a)^(1/2)/c*x-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+3*I*d^2*e*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+d^3/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
152,1,266,272,0.007000," ","int((e*x^2+d)^2/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{2 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d e}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\left(-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}+\frac{\sqrt{c \,x^{4}+a}\, x}{3 c}\right) e^{2}"," ",0,"e^2*(1/3*(c*x^4+a)^(1/2)/c*x-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+2*I*d*e*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+d^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
153,1,169,238,0.004000," ","int((e*x^2+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}"," ",0,"I*e*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
154,1,107,322,0.038000," ","int(1/(e*x^2+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}"," ",0,"1/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)*e/d,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))","C"
155,1,556,562,0.031000," ","int(1/(e*x^2+d)^2/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(e \,x^{2}+d \right) d}"," ",0,"1/2*e^2*x*(c*x^4+a)^(1/2)/d/(a*e^2+c*d^2)/(e*x^2+d)-1/2*c/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I*c^(1/2)*e/(a*e^2+c*d^2)/d*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*I*c^(1/2)*e/(a*e^2+c*d^2)/d*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2/(a*e^2+c*d^2)/d^2*e^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+3/2/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c","C"
156,1,1018,702,0.031000," ","int(1/(e*x^2+d)^3/(c*x^4+a)^(1/2),x)","\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e^{4} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{3}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}+\frac{9 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{9 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{7 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{15 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(e \,x^{2}+d \right)^{2} d}+\frac{3 \left(a \,e^{2}+3 c \,d^{2}\right) \sqrt{c \,x^{4}+a}\, e^{2} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d^{2}}"," ",0,"1/4*e^2*x*(c*x^4+a)^(1/2)/d/(a*e^2+c*d^2)/(e*x^2+d)^2+3/8*e^2*(a*e^2+3*c*d^2)*x*(c*x^4+a)^(1/2)/d^2/(a*e^2+c*d^2)^2/(e*x^2+d)-1/8*c/d/(a*e^2+c*d^2)^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)*a*e^2-7/8*c^2*d/(a*e^2+c*d^2)^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-9/8*I*c^(3/2)*e/(a*e^2+c*d^2)^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-3/8*I*c^(1/2)*e^3/(a*e^2+c*d^2)^2/d^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+9/8*I*c^(3/2)*e/(a*e^2+c*d^2)^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8*I*c^(1/2)*e^3/(a*e^2+c*d^2)^2/d^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8/(a*e^2+c*d^2)^2/d^3*e^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a^2+3/4/(a*e^2+c*d^2)^2/d*e^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a*c+15/8/(a*e^2+c*d^2)^2*d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c^2","C"
157,1,360,175,0.031000," ","int((e*x^2+d)^3/(-c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{3} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d^{2} e}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, \sqrt{c}}+3 \left(\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, c}-\frac{\sqrt{-c \,x^{4}+a}\, x}{3 c}\right) d \,e^{2}+\left(-\frac{\sqrt{-c \,x^{4}+a}\, x^{3}}{5 c}-\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) a^{\frac{3}{2}}}{5 \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, c^{\frac{3}{2}}}\right) e^{3}"," ",0,"e^3*(-1/5/c*x^3*(-c*x^4+a)^(1/2)-3/5*a^(3/2)/c^(3/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(1-1/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*c^(1/2)*x^2)^(1/2)/(-c*x^4+a)^(1/2)*(EllipticF(x*(1/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(1/a^(1/2)*c^(1/2))^(1/2),I)))+3*d*e^2*(-1/3/c*x*(-c*x^4+a)^(1/2)+1/3*a/c/(1/a^(1/2)*c^(1/2))^(1/2)*(1-1/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*c^(1/2)*x^2)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF(x*(1/a^(1/2)*c^(1/2))^(1/2),I))-3*d^2*e*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(1-1/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*c^(1/2)*x^2)^(1/2)/(-c*x^4+a)^(1/2)/c^(1/2)*(EllipticF(x*(1/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(1/a^(1/2)*c^(1/2))^(1/2),I))+d^3/(1/a^(1/2)*c^(1/2))^(1/2)*(1-1/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*c^(1/2)*x^2)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF(x*(1/a^(1/2)*c^(1/2))^(1/2),I)","B"
158,1,246,128,0.009000," ","int((e*x^2+d)^2/(-c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{2} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{2 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d e}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, \sqrt{c}}+\left(\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, c}-\frac{\sqrt{-c \,x^{4}+a}\, x}{3 c}\right) e^{2}"," ",0,"e^2*(-1/3*(-c*x^4+a)^(1/2)/c*x+1/3*a/c/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I))-2*d*e*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I))+d^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)","A"
159,1,154,96,0.005000," ","int((e*x^2+d)/(-c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, \sqrt{c}}"," ",0,"-e*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I))+d/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)","A"
160,1,97,56,0.029000," ","int(1/(e*x^2+d)/(-c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}"," ",0,"1/d/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-e*a^(1/2)/d/c^(1/2),(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))","A"
161,1,523,245,0.030000," ","int(1/(e*x^2+d)^2/(-c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{2} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{2}}+\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}-\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}+\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}-c \,d^{2}\right) \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{\sqrt{-c \,x^{4}+a}\, e^{2} x}{2 \left(a \,e^{2}-c \,d^{2}\right) \left(e \,x^{2}+d \right) d}"," ",0,"1/2*e^2/(a*e^2-c*d^2)/d*x*(-c*x^4+a)^(1/2)/(e*x^2+d)+1/2*c/(a*e^2-c*d^2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*c^(1/2)*e/(a*e^2-c*d^2)/d*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*c^(1/2)*e/(a*e^2-c*d^2)/d*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2/(a*e^2-c*d^2)/d^2*e^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a-3/2/(a*e^2-c*d^2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*c","B"
162,1,961,363,0.032000," ","int(1/(e*x^2+d)^3/(-c*x^4+a)^(1/2),x)","\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e^{4} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{3}}+\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{2}}-\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{2}}+\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}-\frac{3 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{4 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}-\frac{9 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{9 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{7 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{15 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{\sqrt{-c \,x^{4}+a}\, e^{2} x}{4 \left(a \,e^{2}-c \,d^{2}\right) \left(e \,x^{2}+d \right)^{2} d}+\frac{3 \left(a \,e^{2}-3 c \,d^{2}\right) \sqrt{-c \,x^{4}+a}\, e^{2} x}{8 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d^{2}}"," ",0,"1/4*e^2/(a*e^2-c*d^2)/d*x*(-c*x^4+a)^(1/2)/(e*x^2+d)^2+3/8*e^2*(a*e^2-3*c*d^2)/(a*e^2-c*d^2)^2/d^2*x*(-c*x^4+a)^(1/2)/(e*x^2+d)+1/8*c/d/(a*e^2-c*d^2)^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)*a*e^2-7/8*c^2*d/(a*e^2-c*d^2)^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-3/8*c^(1/2)*e^3/(a*e^2-c*d^2)^2/d^2*a^(3/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+9/8*c^(3/2)*e/(a*e^2-c*d^2)^2*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8*c^(1/2)*e^3/(a*e^2-c*d^2)^2/d^2*a^(3/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-9/8*c^(3/2)*e/(a*e^2-c*d^2)^2*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8/(a*e^2-c*d^2)^2/d^3*e^4/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a^2-3/4/(a*e^2-c*d^2)^2/d*e^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a*c+15/8/(a*e^2-c*d^2)^2*d/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*c^2","B"
163,1,1420,489,0.035000," ","int(1/(e*x^2+d)^4/(-c*x^4+a)^(1/2),x)","\frac{5 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{3} e^{6} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{4}}+\frac{5 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} \sqrt{c}\, e^{5} \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{3}}-\frac{5 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} \sqrt{c}\, e^{5} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{3}}+\frac{5 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} c \,e^{4} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{48 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{2}}-\frac{17 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} c \,e^{4} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d^{2}}-\frac{7 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} c^{\frac{3}{2}} e^{3} \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}+\frac{7 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} c^{\frac{3}{2}} e^{3} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}\, d}-\frac{\sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,c^{2} e^{2} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{24 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{7 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,c^{2} e^{2} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{29 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{5}{2}} d e \EllipticE \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{29 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{5}{2}} d e \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{19 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{3} d^{2} \EllipticF \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}-\frac{35 \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{3} d^{2} \EllipticPi \left(\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}+a}}+\frac{\sqrt{-c \,x^{4}+a}\, e^{2} x}{6 \left(a \,e^{2}-c \,d^{2}\right) \left(e \,x^{2}+d \right)^{3} d}+\frac{5 \left(a \,e^{2}-3 c \,d^{2}\right) \sqrt{-c \,x^{4}+a}\, e^{2} x}{24 \left(a \,e^{2}-c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{\left(5 a^{2} e^{4}-14 a c \,d^{2} e^{2}+29 c^{2} d^{4}\right) \sqrt{-c \,x^{4}+a}\, e^{2} x}{16 \left(a \,e^{2}-c \,d^{2}\right)^{3} \left(e \,x^{2}+d \right) d^{3}}"," ",0,"1/6*e^2/(a*e^2-c*d^2)/d*x*(-c*x^4+a)^(1/2)/(e*x^2+d)^3+5/24*e^2*(a*e^2-3*c*d^2)/(a*e^2-c*d^2)^2/d^2*x*(-c*x^4+a)^(1/2)/(e*x^2+d)^2+1/16*e^2*(5*a^2*e^4-14*a*c*d^2*e^2+29*c^2*d^4)/(a*e^2-c*d^2)^3/d^3*x*(-c*x^4+a)^(1/2)/(e*x^2+d)-35/16/(a*e^2-c*d^2)^3*d^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*c^3+5/16/(a*e^2-c*d^2)^3/d^4*e^6/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a^3+7/16/(a*e^2-c*d^2)^3*e^2/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a*c^2+19/16*c^3*d^2/(a*e^2-c*d^2)^3/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+5/48*c/d^2/(a*e^2-c*d^2)^3/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)*a^2*e^4-1/24*c^2/(a*e^2-c*d^2)^3/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)*a*e^2-5/16*c^(1/2)*e^5/(a*e^2-c*d^2)^3/d^3*a^(5/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+7/8*c^(3/2)*e^3/(a*e^2-c*d^2)^3/d*a^(3/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-29/16*c^(5/2)*e/(a*e^2-c*d^2)^3*d*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+5/16*c^(1/2)*e^5/(a*e^2-c*d^2)^3/d^3*a^(5/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-7/8*c^(3/2)*e^3/(a*e^2-c*d^2)^3/d*a^(3/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)+29/16*c^(5/2)*e/(a*e^2-c*d^2)^3*d*a^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticE((1/a^(1/2)*c^(1/2))^(1/2)*x,I)-17/16/(a*e^2-c*d^2)^3/d^2*e^4/(1/a^(1/2)*c^(1/2))^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*c^(1/2))^(1/2)*x,-a^(1/2)/c^(1/2)/d*e,(-1/a^(1/2)*c^(1/2))^(1/2)/(1/a^(1/2)*c^(1/2))^(1/2))*a^2*c","B"
164,1,160,98,0.010000," ","int((e*x^2+d)/(c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}}+\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}\, \sqrt{c}}"," ",0,"e*a^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)/c^(1/2)*(EllipticF(x*(-1/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(-1/a^(1/2)*c^(1/2))^(1/2),I))+d/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticF(x*(-1/a^(1/2)*c^(1/2))^(1/2),I)","A"
165,1,99,57,0.022000," ","int(1/(e*x^2+d)/(c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticPi \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , \frac{\sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}\, d}"," ",0,"1/d/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticPi((-1/a^(1/2)*c^(1/2))^(1/2)*x,a^(1/2)/c^(1/2)/d*e,(1/a^(1/2)*c^(1/2))^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2))","A"
166,1,158,42,0.053000," ","int((a^(1/2)+c^(1/2)*x^2)/(c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}}+\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}}"," ",0,"a^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*(EllipticF((-1/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((-1/a^(1/2)*c^(1/2))^(1/2)*x,I))+a^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticF((-1/a^(1/2)*c^(1/2))^(1/2)*x,I)","B"
167,1,165,44,0.044000," ","int((1+x^2*(c/a)^(1/2))/(c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}}+\frac{\sqrt{\frac{c}{a}}\, \sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}\, \sqrt{c}}"," ",0,"1/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticF((-1/a^(1/2)*c^(1/2))^(1/2)*x,I)+(c/a)^(1/2)*a^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)/c^(1/2)*(EllipticF((-1/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((-1/a^(1/2)*c^(1/2))^(1/2)*x,I))","B"
168,1,175,248,0.011000," ","int((e*x^2+d)/(-c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}-a}}-\frac{i \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}-a}\, \sqrt{c}}"," ",0,"-I*e*a^(1/2)/(-I/a^(1/2)*c^(1/2))^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4-a)^(1/2)/c^(1/2)*(EllipticF(x*(-I/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(-I/a^(1/2)*c^(1/2))^(1/2),I))+d/(-I/a^(1/2)*c^(1/2))^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4-a)^(1/2)*EllipticF(x*(-I/a^(1/2)*c^(1/2))^(1/2),I)","C"
169,1,110,335,0.022000," ","int(1/(e*x^2+d)/(-c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticPi \left(\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{-c \,x^{4}-a}\, d}"," ",0,"1/d/(-I/a^(1/2)*c^(1/2))^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(-c*x^4-a)^(1/2)*EllipticPi((-I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)*e/d,(I/a^(1/2)*c^(1/2))^(1/2)/(-I/a^(1/2)*c^(1/2))^(1/2))","C"
170,1,79,32,0.065000," ","int(1/(b*x^2+a)/(-5*x^4+4)^(1/2),x)","\frac{\sqrt{2}\, 5^{\frac{3}{4}} \sqrt{-\frac{\sqrt{5}\, x^{2}}{2}+1}\, \sqrt{\frac{\sqrt{5}\, x^{2}}{2}+1}\, \EllipticPi \left(\frac{5^{\frac{1}{4}} \sqrt{2}\, x}{2}, -\frac{2 \sqrt{5}\, b}{5 a}, \frac{\sqrt{-\frac{\sqrt{5}}{2}}\, \sqrt{2}\, 5^{\frac{3}{4}}}{5}\right)}{5 \sqrt{-5 x^{4}+4}\, a}"," ",0,"1/5/a*2^(1/2)*5^(3/4)*(1-1/2*x^2*5^(1/2))^(1/2)*(1+1/2*x^2*5^(1/2))^(1/2)/(-5*x^4+4)^(1/2)*EllipticPi(1/2*5^(1/4)*x*2^(1/2),-2/5*b/a*5^(1/2),1/5*(-1/2*5^(1/2))^(1/2)*2^(1/2)*5^(3/4))","B"
171,1,86,320,0.084000," ","int(1/(b*x^2+a)/(5*x^4+4)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{i \sqrt{5}\, x^{2}}{2}+1}\, \sqrt{\frac{i \sqrt{5}\, x^{2}}{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{i \sqrt{5}}\, x}{2}, \frac{2 i \sqrt{5}\, b}{5 a}, \frac{\sqrt{-\frac{i \sqrt{5}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{5}}}\right)}{\sqrt{i \sqrt{5}}\, \sqrt{5 x^{4}+4}\, a}"," ",0,"1/a/(1/2*I*5^(1/2))^(1/2)*(1-1/2*I*x^2*5^(1/2))^(1/2)*(1+1/2*I*x^2*5^(1/2))^(1/2)/(5*x^4+4)^(1/2)*EllipticPi((1/2*I*5^(1/2))^(1/2)*x,2/5*I*5^(1/2)*b/a,(-1/2*I*5^(1/2))^(1/2)/(1/2*I*5^(1/2))^(1/2))","C"
172,1,78,32,0.034000," ","int(1/(b*x^2+a)/(-d*x^4+4)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{\sqrt{d}\, x^{2}}{2}+1}\, \sqrt{\frac{\sqrt{d}\, x^{2}}{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, d^{\frac{1}{4}} x}{2}, -\frac{2 b}{a \sqrt{d}}, \frac{\sqrt{-\frac{\sqrt{d}}{2}}\, \sqrt{2}}{d^{\frac{1}{4}}}\right)}{\sqrt{-d \,x^{4}+4}\, a \,d^{\frac{1}{4}}}"," ",0,"1/a*2^(1/2)/d^(1/4)*(1-1/2*x^2*d^(1/2))^(1/2)*(1+1/2*x^2*d^(1/2))^(1/2)/(-d*x^4+4)^(1/2)*EllipticPi(1/2*d^(1/4)*x*2^(1/2),-2*b/a/d^(1/2),(-1/2*d^(1/2))^(1/2)*2^(1/2)/d^(1/4))","B"
173,1,86,308,0.033000," ","int(1/(b*x^2+a)/(d*x^4+4)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{i \sqrt{d}\, x^{2}}{2}+1}\, \sqrt{\frac{i \sqrt{d}\, x^{2}}{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{i \sqrt{d}}\, x}{2}, \frac{2 i b}{a \sqrt{d}}, \frac{\sqrt{-\frac{i \sqrt{d}}{2}}\, \sqrt{2}}{\sqrt{i \sqrt{d}}}\right)}{\sqrt{i \sqrt{d}}\, \sqrt{d \,x^{4}+4}\, a}"," ",0,"1/a/(1/2*I*d^(1/2))^(1/2)*(1-1/2*I*d^(1/2)*x^2)^(1/2)*(1+1/2*I*d^(1/2)*x^2)^(1/2)/(d*x^4+4)^(1/2)*EllipticPi((1/2*I*d^(1/2))^(1/2)*x,2*I/d^(1/2)*b/a,(-1/2*I*d^(1/2))^(1/2)/(1/2*I*d^(1/2))^(1/2))","C"
174,0,0,98,0.101000," ","int((b*x^2+a)^(1/2)/(-x^4+1)^(1/2),x)","\int \frac{\sqrt{b \,x^{2}+a}}{\sqrt{-x^{4}+1}}\, dx"," ",0,"int((b*x^2+a)^(1/2)/(-x^4+1)^(1/2),x)","F"
175,0,0,21,0.097000," ","int((e*x^2+c)^q*(b*x^4+a)^p,x)","\int \left(b \,x^{4}+a \right)^{p} \left(e \,x^{2}+c \right)^{q}\, dx"," ",0,"int((e*x^2+c)^q*(b*x^4+a)^p,x)","F"
176,0,0,196,0.087000," ","int((e*x^2+c)^3*(b*x^4+a)^p,x)","\int \left(e \,x^{2}+c \right)^{3} \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)^3*(b*x^4+a)^p,x)","F"
177,0,0,144,0.086000," ","int((e*x^2+c)^2*(b*x^4+a)^p,x)","\int \left(e \,x^{2}+c \right)^{2} \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)^2*(b*x^4+a)^p,x)","F"
178,0,0,90,0.082000," ","int((e*x^2+c)*(b*x^4+a)^p,x)","\int \left(e \,x^{2}+c \right) \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)*(b*x^4+a)^p,x)","F"
179,0,0,42,0.082000," ","int((b*x^4+a)^p,x)","\int \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((b*x^4+a)^p,x)","F"
180,0,0,113,0.091000," ","int((b*x^4+a)^p/(e*x^2+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{p}}{e \,x^{2}+c}\, dx"," ",0,"int((b*x^4+a)^p/(e*x^2+c),x)","F"
181,0,0,173,0.090000," ","int((b*x^4+a)^p/(e*x^2+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{p}}{\left(e \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^p/(e*x^2+c)^2,x)","F"
182,1,75,100,0.150000," ","int((-x^2+1)^3*(b*x^4+1)^p,x)","-\frac{x^{7} \hypergeom \left(\left[\frac{7}{4}, -p \right], \left[\frac{11}{4}\right], -b \,x^{4}\right)}{7}+\frac{3 x^{5} \hypergeom \left(\left[\frac{5}{4}, -p \right], \left[\frac{9}{4}\right], -b \,x^{4}\right)}{5}-x^{3} \hypergeom \left(\left[\frac{3}{4}, -p \right], \left[\frac{7}{4}\right], -b \,x^{4}\right)+x \hypergeom \left(\left[\frac{1}{4}, -p \right], \left[\frac{5}{4}\right], -b \,x^{4}\right)"," ",0,"-1/7*x^7*hypergeom([7/4,-p],[11/4],-b*x^4)+3/5*x^5*hypergeom([5/4,-p],[9/4],-b*x^4)-x^3*hypergeom([3/4,-p],[7/4],-b*x^4)+x*hypergeom([1/4,-p],[5/4],-b*x^4)","A"
183,1,56,80,0.093000," ","int((-x^2+1)^2*(b*x^4+1)^p,x)","\frac{x^{5} \hypergeom \left(\left[\frac{5}{4}, -p \right], \left[\frac{9}{4}\right], -b \,x^{4}\right)}{5}-\frac{2 x^{3} \hypergeom \left(\left[\frac{3}{4}, -p \right], \left[\frac{7}{4}\right], -b \,x^{4}\right)}{3}+x \hypergeom \left(\left[\frac{1}{4}, -p \right], \left[\frac{5}{4}\right], -b \,x^{4}\right)"," ",0,"1/5*x^5*hypergeom([5/4,-p],[9/4],-b*x^4)-2/3*x^3*hypergeom([3/4,-p],[7/4],-b*x^4)+x*hypergeom([1/4,-p],[5/4],-b*x^4)","A"
184,1,37,36,0.084000," ","int((-x^2+1)*(b*x^4+1)^p,x)","-\frac{x^{3} \hypergeom \left(\left[\frac{3}{4}, -p \right], \left[\frac{7}{4}\right], -b \,x^{4}\right)}{3}+x \hypergeom \left(\left[\frac{1}{4}, -p \right], \left[\frac{5}{4}\right], -b \,x^{4}\right)"," ",0,"x*hypergeom([1/4,-p],[5/4],-b*x^4)-1/3*x^3*hypergeom([3/4,-p],[7/4],-b*x^4)","A"
185,1,17,16,0.084000," ","int((b*x^4+1)^p,x)","x \hypergeom \left(\left[\frac{1}{4}, -p \right], \left[\frac{5}{4}\right], -b \,x^{4}\right)"," ",0,"x*hypergeom([1/4,-p],[5/4],-b*x^4)","A"
186,0,0,40,0.113000," ","int((b*x^4+1)^p/(-x^2+1),x)","\int \frac{\left(b \,x^{4}+1\right)^{p}}{-x^{2}+1}\, dx"," ",0,"int((b*x^4+1)^p/(-x^2+1),x)","F"
187,0,0,61,0.095000," ","int((b*x^4+1)^p/(-x^2+1)^2,x)","\int \frac{\left(b \,x^{4}+1\right)^{p}}{\left(-x^{2}+1\right)^{2}}\, dx"," ",0,"int((b*x^4+1)^p/(-x^2+1)^2,x)","F"
188,0,0,81,0.093000," ","int((b*x^4+1)^p/(-x^2+1)^3,x)","\int \frac{\left(b \,x^{4}+1\right)^{p}}{\left(-x^{2}+1\right)^{3}}\, dx"," ",0,"int((b*x^4+1)^p/(-x^2+1)^3,x)","F"
189,1,42,39,0.003000," ","int((e*x^2+d)^4/(-e^2*x^4+d^2),x)","-\frac{e^{2} x^{5}}{5}-\frac{4 d e \,x^{3}}{3}+\frac{8 d^{3} \arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-7 d^{2} x"," ",0,"-1/5*e^2*x^5-4/3*d*e*x^3-7*d^2*x+8*d^3/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
190,1,31,28,0.003000," ","int((e*x^2+d)^3/(-e^2*x^4+d^2),x)","-\frac{e \,x^{3}}{3}+\frac{4 d^{2} \arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-3 d x"," ",0,"-1/3*e*x^3-3*d*x+4*d^2/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
191,1,22,21,0.002000," ","int((e*x^2+d)^2/(-e^2*x^4+d^2),x)","\frac{2 d \arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-x"," ",0,"-x+2*d/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
192,1,16,16,0.002000," ","int((e*x^2+d)/(-e^2*x^4+d^2),x)","\frac{\arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}"," ",0,"1/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
193,1,55,50,0.011000," ","int(1/(e*x^2+d)/(-e^2*x^4+d^2),x)","\frac{x}{4 \left(e \,x^{2}+d \right) d^{2}}+\frac{\arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{4 \sqrt{d e}\, d^{2}}+\frac{\arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{2}}"," ",0,"1/4*x/d^2/(e*x^2+d)+1/2/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/4/d^2/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
194,1,73,65,0.011000," ","int(1/(e*x^2+d)^2/(-e^2*x^4+d^2),x)","\frac{5 e \,x^{3}}{16 \left(e \,x^{2}+d \right)^{2} d^{3}}+\frac{7 x}{16 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{\arctanh \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{3}}+\frac{7 \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{3}}"," ",0,"5/16/d^3/(e*x^2+d)^2*x^3*e+7/16*x/d^2/(e*x^2+d)^2+7/16/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/8/d^3/(d*e)^(1/2)*arctanh(1/(d*e)^(1/2)*e*x)","A"
195,1,1442,46,0.059000," ","int((e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x)","\frac{\sqrt{2}\, d^{\frac{3}{2}} e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}+2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}{x -\frac{\sqrt{d e}}{e}}\right)}{\sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{\sqrt{2}\, d^{\frac{3}{2}} e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}-2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}{x +\frac{\sqrt{d e}}{e}}\right)}{\sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{d \sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{-d e}}{e}\right) e +\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\right)}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{d \sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{-d e}}{e}\right) e -\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\right)}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{5 d \sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{d e}}{e}\right) e +\sqrt{d e}}{\sqrt{e}}+\sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\right)}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{5 d \sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{d e}}{e}\right) e -\sqrt{d e}}{\sqrt{e}}+\sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\right)}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{\sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, d e}{\sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{\sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, d e}{\sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{\sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{\sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}+\frac{\left(\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)\right)^{\frac{3}{2}} e}{6 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right) \sqrt{-d e}}-\frac{\left(2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)\right)^{\frac{3}{2}} e}{6 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}-\frac{\left(\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)\right)^{\frac{3}{2}} e}{6 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right) \sqrt{-d e}}+\frac{\left(2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)\right)^{\frac{3}{2}} e}{6 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(-\sqrt{-d e}+\sqrt{d e}\right)}"," ",0,"1/6*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))/(-d*e)^(1/2)*((x-1/e*(-d*e)^(1/2))^2*e+2*(-d*e)^(1/2)*(x-1/e*(-d*e)^(1/2)))^(3/2)+1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x-1/e*(-d*e)^(1/2))^2*e+2*(-d*e)^(1/2)*(x-1/e*(-d*e)^(1/2)))^(1/2)*x+1/4*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*ln(((x-1/e*(-d*e)^(1/2))*e+(-d*e)^(1/2))/e^(1/2)+((x-1/e*(-d*e)^(1/2))^2*e+2*(-d*e)^(1/2)*(x-1/e*(-d*e)^(1/2)))^(1/2))-1/6*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*d)^(3/2)-1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*d)^(1/2)*x-5/4*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*ln(((x-(d*e)^(1/2)/e)*e+(d*e)^(1/2))/e^(1/2)+((x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*d)^(1/2))-e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*((x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*d)^(1/2)+e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d^(3/2)*2^(1/2)*ln((4*d+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*2^(1/2)*d^(1/2)*((x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e)+2*d)^(1/2))/(x-(d*e)^(1/2)/e))-1/6*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))/(-d*e)^(1/2)*((x+1/e*(-d*e)^(1/2))^2*e-2*(-d*e)^(1/2)*(x+1/e*(-d*e)^(1/2)))^(3/2)+1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x+1/e*(-d*e)^(1/2))^2*e-2*(-d*e)^(1/2)*(x+1/e*(-d*e)^(1/2)))^(1/2)*x+1/4*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*ln(((x+1/e*(-d*e)^(1/2))*e-(-d*e)^(1/2))/e^(1/2)+((x+1/e*(-d*e)^(1/2))^2*e-2*(-d*e)^(1/2)*(x+1/e*(-d*e)^(1/2)))^(1/2))+1/6*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*d)^(3/2)-1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*((x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*d)^(1/2)*x-5/4*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*ln(((x+(d*e)^(1/2)/e)*e-(d*e)^(1/2))/e^(1/2)+((x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*d)^(1/2))+e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d*((x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*d)^(1/2)-e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/(-(-d*e)^(1/2)+(d*e)^(1/2))*d^(3/2)*2^(1/2)*ln((4*d-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*2^(1/2)*d^(1/2)*((x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e)+2*d)^(1/2))/(x+(d*e)^(1/2)/e))","B"
196,1,986,29,0.024000," ","int((e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x)","-\frac{\sqrt{2}\, \sqrt{d}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}+2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}{x -\frac{\sqrt{d e}}{e}}\right)}{2 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}+\frac{\sqrt{2}\, \sqrt{d}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}-2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}{x +\frac{\sqrt{d e}}{e}}\right)}{2 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}-\frac{\sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{-d e}}{e}\right) e +\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}-\frac{\sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{-d e}}{e}\right) e -\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}+\frac{\sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{d e}}{e}\right) e +\sqrt{d e}}{\sqrt{e}}+\sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}+\frac{\sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{d e}}{e}\right) e -\sqrt{d e}}{\sqrt{e}}+\sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}-\frac{\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, e}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{-d e}}+\frac{\sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, e}{2 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}+\frac{\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, e}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{-d e}}-\frac{\sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, e}{2 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right)}"," ",0,"-1/2*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/(-d*e)^(1/2)*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/2*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*ln(((x-(-d*e)^(1/2)/e)*e+(-d*e)^(1/2))/e^(1/2)+((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2))+1/2*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)+1/2*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*ln(((x-(d*e)^(1/2)/e)*e+(d*e)^(1/2))/e^(1/2)+(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2))-1/2*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*d^(1/2)*2^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)*d^(1/2)+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))/(x-(d*e)^(1/2)/e))+1/2*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/(-d*e)^(1/2)*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)-1/2*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*ln(((x+(-d*e)^(1/2)/e)*e-(-d*e)^(1/2))/e^(1/2)+((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2))-1/2*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)+1/2*e^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*ln(((x+(d*e)^(1/2)/e)*e-(d*e)^(1/2))/e^(1/2)+(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2))+1/2*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*d^(1/2)*2^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)*d^(1/2)-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))/(x+(d*e)^(1/2)/e))","B"
197,1,441,45,0.022000," ","int(1/(e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x)","-\frac{\sqrt{2}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}+2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}{x -\frac{\sqrt{d e}}{e}}\right)}{4 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{d}}+\frac{\sqrt{2}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}-2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}{x +\frac{\sqrt{d e}}{e}}\right)}{4 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{d}}-\frac{\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \left(x -\frac{\sqrt{-d e}}{e}\right) d}-\frac{\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}}{2 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \left(x +\frac{\sqrt{-d e}}{e}\right) d}"," ",0,"-1/2/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(x-(-d*e)^(1/2)/e)*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/4*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*2^(1/2)/d^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)*d^(1/2)+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))/(x-(d*e)^(1/2)/e))-1/2/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(x+(-d*e)^(1/2)/e)*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)+1/4*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))*2^(1/2)/d^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)*d^(1/2)-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))/(x+(d*e)^(1/2)/e))","B"
198,1,911,60,0.028000," ","int(1/(e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x)","-\frac{\sqrt{2}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}+2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}{x -\frac{\sqrt{d e}}{e}}\right)}{8 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) d^{\frac{3}{2}}}+\frac{\sqrt{2}\, e \ln \left(\frac{4 d +2 \sqrt{2}\, \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, \sqrt{d}-2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}{x +\frac{\sqrt{d e}}{e}}\right)}{8 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) d^{\frac{3}{2}}}+\frac{e}{4 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, d}-\frac{e}{4 \sqrt{d e}\, \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, d}-\frac{e x}{3 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, d^{2}}-\frac{e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{2 d +\left(x -\frac{\sqrt{d e}}{e}\right)^{2} e +2 \sqrt{d e}\, \left(x -\frac{\sqrt{d e}}{e}\right)}\, d^{2}}-\frac{e x}{3 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, d^{2}}-\frac{e x}{4 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \sqrt{2 d +\left(x +\frac{\sqrt{d e}}{e}\right)^{2} e -2 \sqrt{d e}\, \left(x +\frac{\sqrt{d e}}{e}\right)}\, d^{2}}-\frac{1}{6 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \left(x -\frac{\sqrt{-d e}}{e}\right) \sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, d}-\frac{1}{6 \left(\sqrt{-d e}+\sqrt{d e}\right) \left(\sqrt{-d e}-\sqrt{d e}\right) \left(x +\frac{\sqrt{-d e}}{e}\right) \sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, d}"," ",0,"-1/6/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(x-(-d*e)^(1/2)/e)/((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/3*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^2/((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)*x+1/4*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)-1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^2/(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)*x-1/8*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^(3/2)*2^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x-(d*e)^(1/2)/e)^2*e+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))^(1/2)*d^(1/2)+2*(d*e)^(1/2)*(x-(d*e)^(1/2)/e))/(x-(d*e)^(1/2)/e))-1/6/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(x+(-d*e)^(1/2)/e)/((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)-1/3*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^2/((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)*x-1/4*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d/(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)-1/4*e/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^2/(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)*x+1/8*e/(d*e)^(1/2)/((-d*e)^(1/2)+(d*e)^(1/2))/((-d*e)^(1/2)-(d*e)^(1/2))/d^(3/2)*2^(1/2)*ln((4*d+2*2^(1/2)*(2*d+(x+(d*e)^(1/2)/e)^2*e-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))^(1/2)*d^(1/2)-2*(d*e)^(1/2)*(x+(d*e)^(1/2)/e))/(x+(d*e)^(1/2)/e))","B"
199,1,132,127,0.073000," ","int((b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \left(2 \sqrt{-b \,x^{2}+a}\, b^{\frac{3}{2}} x^{3}-32 a^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+13 a^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)+11 \sqrt{-b \,x^{2}+a}\, a \sqrt{b}\, x \right)}{8 \sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \sqrt{b}}"," ",0,"-1/8*(-b^2*x^4+a^2)^(1/2)*(2*x^3*b^(3/2)*(-b*x^2+a)^(1/2)+11*(-b*x^2+a)^(1/2)*b^(1/2)*x*a+13*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*a^2-32*arctan(b^(1/2)*x/((-b*x+(a*b)^(1/2))/b*(b*x+(a*b)^(1/2)))^(1/2))*a^2)/(b*x^2+a)^(1/2)/(-b*x^2+a)^(1/2)/b^(1/2)","A"
200,1,107,90,0.022000," ","int((b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \left(-4 a \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+a \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)+\sqrt{-b \,x^{2}+a}\, \sqrt{b}\, x \right)}{2 \sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \sqrt{b}}"," ",0,"-1/2/(b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*(x*(-b*x^2+a)^(1/2)*b^(1/2)+a*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)-4*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*a)/(-b*x^2+a)^(1/2)/b^(1/2)","A"
201,1,69,53,0.024000," ","int((b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)}{\sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \sqrt{b}}"," ",0,"1/(b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)/(-b*x^2+a)^(1/2)/b^(1/2)","A"
202,1,249,63,0.055000," ","int(1/(b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \left(\sqrt{2}\, \sqrt{a}\, \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-\sqrt{2}\, \sqrt{a}\, \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-2 \sqrt{-a b}\, \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+2 \sqrt{-a b}\, \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)\right) \sqrt{b}}{2 \sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \left(\sqrt{-a b}+\sqrt{a b}\right) \left(\sqrt{-a b}-\sqrt{a b}\right) \sqrt{-a b}}"," ",0,"1/2*(-b^2*x^4+a^2)^(1/2)*b^(1/2)*(a^(1/2)*2^(1/2)*ln(2*b*(2^(1/2)*a^(1/2)*(-b*x^2+a)^(1/2)-(-a*b)^(1/2)*x+a)/(b*x-(-a*b)^(1/2)))*b^(1/2)-a^(1/2)*2^(1/2)*ln(2*b*(2^(1/2)*a^(1/2)*(-b*x^2+a)^(1/2)+(-a*b)^(1/2)*x+a)/(b*x+(-a*b)^(1/2)))*b^(1/2)-2*(-a*b)^(1/2)*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)+2*(-a*b)^(1/2)*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x))/(b*x^2+a)^(1/2)/(-b*x^2+a)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))/((-a*b)^(1/2)-(a*b)^(1/2))/(-a*b)^(1/2)","B"
203,1,488,101,0.056000," ","int(1/(b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \left(3 \sqrt{2}\, \sqrt{a}\, b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-3 \sqrt{2}\, \sqrt{a}\, b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-4 \sqrt{-a b}\, b \,x^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+4 \sqrt{-a b}\, b \,x^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)+3 \sqrt{2}\, a^{\frac{3}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-3 \sqrt{2}\, a^{\frac{3}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-4 \sqrt{-a b}\, a \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+4 \sqrt{-a b}\, a \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)-4 \sqrt{-a b}\, \sqrt{-b \,x^{2}+a}\, \sqrt{b}\, x \right) b^{\frac{5}{2}}}{4 \sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \left(\sqrt{-a b}+\sqrt{a b}\right)^{2} \left(\sqrt{-a b}-\sqrt{a b}\right)^{2} \sqrt{-a b}\, \left(b x +\sqrt{-a b}\right) \left(b x -\sqrt{-a b}\right)}"," ",0,"-1/4*(-b^2*x^4+a^2)^(1/2)*b^(5/2)*(3*2^(1/2)*ln(2*(a-(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x-(-a*b)^(1/2))*b)*x^2*b^(3/2)*a^(1/2)-3*2^(1/2)*ln(2*(a+(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x+(-a*b)^(1/2))*b)*x^2*b^(3/2)*a^(1/2)+3*2^(1/2)*ln(2*(a-(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x-(-a*b)^(1/2))*b)*a^(3/2)*b^(1/2)-3*2^(1/2)*ln(2*(a+(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x+(-a*b)^(1/2))*b)*a^(3/2)*b^(1/2)+4*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*x^2*b*(-a*b)^(1/2)-4*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*x^2*b*(-a*b)^(1/2)-4*b^(1/2)*(-a*b)^(1/2)*(-b*x^2+a)^(1/2)*x+4*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*a*(-a*b)^(1/2)-4*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*a*(-a*b)^(1/2))/(b*x^2+a)^(1/2)/(-b*x^2+a)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))^2/((-a*b)^(1/2)-(a*b)^(1/2))^2/(-a*b)^(1/2)/(b*x+(-a*b)^(1/2))/(b*x-(-a*b)^(1/2))","B"
204,1,711,138,0.059000," ","int(1/(b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \left(19 \sqrt{2}\, \sqrt{a}\, b^{\frac{5}{2}} x^{4} \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-19 \sqrt{2}\, \sqrt{a}\, b^{\frac{5}{2}} x^{4} \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-16 \sqrt{-a b}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+16 \sqrt{-a b}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)+38 \sqrt{2}\, a^{\frac{3}{2}} b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-38 \sqrt{2}\, a^{\frac{3}{2}} b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-32 \sqrt{-a b}\, a b \,x^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+32 \sqrt{-a b}\, a b \,x^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)-36 \sqrt{-a b}\, \sqrt{-b \,x^{2}+a}\, b^{\frac{3}{2}} x^{3}+19 \sqrt{2}\, a^{\frac{5}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{-a b}}\right)-19 \sqrt{2}\, a^{\frac{5}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{-a b}\, x +\sqrt{2}\, \sqrt{-b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{-a b}}\right)-16 \sqrt{-a b}\, a^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{\frac{\left(-b x +\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}{b}}}\right)+16 \sqrt{-a b}\, a^{2} \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)-52 \sqrt{-a b}\, \sqrt{-b \,x^{2}+a}\, a \sqrt{b}\, x \right) b^{\frac{9}{2}}}{16 \sqrt{b \,x^{2}+a}\, \sqrt{-b \,x^{2}+a}\, \sqrt{-a b}\, \left(\sqrt{-a b}+\sqrt{a b}\right)^{3} \left(-\sqrt{-a b}+\sqrt{a b}\right)^{3} \left(b x +\sqrt{-a b}\right)^{2} \left(b x -\sqrt{-a b}\right)^{2}}"," ",0,"-1/16*(-b^2*x^4+a^2)^(1/2)*b^(9/2)*(19*2^(1/2)*ln(2*(a-(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x-(-a*b)^(1/2))*b)*x^4*b^(5/2)*a^(1/2)-19*2^(1/2)*ln(2*(a+(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x+(-a*b)^(1/2))*b)*x^4*b^(5/2)*a^(1/2)+38*2^(1/2)*ln(2*(a-(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x-(-a*b)^(1/2))*b)*x^2*a^(3/2)*b^(3/2)-38*2^(1/2)*ln(2*(a+(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x+(-a*b)^(1/2))*b)*x^2*a^(3/2)*b^(3/2)+16*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*x^4*b^2*(-a*b)^(1/2)-16*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*x^4*b^2*(-a*b)^(1/2)-36*b^(3/2)*(-a*b)^(1/2)*(-b*x^2+a)^(1/2)*x^3+19*2^(1/2)*ln(2*(a-(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x-(-a*b)^(1/2))*b)*a^(5/2)*b^(1/2)-19*2^(1/2)*ln(2*(a+(-a*b)^(1/2)*x+2^(1/2)*(-b*x^2+a)^(1/2)*a^(1/2))/(b*x+(-a*b)^(1/2))*b)*a^(5/2)*b^(1/2)+32*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*x^2*a*b*(-a*b)^(1/2)-32*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*x^2*a*b*(-a*b)^(1/2)-52*a*(-a*b)^(1/2)*b^(1/2)*(-b*x^2+a)^(1/2)*x+16*arctan(1/(-b*x^2+a)^(1/2)*b^(1/2)*x)*a^2*(-a*b)^(1/2)-16*arctan(1/((-b*x+(a*b)^(1/2))*(b*x+(a*b)^(1/2))/b)^(1/2)*b^(1/2)*x)*a^2*(-a*b)^(1/2))/(b*x^2+a)^(1/2)/(-b*x^2+a)^(1/2)/(-a*b)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))^3/(-(-a*b)^(1/2)+(a*b)^(1/2))^3/(b*x+(-a*b)^(1/2))^2/(b*x-(-a*b)^(1/2))^2","B"
205,1,105,126,0.020000," ","int((-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-b^{2} x^{4}+a^{2}}\, \left(2 \sqrt{b \,x^{2}+a}\, b^{\frac{3}{2}} x^{3}+19 a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-11 \sqrt{b \,x^{2}+a}\, a \sqrt{b}\, x \right)}{8 \left(b \,x^{2}-a \right) \sqrt{b \,x^{2}+a}\, \sqrt{b}}"," ",0,"-1/8*(-b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*(2*x^3*b^(3/2)*(b*x^2+a)^(1/2)-11*x*a*b^(1/2)*(b*x^2+a)^(1/2)+19*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*a^2)/(b*x^2-a)/(b*x^2+a)^(1/2)/b^(1/2)","A"
206,1,85,89,0.014000," ","int((-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x)","-\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-b^{2} x^{4}+a^{2}}\, \left(3 a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)-\sqrt{b \,x^{2}+a}\, \sqrt{b}\, x \right)}{2 \left(b \,x^{2}-a \right) \sqrt{b \,x^{2}+a}\, \sqrt{b}}"," ",0,"-1/2*(-b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*(-x*(b*x^2+a)^(1/2)*b^(1/2)+3*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*a)/(b*x^2-a)/(b*x^2+a)^(1/2)/b^(1/2)","A"
207,1,54,52,0.014000," ","int((-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b^{2} x^{4}+a^{2}}\, \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{-b \,x^{2}+a}\, \sqrt{b \,x^{2}+a}\, \sqrt{b}}"," ",0,"1/(-b*x^2+a)^(1/2)/(b*x^2+a)^(1/2)/b^(1/2)*(-b^2*x^4+a^2)^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
208,1,267,62,0.063000," ","int(1/(-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-b^{2} x^{4}+a^{2}}\, \left(\sqrt{2}\, \sqrt{a}\, \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)-\sqrt{2}\, \sqrt{a}\, \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)-2 \sqrt{a b}\, \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)+2 \sqrt{a b}\, \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)\right) \sqrt{b}}{2 \left(b \,x^{2}-a \right) \sqrt{b \,x^{2}+a}\, \left(\sqrt{-a b}+\sqrt{a b}\right) \left(-\sqrt{-a b}+\sqrt{a b}\right) \sqrt{a b}}"," ",0,"1/2*(-b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*b^(1/2)*(a^(1/2)*2^(1/2)*ln(2*b*(2^(1/2)*a^(1/2)*(b*x^2+a)^(1/2)-(a*b)^(1/2)*x+a)/(b*x+(a*b)^(1/2)))*b^(1/2)-a^(1/2)*2^(1/2)*ln(2*b*(2^(1/2)*a^(1/2)*(b*x^2+a)^(1/2)+(a*b)^(1/2)*x+a)/(b*x-(a*b)^(1/2)))*b^(1/2)-2*(a*b)^(1/2)*ln((b^(1/2)*(-(b*x+(-a*b)^(1/2))/b*(-b*x+(-a*b)^(1/2)))^(1/2)+b*x)/b^(1/2))+2*(a*b)^(1/2)*ln((b^(1/2)*(b*x^2+a)^(1/2)+b*x)/b^(1/2)))/(b*x^2-a)/(b*x^2+a)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))/(-(-a*b)^(1/2)+(a*b)^(1/2))/(a*b)^(1/2)","B"
209,1,510,100,0.042000," ","int(1/(-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-b^{2} x^{4}+a^{2}}\, \left(3 \sqrt{2}\, \sqrt{a}\, b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)-3 \sqrt{2}\, \sqrt{a}\, b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)-4 \sqrt{a b}\, b \,x^{2} \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)+4 \sqrt{a b}\, b \,x^{2} \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)-3 \sqrt{2}\, a^{\frac{3}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)+3 \sqrt{2}\, a^{\frac{3}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)+4 \sqrt{a b}\, a \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)-4 \sqrt{a b}\, a \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)+4 \sqrt{a b}\, \sqrt{b \,x^{2}+a}\, \sqrt{b}\, x \right) b^{\frac{5}{2}}}{4 \left(b \,x^{2}-a \right) \sqrt{b \,x^{2}+a}\, \left(\sqrt{-a b}+\sqrt{a b}\right)^{2} \left(\sqrt{-a b}-\sqrt{a b}\right)^{2} \sqrt{a b}\, \left(b x -\sqrt{a b}\right) \left(b x +\sqrt{a b}\right)}"," ",0,"1/4*(-b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*b^(5/2)*(3*2^(1/2)*ln(2*(a-(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x+(a*b)^(1/2))*b)*x^2*b^(3/2)*a^(1/2)-3*2^(1/2)*ln(2*(a+(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x-(a*b)^(1/2))*b)*x^2*b^(3/2)*a^(1/2)-3*2^(1/2)*ln(2*(a-(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x+(a*b)^(1/2))*b)*a^(3/2)*b^(1/2)+3*2^(1/2)*ln(2*(a+(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x-(a*b)^(1/2))*b)*a^(3/2)*b^(1/2)+4*ln((b*x+(b*x^2+a)^(1/2)*b^(1/2))/b^(1/2))*x^2*b*(a*b)^(1/2)-4*ln((b*x+(-(b*x+(-a*b)^(1/2))*(-b*x+(-a*b)^(1/2))/b)^(1/2)*b^(1/2))/b^(1/2))*x^2*b*(a*b)^(1/2)+4*b^(1/2)*(a*b)^(1/2)*(b*x^2+a)^(1/2)*x-4*ln((b*x+(b*x^2+a)^(1/2)*b^(1/2))/b^(1/2))*a*(a*b)^(1/2)+4*ln((b*x+(-(b*x+(-a*b)^(1/2))*(-b*x+(-a*b)^(1/2))/b)^(1/2)*b^(1/2))/b^(1/2))*a*(a*b)^(1/2))/(b*x^2-a)/(b*x^2+a)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))^2/((-a*b)^(1/2)-(a*b)^(1/2))^2/(a*b)^(1/2)/(b*x-(a*b)^(1/2))/(b*x+(a*b)^(1/2))","B"
210,1,739,137,0.053000," ","int(1/(-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-b^{2} x^{4}+a^{2}}\, \left(19 \sqrt{2}\, \sqrt{a}\, b^{\frac{5}{2}} x^{4} \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)-19 \sqrt{2}\, \sqrt{a}\, b^{\frac{5}{2}} x^{4} \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)-16 \sqrt{a b}\, b^{2} x^{4} \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)+16 \sqrt{a b}\, b^{2} x^{4} \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)-38 \sqrt{2}\, a^{\frac{3}{2}} b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)+38 \sqrt{2}\, a^{\frac{3}{2}} b^{\frac{3}{2}} x^{2} \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)+32 \sqrt{a b}\, a b \,x^{2} \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)-32 \sqrt{a b}\, a b \,x^{2} \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)+36 \sqrt{a b}\, \sqrt{b \,x^{2}+a}\, b^{\frac{3}{2}} x^{3}+19 \sqrt{2}\, a^{\frac{5}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a -\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x +\sqrt{a b}}\right)-19 \sqrt{2}\, a^{\frac{5}{2}} \sqrt{b}\, \ln \left(\frac{2 \left(a +\sqrt{a b}\, x +\sqrt{2}\, \sqrt{b \,x^{2}+a}\, \sqrt{a}\right) b}{b x -\sqrt{a b}}\right)-16 \sqrt{a b}\, a^{2} \ln \left(\frac{b x +\sqrt{-\frac{\left(b x +\sqrt{-a b}\right) \left(-b x +\sqrt{-a b}\right)}{b}}\, \sqrt{b}}{\sqrt{b}}\right)+16 \sqrt{a b}\, a^{2} \ln \left(\frac{b x +\sqrt{b \,x^{2}+a}\, \sqrt{b}}{\sqrt{b}}\right)-52 \sqrt{a b}\, \sqrt{b \,x^{2}+a}\, a \sqrt{b}\, x \right) b^{\frac{9}{2}}}{16 \left(b \,x^{2}-a \right) \sqrt{b \,x^{2}+a}\, \left(\sqrt{-a b}+\sqrt{a b}\right)^{3} \left(-\sqrt{-a b}+\sqrt{a b}\right)^{3} \sqrt{a b}\, \left(b x -\sqrt{a b}\right)^{2} \left(b x +\sqrt{a b}\right)^{2}}"," ",0,"1/16*(-b*x^2+a)^(1/2)*(-b^2*x^4+a^2)^(1/2)*b^(9/2)*(19*ln(2*(a-(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x+(a*b)^(1/2))*b)*2^(1/2)*x^4*b^(5/2)*a^(1/2)-19*ln(2*(a+(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x-(a*b)^(1/2))*b)*2^(1/2)*x^4*b^(5/2)*a^(1/2)+16*ln((b*x+(b*x^2+a)^(1/2)*b^(1/2))/b^(1/2))*x^4*b^2*(a*b)^(1/2)-16*ln((b*x+(-(b*x+(-a*b)^(1/2))*(-b*x+(-a*b)^(1/2))/b)^(1/2)*b^(1/2))/b^(1/2))*x^4*b^2*(a*b)^(1/2)-38*ln(2*(a-(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x+(a*b)^(1/2))*b)*2^(1/2)*x^2*a^(3/2)*b^(3/2)+38*ln(2*(a+(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x-(a*b)^(1/2))*b)*2^(1/2)*x^2*a^(3/2)*b^(3/2)+36*b^(3/2)*(a*b)^(1/2)*(b*x^2+a)^(1/2)*x^3-32*ln((b*x+(b*x^2+a)^(1/2)*b^(1/2))/b^(1/2))*x^2*a*b*(a*b)^(1/2)+32*ln((b*x+(-(b*x+(-a*b)^(1/2))*(-b*x+(-a*b)^(1/2))/b)^(1/2)*b^(1/2))/b^(1/2))*x^2*a*b*(a*b)^(1/2)+19*ln(2*(a-(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x+(a*b)^(1/2))*b)*2^(1/2)*a^(5/2)*b^(1/2)-19*ln(2*(a+(a*b)^(1/2)*x+2^(1/2)*(b*x^2+a)^(1/2)*a^(1/2))/(b*x-(a*b)^(1/2))*b)*2^(1/2)*a^(5/2)*b^(1/2)-52*a*(a*b)^(1/2)*(b*x^2+a)^(1/2)*b^(1/2)*x+16*ln((b*x+(b*x^2+a)^(1/2)*b^(1/2))/b^(1/2))*a^2*(a*b)^(1/2)-16*ln((b*x+(-(b*x+(-a*b)^(1/2))*(-b*x+(-a*b)^(1/2))/b)^(1/2)*b^(1/2))/b^(1/2))*a^2*(a*b)^(1/2))/(b*x^2-a)/(b*x^2+a)^(1/2)/((-a*b)^(1/2)+(a*b)^(1/2))^3/(-(-a*b)^(1/2)+(a*b)^(1/2))^3/(a*b)^(1/2)/(b*x-(a*b)^(1/2))^2/(b*x+(a*b)^(1/2))^2","B"
211,1,25,24,0.013000," ","int((x^2-1)^(1/2)/(x^4-1)^(1/2),x)","\frac{\sqrt{x^{4}-1}\, \arcsinh \left(x \right)}{\sqrt{x^{2}-1}\, \sqrt{x^{2}+1}}"," ",0,"1/(x^2-1)^(1/2)*(x^4-1)^(1/2)/(x^2+1)^(1/2)*arcsinh(x)","A"
212,1,33,20,0.011000," ","int((x^2+1)^(1/2)/(x^4-1)^(1/2),x)","\frac{\sqrt{x^{4}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)}{\sqrt{x^{2}+1}\, \sqrt{x^{2}-1}}"," ",0,"1/(x^2+1)^(1/2)*(x^4-1)^(1/2)/(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
213,1,59,61,0.002000," ","int((-(x^2-1)^(1/2)+(x^2+1)^(1/2))/(x^4-1)^(1/2),x)","-\frac{\sqrt{x^{4}-1}\, \arcsinh \left(x \right)}{\sqrt{x^{2}-1}\, \sqrt{x^{2}+1}}+\frac{\sqrt{x^{4}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)}{\sqrt{x^{2}+1}\, \sqrt{x^{2}-1}}"," ",0,"-1/(x^2-1)^(1/2)*(x^4-1)^(1/2)/(x^2+1)^(1/2)*arcsinh(x)+1/(x^2+1)^(1/2)*(x^4-1)^(1/2)/(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
214,1,226,105,0.010000," ","int((e*x^2+d)^4/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{e^{2} x^{5}}{5 c}-\frac{b^{3} e^{3} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c^{3}}+\frac{6 b^{2} d \,e^{2} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c^{2}}-\frac{12 b \,d^{2} e \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c}-\frac{b \,e^{2} x^{3}}{3 c^{2}}+\frac{4 d e \,x^{3}}{3 c}+\frac{8 d^{3} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}}+\frac{b^{2} e^{2} x}{c^{3}}-\frac{5 b d e x}{c^{2}}+\frac{7 d^{2} x}{c}"," ",0,"1/5*e^2*x^5/c-1/3/c^2*x^3*b*e^2+4/3/c*x^3*d*e+1/c^3*b^2*e^2*x-5/c^2*b*d*e*x+7/c*d^2*x-1/c^3/((b*e-c*d)*c*e)^(1/2)*arctan(c*e*x/((b*e-c*d)*c*e)^(1/2))*b^3*e^3+6/c^2/((b*e-c*d)*c*e)^(1/2)*arctan(c*e*x/((b*e-c*d)*c*e)^(1/2))*b^2*d*e^2-12/c/((b*e-c*d)*c*e)^(1/2)*arctan(c*e*x/((b*e-c*d)*c*e)^(1/2))*b*d^2*e+8/((b*e-c*d)*c*e)^(1/2)*arctan(c*e*x/((b*e-c*d)*c*e)^(1/2))*d^3","B"
215,1,142,72,0.005000," ","int((e*x^2+d)^3/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{b^{2} e^{2} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c^{2}}-\frac{4 b d e \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c}+\frac{e \,x^{3}}{3 c}+\frac{4 d^{2} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}}-\frac{b e x}{c^{2}}+\frac{3 d x}{c}"," ",0,"1/3*e*x^3/c-1/c^2*b*e*x+3/c*d*x+1/c^2/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)*b^2*e^2-4/c/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)*b*d*e+4/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)*d^2","A"
216,1,79,52,0.004000," ","int((e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","-\frac{b e \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}\, c}+\frac{2 d \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}}+\frac{x}{c}"," ",0,"1/c*x-1/c/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)*b*e+2/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)*d","A"
217,1,33,37,0.002000," ","int((e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{\arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\sqrt{\left(b e -c d \right) c e}}"," ",0,"1/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)","A"
218,1,155,112,0.013000," ","int(1/(e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{c^{2} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\left(b e -2 c d \right)^{2} \sqrt{\left(b e -c d \right) c e}}+\frac{b e x}{2 \left(b e -2 c d \right)^{2} \left(e \,x^{2}+d \right) d}+\frac{b e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(b e -2 c d \right)^{2} \sqrt{d e}\, d}-\frac{c x}{\left(b e -2 c d \right)^{2} \left(e \,x^{2}+d \right)}-\frac{2 c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(b e -2 c d \right)^{2} \sqrt{d e}}"," ",0,"c^2/(b*e-2*c*d)^2/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)+1/2/(b*e-2*c*d)^2/d*x/(e*x^2+d)*b*e-1/(b*e-2*c*d)^2*x/(e*x^2+d)*c+1/2/(b*e-2*c*d)^2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*e-2/(b*e-2*c*d)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
219,1,319,161,0.013000," ","int(1/(e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{3 b^{2} e^{3} x^{3}}{8 \left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2} d^{2}}-\frac{2 b c \,e^{2} x^{3}}{\left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2} d}+\frac{5 c^{2} e \,x^{3}}{2 \left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2}}+\frac{5 b^{2} e^{2} x}{8 \left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2} d}-\frac{3 b c e x}{\left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2}}-\frac{c^{3} \arctan \left(\frac{c e x}{\sqrt{\left(b e -c d \right) c e}}\right)}{\left(b e -2 c d \right)^{3} \sqrt{\left(b e -c d \right) c e}}+\frac{7 c^{2} d x}{2 \left(b e -2 c d \right)^{3} \left(e \,x^{2}+d \right)^{2}}+\frac{3 b^{2} e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \left(b e -2 c d \right)^{3} \sqrt{d e}\, d^{2}}-\frac{2 b c e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(b e -2 c d \right)^{3} \sqrt{d e}\, d}+\frac{7 c^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(b e -2 c d \right)^{3} \sqrt{d e}}"," ",0,"-c^3/(b*e-2*c*d)^3/((b*e-c*d)*c*e)^(1/2)*arctan(1/((b*e-c*d)*c*e)^(1/2)*c*e*x)+3/8/(b*e-2*c*d)^3/(e*x^2+d)^2*e^3/d^2*x^3*b^2-2/(b*e-2*c*d)^3/(e*x^2+d)^2*e^2/d*x^3*b*c+5/2/(b*e-2*c*d)^3/(e*x^2+d)^2*e*x^3*c^2+5/8/(b*e-2*c*d)^3/(e*x^2+d)^2/d*x*b^2*e^2-3/(b*e-2*c*d)^3/(e*x^2+d)^2*x*b*c*e+7/2/(b*e-2*c*d)^3/(e*x^2+d)^2*d*x*c^2+3/8/(b*e-2*c*d)^3/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2*e^2-2/(b*e-2*c*d)^3/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c*e+7/2/(b*e-2*c*d)^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c^2","A"
220,1,7043,113,0.063000," ","int((e*x^2+d)^(5/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
221,1,4308,88,0.023000," ","int((e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\text{output too large to display}"," ",0,"-1/6*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(3/2)+1/4*c*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*x+5/4*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln((-(-(b*e-c*d)*c*e)^(1/2)/c+(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))*d+1/2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*b-c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*d-1/2*e^(3/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln((-(-(b*e-c*d)*c*e)^(1/2)/c+(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))*b+1/2*e^3/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))*b^2-2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))*b*d+2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))*d^2-1/6*c*e/(-d*e)^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(3/2)-1/4*c*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)*x-1/4*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*d*ln(((x-(-d*e)^(1/2)/e)*e+(-d*e)^(1/2))/e^(1/2)+((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2))+1/6*c*e/(-d*e)^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(3/2)-1/4*c*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)*x-1/4*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*d*ln(((x+(-d*e)^(1/2)/e)*e-(-d*e)^(1/2))/e^(1/2)+((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2))+1/6*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(3/2)+1/4*c*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*x+5/4*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln(((-(b*e-c*d)*c*e)^(1/2)/c+(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))*d-1/2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*b+c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)*d-1/2*e^(3/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln(((-(b*e-c*d)*c*e)^(1/2)/c+(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))*b-1/2*e^3/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))*b^2+2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))*b*d-2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))*d^2","B"
222,1,2252,62,0.023000," ","int((e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{b c \,e^{2} \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}+\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}-\frac{b c \,e^{2} \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}-\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}-\frac{c^{2} d e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}+\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{\left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}+\frac{c^{2} d e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}-\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{\left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}-\frac{\sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\, c^{2} e}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}}+\frac{\sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\, c^{2} e}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}}+\frac{c \sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right) e -\frac{\sqrt{-\left(b e -c d \right) c e}}{c}}{\sqrt{e}}+\sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}+\frac{c \sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right) e +\frac{\sqrt{-\left(b e -c d \right) c e}}{c}}{\sqrt{e}}+\sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}-\frac{c \sqrt{e}\, \ln \left(\frac{\left(x -\frac{\sqrt{-d e}}{e}\right) e +\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}-\frac{c \sqrt{e}\, \ln \left(\frac{\left(x +\frac{\sqrt{-d e}}{e}\right) e -\sqrt{-d e}}{\sqrt{e}}+\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}-\frac{\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, c e}{2 \sqrt{-d e}\, \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}+\frac{\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, c e}{2 \sqrt{-d e}\, \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right)}"," ",0,"-1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)+1/2*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln((-(-(b*e-c*d)*c*e)^(1/2)/c+(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))-1/2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))*b+c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)/c*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))*d-1/2*c*e/(-d*e)^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/2*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln(((x-(-d*e)^(1/2)/e)*e+(-d*e)^(1/2))/e^(1/2)+((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2))+1/2*c*e/(-d*e)^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)-1/2*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln(((x+(-d*e)^(1/2)/e)*e-(-d*e)^(1/2))/e^(1/2)+((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2))+1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2)+1/2*c*e^(1/2)/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))*ln(((-(b*e-c*d)*c*e)^(1/2)/c+(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)*e)/e^(1/2)+((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))+1/2*c*e^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))*b-c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)/c*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))*d","B"
223,1,771,90,0.021000," ","int(1/(e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","-\frac{c^{2} e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}+\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}+\frac{c^{2} e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}-\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \sqrt{-\frac{b e -2 c d}{c}}}-\frac{\sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, c}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(x -\frac{\sqrt{-d e}}{e}\right) d}-\frac{\sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, c}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(x +\frac{\sqrt{-d e}}{e}\right) d}"," ",0,"1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))-1/2*c/d/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(x-(-d*e)^(1/2)/e)*((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/2*c/d/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(x+(-d*e)^(1/2)/e)*((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)-1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))","B"
224,1,1637,127,0.021000," ","int(1/(e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x)","\frac{c^{3} e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}+\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \left(b e -2 c d \right) \sqrt{-\frac{b e -2 c d}{c}}}-\frac{c^{3} e \ln \left(\frac{-\frac{2 \left(b e -2 c d \right)}{c}-\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}+2 \sqrt{-\frac{b e -2 c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}{x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}}\right)}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \left(b e -2 c d \right) \sqrt{-\frac{b e -2 c d}{c}}}+\frac{c^{3} e}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \left(b e -2 c d \right) \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}-\frac{c^{3} e}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{-\left(b e -c d \right) c e}\, \left(b e -2 c d \right) \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}}+\frac{c^{2} e x}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(b e -2 c d \right) \sqrt{\left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e -\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x +\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\, d}+\frac{c^{2} e x}{2 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(b e -2 c d \right) \sqrt{\left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)^{2} e +\frac{2 \sqrt{-\left(b e -c d \right) c e}\, \left(x -\frac{\sqrt{-\left(b e -c d \right) c e}}{c e}\right)}{c}-\frac{b e -2 c d}{c}}\, d}-\frac{c e x}{3 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, d^{2}}-\frac{c e x}{3 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, d^{2}}-\frac{c}{6 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(x -\frac{\sqrt{-d e}}{e}\right) \sqrt{\left(x -\frac{\sqrt{-d e}}{e}\right)^{2} e +2 \sqrt{-d e}\, \left(x -\frac{\sqrt{-d e}}{e}\right)}\, d}-\frac{c}{6 \left(\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(-\sqrt{-d e}\, c +\sqrt{-\left(b e -c d \right) c e}\right) \left(x +\frac{\sqrt{-d e}}{e}\right) \sqrt{\left(x +\frac{\sqrt{-d e}}{e}\right)^{2} e -2 \sqrt{-d e}\, \left(x +\frac{\sqrt{-d e}}{e}\right)}\, d}"," ",0,"1/2*c^3*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(b*e-2*c*d)/((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2)+1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(b*e-2*c*d)/d/((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2)*x-1/2*c^3*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(b*e-2*c*d)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c+2*(-(b*e-2*c*d)/c)^(1/2)*((x+(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e-2*(-(b*e-c*d)*c*e)^(1/2)*(x+(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2))/(x+(-(b*e-c*d)*c*e)^(1/2)/c/e))-1/6*c/d/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(x-(-d*e)^(1/2)/e)/((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)-1/3*c*e/d^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/((x-(-d*e)^(1/2)/e)^2*e+2*(-d*e)^(1/2)*(x-(-d*e)^(1/2)/e))^(1/2)*x-1/6*c/d/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(x+(-d*e)^(1/2)/e)/((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)-1/3*c*e/d^2/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/((x+(-d*e)^(1/2)/e)^2*e-2*(-d*e)^(1/2)*(x+(-d*e)^(1/2)/e))^(1/2)*x-1/2*c^3*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(b*e-2*c*d)/((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2)+1/2*c^2*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(b*e-2*c*d)/d/((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2)*x+1/2*c^3*e/((-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(-d*e)^(1/2)*c+(-(b*e-c*d)*c*e)^(1/2))/(-(b*e-c*d)*c*e)^(1/2)/(b*e-2*c*d)/(-(b*e-2*c*d)/c)^(1/2)*ln((-2*(b*e-2*c*d)/c+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c+2*(-(b*e-2*c*d)/c)^(1/2)*((x-(-(b*e-c*d)*c*e)^(1/2)/c/e)^2*e+2*(-(b*e-c*d)*c*e)^(1/2)*(x-(-(b*e-c*d)*c*e)^(1/2)/c/e)/c-(b*e-2*c*d)/c)^(1/2))/(x-(-(b*e-c*d)*c*e)^(1/2)/c/e))","B"
225,1,263,185,0.155000," ","int((x^2+1)^3*(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x^{7}}{9}+\frac{4 \sqrt{x^{4}+x^{2}+1}\, x^{5}}{9}+\frac{32 \sqrt{x^{4}+x^{2}+1}\, x^{3}}{45}+\frac{29 \sqrt{x^{4}+x^{2}+1}\, x}{45}+\frac{32 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{45 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{104 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{45 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/9*x^7*(x^4+x^2+1)^(1/2)+4/9*x^5*(x^4+x^2+1)^(1/2)+32/45*x^3*(x^4+x^2+1)^(1/2)+29/45*x*(x^4+x^2+1)^(1/2)+32/45/(-2+2*I*3^(1/2))^(1/2)*(1-(-1/2+1/2*I*3^(1/2))*x^2)^(1/2)*(1-(-1/2-1/2*I*3^(1/2))*x^2)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*x*(-2+2*I*3^(1/2))^(1/2),1/2*(-2+2*I*3^(1/2))^(1/2))-104/45/(-2+2*I*3^(1/2))^(1/2)*(1-(-1/2+1/2*I*3^(1/2))*x^2)^(1/2)*(1-(-1/2-1/2*I*3^(1/2))*x^2)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*x*(-2+2*I*3^(1/2))^(1/2),1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*x*(-2+2*I*3^(1/2))^(1/2),1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
226,1,248,170,0.009000," ","int((x^2+1)^2*(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x^{5}}{7}+\frac{3 \sqrt{x^{4}+x^{2}+1}\, x^{3}}{7}+\frac{11 \sqrt{x^{4}+x^{2}+1}\, x}{21}+\frac{20 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{21 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{8 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/7*(x^4+x^2+1)^(1/2)*x^5+3/7*(x^4+x^2+1)^(1/2)*x^3+11/21*(x^4+x^2+1)^(1/2)*x+20/21/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-8/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
227,1,233,155,0.005000," ","int((x^2+1)*(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x^{3}}{5}+\frac{2 \sqrt{x^{4}+x^{2}+1}\, x}{5}+\frac{6 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{5 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{12 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{5 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/5*(x^4+x^2+1)^(1/2)*x^3+2/5*(x^4+x^2+1)^(1/2)*x+6/5/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-12/5/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
228,1,293,151,0.107000," ","int((x^4+x^2+1)^(1/2)/(x^2+1),x)","\frac{4 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{4 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"-4/(-2+2*I*3^(1/2))^(1/2)*(1+1/2*x^2-1/2*I*x^2*3^(1/2))^(1/2)*(1+1/2*x^2+1/2*I*x^2*3^(1/2))^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+4/(-2+2*I*3^(1/2))^(1/2)*(1+1/2*x^2-1/2*I*x^2*3^(1/2))^(1/2)*(1+1/2*x^2+1/2*I*x^2*3^(1/2))^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/(-1/2+1/2*I*3^(1/2))^(1/2)*(1+1/2*x^2-1/2*I*x^2*3^(1/2))^(1/2)*(1+1/2*x^2+1/2*I*x^2*3^(1/2))^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
229,1,224,58,0.020000," ","int((x^4+x^2+1)^(1/2)/(x^2+1)^2,x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{2 x^{2}+2}+\frac{\sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/2*x*(x^4+x^2+1)^(1/2)/(x^2+1)+1/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+2/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
230,1,333,94,0.025000," ","int((x^4+x^2+1)^(1/2)/(x^2+1)^3,x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{4 \left(x^{2}+1\right)^{2}}+\frac{\sqrt{x^{4}+x^{2}+1}\, x}{4 x^{2}+4}-\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"1/4*x*(x^4+x^2+1)^(1/2)/(x^2+1)^2+1/4*(x^4+x^2+1)^(1/2)/(x^2+1)*x+1/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-1/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/2/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
231,1,438,172,0.026000," ","int((x^4+x^2+1)^(1/2)/(x^2+1)^4,x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{6 \left(x^{2}+1\right)^{3}}+\frac{\sqrt{x^{4}+x^{2}+1}\, x}{6 \left(x^{2}+1\right)^{2}}+\frac{\sqrt{x^{4}+x^{2}+1}\, x}{3 x^{2}+3}-\frac{4 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{4 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"1/6*x*(x^4+x^2+1)^(1/2)/(x^2+1)^3+1/6*(x^4+x^2+1)^(1/2)/(x^2+1)^2*x+1/3*(x^4+x^2+1)^(1/2)/(x^2+1)*x-1/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+4/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-4/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/2/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
232,1,233,165,0.031000," ","int((x^2+1)^3/(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x^{3}}{5}+\frac{11 \sqrt{x^{4}+x^{2}+1}\, x}{15}+\frac{8 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{15 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{56 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{15 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/5*(x^4+x^2+1)^(1/2)*x^3+11/15*(x^4+x^2+1)^(1/2)*x+8/15/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-56/15/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
233,1,218,149,0.009000," ","int((x^2+1)^2/(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{3}+\frac{4 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{16 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"1/3*(x^4+x^2+1)^(1/2)*x+4/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-16/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))","C"
234,1,205,135,0.007000," ","int((x^2+1)/(x^4+x^2+1)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{4 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}"," ",0,"-4/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))+2/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))","C"
235,1,104,74,0.020000," ","int(1/(x^2+1)/(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"1/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
236,1,397,132,0.024000," ","int(1/(x^2+1)^2/(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{2 x^{2}+2}-\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"1/2*(x^4+x^2+1)^(1/2)/(x^2+1)*x-1/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+2/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-2/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
237,1,418,152,0.024000," ","int(1/(x^2+1)^3/(x^4+x^2+1)^(1/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{4 \left(x^{2}+1\right)^{2}}+\frac{3 \sqrt{x^{4}+x^{2}+1}\, x}{4 \left(x^{2}+1\right)}-\frac{3 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{3 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}"," ",0,"1/4*(x^4+x^2+1)^(1/2)/(x^2+1)^2*x+3/4*(x^4+x^2+1)^(1/2)/(x^2+1)*x-1/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/2/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
238,1,268,156,0.037000," ","int((x^2+1)^3/(x^4+x^2+1)^(3/2),x)","\frac{8 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{4 \left(\frac{1}{6} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}-\frac{8 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{6 \left(\frac{1}{6} x^{3}+\frac{1}{3} x \right)}{\sqrt{x^{4}+x^{2}+1}}-\frac{6 \left(-\frac{1}{3} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"-4*(-1/6*x+1/6*x^3)/(x^4+x^2+1)^(1/2)+8/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-8/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))-6*(1/6*x^3+1/3*x)/(x^4+x^2+1)^(1/2)-6*(-1/3*x^3-1/6*x)/(x^4+x^2+1)^(1/2)","C"
239,1,268,99,0.008000," ","int((x^2+1)^2/(x^4+x^2+1)^(3/2),x)","\frac{4 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(\frac{1}{6} x^{3}+\frac{1}{3} x \right)}{\sqrt{x^{4}+x^{2}+1}}+\frac{8 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{4 \left(-\frac{1}{3} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(\frac{1}{6} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"-2*(1/6*x^3+1/3*x)/(x^4+x^2+1)^(1/2)+4/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+8/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))-4*(-1/3*x^3-1/6*x)/(x^4+x^2+1)^(1/2)-2*(1/6*x^3-1/6*x)/(x^4+x^2+1)^(1/2)","C"
240,1,247,97,0.009000," ","int((x^2+1)/(x^4+x^2+1)^(3/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(-\frac{1}{3} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}+\frac{4 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)+\EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{2 \left(\frac{1}{6} x^{3}-\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"-2*(-1/3*x^3-1/6*x)/(x^4+x^2+1)^(1/2)+2/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+4/3/(-2+2*I*3^(1/2))^(1/2)*(-(-1/2+1/2*I*3^(1/2))*x^2+1)^(1/2)*(-(-1/2-1/2*I*3^(1/2))*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*(EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2)))-2*(1/6*x^3-1/6*x)/(x^4+x^2+1)^(1/2)","C"
241,1,398,172,0.022000," ","int(1/(x^2+1)/(x^4+x^2+1)^(3/2),x)","\frac{8 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{8 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{\sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(\frac{1}{3} x^{3}+\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"-2*(1/3*x^3+1/6*x)/(x^4+x^2+1)^(1/2)+2/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-8/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+8/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+1/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
242,1,419,110,0.026000," ","int(1/(x^2+1)^2/(x^4+x^2+1)^(3/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{2 x^{2}+2}-\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{5 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{2 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(\frac{1}{6} x^{3}+\frac{1}{3} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"1/2*(x^4+x^2+1)^(1/2)/(x^2+1)*x-2*(1/6*x^3+1/3*x)/(x^4+x^2+1)^(1/2)-5/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+2/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-2/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+2/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
243,1,439,192,0.028000," ","int(1/(x^2+1)^3/(x^4+x^2+1)^(3/2),x)","\frac{\sqrt{x^{4}+x^{2}+1}\, x}{4 \left(x^{2}+1\right)^{2}}+\frac{5 \sqrt{x^{4}+x^{2}+1}\, x}{4 \left(x^{2}+1\right)}-\frac{19 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticE \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}-\frac{10 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{19 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{3}}\, x}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{3 \sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}\, \left(1+i \sqrt{3}\right)}+\frac{3 \sqrt{\frac{x^{2}}{2}-\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \sqrt{\frac{x^{2}}{2}+\frac{i \sqrt{3}\, x^{2}}{2}+1}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}-\frac{2 \left(-\frac{1}{6} x^{3}+\frac{1}{6} x \right)}{\sqrt{x^{4}+x^{2}+1}}"," ",0,"1/4*(x^4+x^2+1)^(1/2)/(x^2+1)^2*x+5/4*(x^4+x^2+1)^(1/2)/(x^2+1)*x-2*(1/6*x-1/6*x^3)/(x^4+x^2+1)^(1/2)-10/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+19/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticF(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))-19/3/(-2+2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)/(1+I*3^(1/2))*EllipticE(1/2*(-2+2*I*3^(1/2))^(1/2)*x,1/2*(-2+2*I*3^(1/2))^(1/2))+3/2/(-1/2+1/2*I*3^(1/2))^(1/2)*(1/2*x^2-1/2*I*3^(1/2)*x^2+1)^(1/2)*(1/2*x^2+1/2*I*3^(1/2)*x^2+1)^(1/2)/(x^4+x^2+1)^(1/2)*EllipticPi((-1/2+1/2*I*3^(1/2))^(1/2)*x,-1/(-1/2+1/2*I*3^(1/2)),(-1/2-1/2*I*3^(1/2))^(1/2)/(-1/2+1/2*I*3^(1/2))^(1/2))","C"
244,1,136,123,0.001000," ","int((e*x^2+d)^4*(c*x^4+b*x^2+a),x)","\frac{c \,e^{4} x^{13}}{13}+\frac{\left(e^{4} b +4 d \,e^{3} c \right) x^{11}}{11}+\frac{\left(e^{4} a +4 d \,e^{3} b +6 d^{2} e^{2} c \right) x^{9}}{9}+\frac{\left(4 d \,e^{3} a +6 d^{2} e^{2} b +4 d^{3} e c \right) x^{7}}{7}+a \,d^{4} x +\frac{\left(6 d^{2} e^{2} a +4 d^{3} e b +d^{4} c \right) x^{5}}{5}+\frac{\left(4 d^{3} e a +d^{4} b \right) x^{3}}{3}"," ",0,"1/13*c*e^4*x^13+1/11*(b*e^4+4*c*d*e^3)*x^11+1/9*(a*e^4+4*b*d*e^3+6*c*d^2*e^2)*x^9+1/7*(4*a*d*e^3+6*b*d^2*e^2+4*c*d^3*e)*x^7+1/5*(6*a*d^2*e^2+4*b*d^3*e+c*d^4)*x^5+1/3*(4*a*d^3*e+b*d^4)*x^3+a*d^4*x","A"
245,1,103,93,0.001000," ","int((e*x^2+d)^3*(c*x^4+b*x^2+a),x)","\frac{c \,e^{3} x^{11}}{11}+\frac{\left(e^{3} b +3 d \,e^{2} c \right) x^{9}}{9}+\frac{\left(a \,e^{3}+3 d \,e^{2} b +3 c \,d^{2} e \right) x^{7}}{7}+a \,d^{3} x +\frac{\left(3 d \,e^{2} a +3 d^{2} e b +d^{3} c \right) x^{5}}{5}+\frac{\left(3 d^{2} e a +d^{3} b \right) x^{3}}{3}"," ",0,"1/11*c*e^3*x^11+1/9*(b*e^3+3*c*d*e^2)*x^9+1/7*(a*e^3+3*b*d*e^2+3*c*d^2*e)*x^7+1/5*(3*a*d*e^2+3*b*d^2*e+c*d^3)*x^5+1/3*(3*a*d^2*e+b*d^3)*x^3+a*d^3*x","A"
246,1,70,65,0.001000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a),x)","\frac{c \,e^{2} x^{9}}{9}+\frac{\left(b \,e^{2}+2 d c e \right) x^{7}}{7}+\frac{\left(a \,e^{2}+2 b d e +c \,d^{2}\right) x^{5}}{5}+a \,d^{2} x +\frac{\left(2 d e a +b \,d^{2}\right) x^{3}}{3}"," ",0,"1/9*c*e^2*x^9+1/7*(b*e^2+2*c*d*e)*x^7+1/5*(a*e^2+2*b*d*e+c*d^2)*x^5+1/3*(2*a*d*e+b*d^2)*x^3+a*d^2*x","A"
247,1,37,36,0.001000," ","int((e*x^2+d)*(c*x^4+b*x^2+a),x)","\frac{c e \,x^{7}}{7}+\frac{\left(b e +c d \right) x^{5}}{5}+a d x +\frac{\left(a e +b d \right) x^{3}}{3}"," ",0,"a*d*x+1/3*(a*e+b*d)*x^3+1/5*(b*e+c*d)*x^5+1/7*c*e*x^7","A"
248,1,84,56,0.004000," ","int((c*x^4+b*x^2+a)/(e*x^2+d),x)","\frac{c \,x^{3}}{3 e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-\frac{b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e}+\frac{c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}+\frac{b x}{e}-\frac{c d x}{e^{2}}"," ",0,"1/3*c/e*x^3+1/e*b*x-c*d/e^2*x+1/(d*e)^(1/2)*a*arctan(1/(d*e)^(1/2)*e*x)-1/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*d+1/(d*e)^(1/2)*c*d^2/e^2*arctan(1/(d*e)^(1/2)*e*x)","A"
249,1,118,71,0.009000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{a x}{2 \left(e \,x^{2}+d \right) d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{b x}{2 \left(e \,x^{2}+d \right) e}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}+\frac{c d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}+\frac{c x}{e^{2}}"," ",0,"c/e^2*x+1/2/(e*x^2+d)*a/d*x-1/2/e*x/(e*x^2+d)*b+1/2/(e*x^2+d)*c*d/e^2*x+1/2/(d*e)^(1/2)*a/d*arctan(1/(d*e)^(1/2)*e*x)+1/2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-3/2/(d*e)^(1/2)*c*d/e^2*arctan(1/(d*e)^(1/2)*e*x)","A"
250,1,131,101,0.008000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^3,x)","\frac{3 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d e}+\frac{3 c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}+\frac{\frac{\left(3 a \,e^{2}+b d e -5 c \,d^{2}\right) x^{3}}{8 d^{2} e}+\frac{\left(5 a \,e^{2}-b d e -3 c \,d^{2}\right) x}{8 d \,e^{2}}}{\left(e \,x^{2}+d \right)^{2}}"," ",0,"(1/8*(3*a*e^2+b*d*e-5*c*d^2)/d^2/e*x^3+1/8*(5*a*e^2-b*d*e-3*c*d^2)/d/e^2*x)/(e*x^2+d)^2+3/8/(d*e)^(1/2)*a/d^2*arctan(1/(d*e)^(1/2)*e*x)+1/8/d/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+3/8/(d*e)^(1/2)*c/e^2*arctan(1/(d*e)^(1/2)*e*x)","A"
251,1,158,134,0.009000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^4,x)","\frac{5 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{3}}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{2} e}+\frac{c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d \,e^{2}}+\frac{\frac{\left(5 a \,e^{2}+b d e +c \,d^{2}\right) x^{5}}{16 d^{3}}+\frac{\left(5 a \,e^{2}+b d e -c \,d^{2}\right) x^{3}}{6 d^{2} e}+\frac{\left(11 a \,e^{2}-b d e -c \,d^{2}\right) x}{16 d \,e^{2}}}{\left(e \,x^{2}+d \right)^{3}}"," ",0,"(1/16*(5*a*e^2+b*d*e+c*d^2)/d^3*x^5+1/6*(5*a*e^2+b*d*e-c*d^2)/d^2/e*x^3+1/16*(11*a*e^2-b*d*e-c*d^2)/d/e^2*x)/(e*x^2+d)^3+5/16/(d*e)^(1/2)*a/d^3*arctan(1/(d*e)^(1/2)*e*x)+1/16/d^2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+1/16/(d*e)^(1/2)*c/d/e^2*arctan(1/(d*e)^(1/2)*e*x)","A"
252,1,219,209,0.001000," ","int((e*x^2+d)^3*(c*x^4+b*x^2+a)^2,x)","\frac{c^{2} e^{3} x^{15}}{15}+\frac{\left(2 e^{3} b c +3 d \,e^{2} c^{2}\right) x^{13}}{13}+\frac{\left(6 b c d \,e^{2}+3 c^{2} d^{2} e +\left(2 a c +b^{2}\right) e^{3}\right) x^{11}}{11}+\frac{\left(2 a b \,e^{3}+6 b c \,d^{2} e +c^{2} d^{3}+3 \left(2 a c +b^{2}\right) d \,e^{2}\right) x^{9}}{9}+\frac{\left(a^{2} e^{3}+6 a b d \,e^{2}+2 b c \,d^{3}+3 \left(2 a c +b^{2}\right) d^{2} e \right) x^{7}}{7}+a^{2} d^{3} x +\frac{\left(3 a^{2} d \,e^{2}+6 a b \,d^{2} e +\left(2 a c +b^{2}\right) d^{3}\right) x^{5}}{5}+\frac{\left(3 d^{2} e \,a^{2}+2 d^{3} a b \right) x^{3}}{3}"," ",0,"1/15*c^2*e^3*x^15+1/13*(2*b*c*e^3+3*c^2*d*e^2)*x^13+1/11*(3*d^2*e*c^2+6*d*e^2*b*c+e^3*(2*a*c+b^2))*x^11+1/9*(c^2*d^3+6*d^2*e*b*c+3*d*e^2*(2*a*c+b^2)+2*e^3*a*b)*x^9+1/7*(2*b*c*d^3+3*d^2*e*(2*a*c+b^2)+6*a*b*d*e^2+a^2*e^3)*x^7+1/5*(d^3*(2*a*c+b^2)+6*d^2*e*a*b+3*d*e^2*a^2)*x^5+1/3*(3*a^2*d^2*e+2*a*b*d^3)*x^3+a^2*d^3*x","A"
253,1,155,143,0.000000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a)^2,x)","\frac{c^{2} e^{2} x^{13}}{13}+\frac{\left(2 b c \,e^{2}+2 c^{2} d e \right) x^{11}}{11}+\frac{\left(4 b c d e +c^{2} d^{2}+\left(2 a c +b^{2}\right) e^{2}\right) x^{9}}{9}+\frac{\left(2 a b \,e^{2}+2 b c \,d^{2}+2 \left(2 a c +b^{2}\right) d e \right) x^{7}}{7}+a^{2} d^{2} x +\frac{\left(a^{2} e^{2}+4 a b d e +\left(2 a c +b^{2}\right) d^{2}\right) x^{5}}{5}+\frac{\left(2 d e \,a^{2}+2 d^{2} a b \right) x^{3}}{3}"," ",0,"1/13*c^2*e^2*x^13+1/11*(2*b*c*e^2+2*c^2*d*e)*x^11+1/9*(c^2*d^2+4*d*e*b*c+e^2*(2*a*c+b^2))*x^9+1/7*(2*b*c*d^2+2*d*e*(2*a*c+b^2)+2*a*b*e^2)*x^7+1/5*(d^2*(2*a*c+b^2)+4*a*b*d*e+e^2*a^2)*x^5+1/3*(2*a^2*d*e+2*a*b*d^2)*x^3+a^2*d^2*x","A"
254,1,91,86,0.000000," ","int((e*x^2+d)*(c*x^4+b*x^2+a)^2,x)","\frac{c^{2} e \,x^{11}}{11}+\frac{\left(2 e b c +d \,c^{2}\right) x^{9}}{9}+\frac{\left(2 b c d +\left(2 a c +b^{2}\right) e \right) x^{7}}{7}+\frac{\left(2 a b e +\left(2 a c +b^{2}\right) d \right) x^{5}}{5}+a^{2} d x +\frac{\left(e \,a^{2}+2 d a b \right) x^{3}}{3}"," ",0,"1/11*c^2*e*x^11+1/9*(2*b*c*e+c^2*d)*x^9+1/7*(2*b*c*d+e*(2*a*c+b^2))*x^7+1/5*(d*(2*a*c+b^2)+2*a*b*e)*x^5+1/3*(a^2*e+2*a*b*d)*x^3+a^2*d*x","A"
255,1,42,41,0.001000," ","int((c*x^4+b*x^2+a)^2,x)","\frac{c^{2} x^{9}}{9}+\frac{2 b c \,x^{7}}{7}+\frac{2 a b \,x^{3}}{3}+\frac{\left(2 a c +b^{2}\right) x^{5}}{5}+a^{2} x"," ",0,"1/9*c^2*x^9+2/7*b*c*x^7+2/3*a*b*x^3+1/5*(2*a*c+b^2)*x^5+a^2*x","A"
256,1,267,129,0.005000," ","int((c*x^4+b*x^2+a)^2/(e*x^2+d),x)","\frac{c^{2} x^{7}}{7 e}+\frac{2 b c \,x^{5}}{5 e}-\frac{c^{2} d \,x^{5}}{5 e^{2}}+\frac{2 a c \,x^{3}}{3 e}+\frac{b^{2} x^{3}}{3 e}-\frac{2 b c d \,x^{3}}{3 e^{2}}+\frac{c^{2} d^{2} x^{3}}{3 e^{3}}+\frac{a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}}-\frac{2 a b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e}+\frac{2 a c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}+\frac{b^{2} d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}-\frac{2 b c \,d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{3}}+\frac{c^{2} d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{4}}+\frac{2 a b x}{e}-\frac{2 a c d x}{e^{2}}-\frac{b^{2} d x}{e^{2}}+\frac{2 b c \,d^{2} x}{e^{3}}-\frac{c^{2} d^{3} x}{e^{4}}"," ",0,"1/7*c^2/e*x^7+2/5/e*x^5*b*c-1/5*c^2*d/e^2*x^5+2/3*a*c/e*x^3+1/3/e*x^3*b^2-2/3/e^2*x^3*b*c*d+1/3*c^2*d^2/e^3*x^3+2/e*a*b*x-2*a*c*d/e^2*x-1/e^2*b^2*d*x+2/e^3*b*c*d^2*x-c^2*d^3/e^4*x+1/(d*e)^(1/2)*a^2*arctan(1/(d*e)^(1/2)*e*x)-2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*b*d+2/(d*e)^(1/2)*a*c*d^2/e^2*arctan(1/(d*e)^(1/2)*e*x)+1/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2*d^2-2/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c*d^3+1/(d*e)^(1/2)*c^2*d^4/e^4*arctan(1/(d*e)^(1/2)*e*x)","B"
257,1,320,150,0.011000," ","int((c*x^4+b*x^2+a)^2/(e*x^2+d)^2,x)","\frac{c^{2} x^{5}}{5 e^{2}}+\frac{2 b c \,x^{3}}{3 e^{2}}-\frac{2 c^{2} d \,x^{3}}{3 e^{3}}+\frac{a^{2} x}{2 \left(e \,x^{2}+d \right) d}+\frac{a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{a b x}{\left(e \,x^{2}+d \right) e}+\frac{a b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e}+\frac{a c d x}{\left(e \,x^{2}+d \right) e^{2}}-\frac{3 a c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{2}}+\frac{b^{2} d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 b^{2} d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}-\frac{b c \,d^{2} x}{\left(e \,x^{2}+d \right) e^{3}}+\frac{5 b c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\sqrt{d e}\, e^{3}}+\frac{c^{2} d^{3} x}{2 \left(e \,x^{2}+d \right) e^{4}}-\frac{7 c^{2} d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{4}}+\frac{2 a c x}{e^{2}}+\frac{b^{2} x}{e^{2}}-\frac{4 b c d x}{e^{3}}+\frac{3 c^{2} d^{2} x}{e^{4}}"," ",0,"1/5*c^2/e^2*x^5+2/3/e^2*x^3*b*c-2/3*c^2*d/e^3*x^3+2*a*c/e^2*x+1/e^2*b^2*x-4/e^3*b*c*d*x+3*c^2*d^2/e^4*x+1/2/(e*x^2+d)*a^2/d*x-1/e*x/(e*x^2+d)*a*b+1/(e*x^2+d)*a*c*d/e^2*x+1/2/e^2*d*x/(e*x^2+d)*b^2-1/e^3*d^2*x/(e*x^2+d)*b*c+1/2/(e*x^2+d)*c^2*d^3/e^4*x+1/2/(d*e)^(1/2)*a^2/d*arctan(1/(d*e)^(1/2)*e*x)+1/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*b-3/(d*e)^(1/2)*a*c*d/e^2*arctan(1/(d*e)^(1/2)*e*x)-3/2/e^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2+5/e^3*d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c-7/2/(d*e)^(1/2)*c^2*d^3/e^4*arctan(1/(d*e)^(1/2)*e*x)","B"
258,1,402,185,0.013000," ","int((c*x^4+b*x^2+a)^2/(e*x^2+d)^3,x)","\frac{3 a^{2} e \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{a b \,x^{3}}{4 \left(e \,x^{2}+d \right)^{2} d}-\frac{5 a c \,x^{3}}{4 \left(e \,x^{2}+d \right)^{2} e}-\frac{5 b^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e}+\frac{9 b c d \,x^{3}}{4 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{13 c^{2} d^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}+\frac{5 a^{2} x}{8 \left(e \,x^{2}+d \right)^{2} d}-\frac{a b x}{4 \left(e \,x^{2}+d \right)^{2} e}-\frac{3 a c d x}{4 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{3 b^{2} d x}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}+\frac{7 b c \,d^{2} x}{4 \left(e \,x^{2}+d \right)^{2} e^{3}}-\frac{11 c^{2} d^{3} x}{8 \left(e \,x^{2}+d \right)^{2} e^{4}}+\frac{c^{2} x^{3}}{3 e^{3}}+\frac{3 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{a b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{4 \sqrt{d e}\, d e}+\frac{3 a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{4 \sqrt{d e}\, e^{2}}+\frac{3 b^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}-\frac{15 b c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{4 \sqrt{d e}\, e^{3}}+\frac{35 c^{2} d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{4}}+\frac{2 b c x}{e^{3}}-\frac{3 c^{2} d x}{e^{4}}"," ",0,"1/3*c^2/e^3*x^3+2*c/e^3*b*x-3*c^2*d/e^4*x+3/8/(e*x^2+d)^2*a^2/d^2*e*x^3+1/4/(e*x^2+d)^2/d*x^3*a*b-5/4/(e*x^2+d)^2*a*c/e*x^3-5/8/e/(e*x^2+d)^2*x^3*b^2+9/4/e^2/(e*x^2+d)^2*x^3*b*c*d-13/8/(e*x^2+d)^2*c^2*d^2/e^3*x^3+5/8/(e*x^2+d)^2*a^2/d*x-1/4/e/(e*x^2+d)^2*a*b*x-3/4/(e*x^2+d)^2*a*c*d/e^2*x-3/8/e^2/(e*x^2+d)^2*b^2*d*x+7/4/e^3/(e*x^2+d)^2*b*c*d^2*x-11/8/(e*x^2+d)^2*c^2*d^3/e^4*x+3/8/(d*e)^(1/2)*a^2/d^2*arctan(1/(d*e)^(1/2)*e*x)+1/4/e/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*b+3/4/(d*e)^(1/2)*a*c/e^2*arctan(1/(d*e)^(1/2)*e*x)+3/8/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2-15/4/e^3*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c+35/8/(d*e)^(1/2)*c^2*d^2/e^4*arctan(1/(d*e)^(1/2)*e*x)","B"
259,1,506,234,0.014000," ","int((c*x^4+b*x^2+a)^2/(e*x^2+d)^4,x)","\frac{5 a^{2} e^{2} x^{5}}{16 \left(e \,x^{2}+d \right)^{3} d^{3}}+\frac{a b e \,x^{5}}{8 \left(e \,x^{2}+d \right)^{3} d^{2}}+\frac{a c \,x^{5}}{8 \left(e \,x^{2}+d \right)^{3} d}+\frac{b^{2} x^{5}}{16 \left(e \,x^{2}+d \right)^{3} d}-\frac{11 b c \,x^{5}}{8 \left(e \,x^{2}+d \right)^{3} e}+\frac{29 c^{2} d \,x^{5}}{16 \left(e \,x^{2}+d \right)^{3} e^{2}}+\frac{5 a^{2} e \,x^{3}}{6 \left(e \,x^{2}+d \right)^{3} d^{2}}+\frac{a b \,x^{3}}{3 \left(e \,x^{2}+d \right)^{3} d}-\frac{a c \,x^{3}}{3 \left(e \,x^{2}+d \right)^{3} e}-\frac{b^{2} x^{3}}{6 \left(e \,x^{2}+d \right)^{3} e}-\frac{5 b c d \,x^{3}}{3 \left(e \,x^{2}+d \right)^{3} e^{2}}+\frac{17 c^{2} d^{2} x^{3}}{6 \left(e \,x^{2}+d \right)^{3} e^{3}}+\frac{11 a^{2} x}{16 \left(e \,x^{2}+d \right)^{3} d}-\frac{a b x}{8 \left(e \,x^{2}+d \right)^{3} e}-\frac{a c d x}{8 \left(e \,x^{2}+d \right)^{3} e^{2}}-\frac{b^{2} d x}{16 \left(e \,x^{2}+d \right)^{3} e^{2}}-\frac{5 b c \,d^{2} x}{8 \left(e \,x^{2}+d \right)^{3} e^{3}}+\frac{19 c^{2} d^{3} x}{16 \left(e \,x^{2}+d \right)^{3} e^{4}}+\frac{5 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d^{3}}+\frac{a b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2} e}+\frac{a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d \,e^{2}}+\frac{b^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, d \,e^{2}}+\frac{5 b c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{3}}-\frac{35 c^{2} d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{16 \sqrt{d e}\, e^{4}}+\frac{c^{2} x}{e^{4}}"," ",0,"c^2/e^4*x-1/6/e/(e*x^2+d)^3*x^3*b^2+1/16/(e*x^2+d)^3/d*x^5*b^2+11/16/(e*x^2+d)^3*a^2/d*x+5/16/(d*e)^(1/2)*a^2/d^3*arctan(1/(d*e)^(1/2)*e*x)-1/8/(e*x^2+d)^3*a*c*d/e^2*x+1/8/(d*e)^(1/2)*a*c/d/e^2*arctan(1/(d*e)^(1/2)*e*x)+1/8*e/(e*x^2+d)^3/d^2*x^5*a*b-5/3/e^2/(e*x^2+d)^3*x^3*b*c*d-5/8/e^3/(e*x^2+d)^3*b*c*d^2*x+1/8/e/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*b-11/8/e/(e*x^2+d)^3*x^5*b*c-1/8/e/(e*x^2+d)^3*a*b*x-1/16/e^2/(e*x^2+d)^3*b^2*d*x+1/16/e^2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2+5/8/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c+1/3/(e*x^2+d)^3/d*x^3*a*b+29/16/(e*x^2+d)^3*c^2*d/e^2*x^5+5/6/(e*x^2+d)^3*a^2/d^2*e*x^3-1/3/(e*x^2+d)^3*a*c/e*x^3+17/6/(e*x^2+d)^3*c^2*d^2/e^3*x^3+19/16/(e*x^2+d)^3*c^2*d^3/e^4*x-35/16/(d*e)^(1/2)*c^2*d/e^4*arctan(1/(d*e)^(1/2)*e*x)+5/16/(e*x^2+d)^3*a^2/d^3*e^2*x^5+1/8/(e*x^2+d)^3*a*c/d*x^5","B"
260,1,412,299,0.013000," ","int((c*x^4+b*x^2+a)^2/(e*x^2+d)^5,x)","\frac{35 a^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{128 \sqrt{d e}\, d^{4}}+\frac{5 a b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{64 \sqrt{d e}\, d^{3} e}+\frac{3 a c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{64 \sqrt{d e}\, d^{2} e^{2}}+\frac{3 b^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{128 \sqrt{d e}\, d^{2} e^{2}}+\frac{5 b c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{64 \sqrt{d e}\, d \,e^{3}}+\frac{35 c^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{128 \sqrt{d e}\, e^{4}}+\frac{\frac{\left(35 a^{2} e^{4}+10 d a b \,e^{3}+6 a c \,d^{2} e^{2}+3 b^{2} d^{2} e^{2}+10 b c \,d^{3} e -93 c^{2} d^{4}\right) x^{7}}{128 d^{4} e}+\frac{\left(385 a^{2} e^{4}+110 d a b \,e^{3}+66 a c \,d^{2} e^{2}+33 b^{2} d^{2} e^{2}-146 b c \,d^{3} e -511 c^{2} d^{4}\right) x^{5}}{384 d^{3} e^{2}}+\frac{\left(511 a^{2} e^{4}+146 d a b \,e^{3}-66 a c \,d^{2} e^{2}-33 b^{2} d^{2} e^{2}-110 b c \,d^{3} e -385 c^{2} d^{4}\right) x^{3}}{384 d^{2} e^{3}}+\frac{\left(93 a^{2} e^{4}-10 d a b \,e^{3}-6 a c \,d^{2} e^{2}-3 b^{2} d^{2} e^{2}-10 b c \,d^{3} e -35 c^{2} d^{4}\right) x}{128 d \,e^{4}}}{\left(e \,x^{2}+d \right)^{4}}"," ",0,"(1/128*(35*a^2*e^4+10*a*b*d*e^3+6*a*c*d^2*e^2+3*b^2*d^2*e^2+10*b*c*d^3*e-93*c^2*d^4)/d^4/e*x^7+1/384*(385*a^2*e^4+110*a*b*d*e^3+66*a*c*d^2*e^2+33*b^2*d^2*e^2-146*b*c*d^3*e-511*c^2*d^4)/d^3/e^2*x^5+1/384*(511*a^2*e^4+146*a*b*d*e^3-66*a*c*d^2*e^2-33*b^2*d^2*e^2-110*b*c*d^3*e-385*c^2*d^4)/d^2/e^3*x^3+1/128*(93*a^2*e^4-10*a*b*d*e^3-6*a*c*d^2*e^2-3*b^2*d^2*e^2-10*b*c*d^3*e-35*c^2*d^4)/d/e^4*x)/(e*x^2+d)^4+35/128/(d*e)^(1/2)*a^2/d^4*arctan(1/(d*e)^(1/2)*e*x)+5/64/d^3/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*b+3/64/(d*e)^(1/2)*a*c/d^2/e^2*arctan(1/(d*e)^(1/2)*e*x)+3/128/d^2/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b^2+5/64/d/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b*c+35/128/(d*e)^(1/2)*c^2/e^4*arctan(1/(d*e)^(1/2)*e*x)","A"
261,1,118,71,0.000000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{a x}{2 \left(e \,x^{2}+d \right) d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{b x}{2 \left(e \,x^{2}+d \right) e}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}+\frac{c d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}+\frac{c x}{e^{2}}"," ",0,"1/2/(e*x^2+d)*a/d*x+1/2/(d*e)^(1/2)*a/d*arctan(1/(d*e)^(1/2)*e*x)-1/2/(e*x^2+d)*b/e*x+1/2/(d*e)^(1/2)*b/e*arctan(1/(d*e)^(1/2)*e*x)+1/2/(e*x^2+d)*c*d/e^2*x-3/2/(d*e)^(1/2)*c*d/e^2*arctan(1/(d*e)^(1/2)*e*x)+c/e^2*x","A"
262,1,118,71,0.009000," ","int((a+x^2*(c*x^2+b))/(e*x^2+d)^2,x)","\frac{a x}{2 \left(e \,x^{2}+d \right) d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{b x}{2 \left(e \,x^{2}+d \right) e}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}+\frac{c d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}+\frac{c x}{e^{2}}"," ",0,"1/2/(e*x^2+d)*a/d*x+1/2/(d*e)^(1/2)*a/d*arctan(1/(d*e)^(1/2)*e*x)-1/2/(e*x^2+d)*b/e*x+1/2/(d*e)^(1/2)*b/e*arctan(1/(d*e)^(1/2)*e*x)+1/2/(e*x^2+d)*c*d/e^2*x-3/2/(d*e)^(1/2)*c*d/e^2*arctan(1/(d*e)^(1/2)*e*x)+c/e^2*x","A"
263,1,1888,421,0.049000," ","int((e*x^2+d)^4/(c*x^4+b*x^2+a),x)","\frac{e^{4} x^{5}}{5 c}-\frac{\sqrt{2}\, a^{2} e^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a^{2} e^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a \,b^{2} e^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a \,b^{2} e^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{6 \sqrt{2}\, a b d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{6 \sqrt{2}\, a b d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{6 \sqrt{2}\, a \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{6 \sqrt{2}\, a \,d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{4} e^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{4} e^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}+\frac{2 \sqrt{2}\, b^{3} d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, b^{3} d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{3 \sqrt{2}\, b^{2} d^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{2} d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{b \,e^{4} x^{3}}{3 c^{2}}+\frac{2 \sqrt{2}\, b \,d^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, b \,d^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 d \,e^{3} x^{3}}{3 c}-\frac{\sqrt{2}\, a b \,e^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a b \,e^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} e^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{3} e^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{2 \sqrt{2}\, b^{2} d \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, b^{2} d \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b \,d^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b \,d^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, d^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, d^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{a \,e^{4} x}{c^{2}}+\frac{b^{2} e^{4} x}{c^{3}}-\frac{4 b d \,e^{3} x}{c^{2}}+\frac{6 d^{2} e^{2} x}{c}"," ",0,"4/3/c*d*e^3*x^3-1/3*e^4/c^2*x^3*b+e^4/c^3*b^2*x-a/c^2*e^4*x+6/c*d^2*e^2*x-4*e^3/c^2*b*d*x-2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3*e-6/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d*e^3-6/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d*e^3+1/2/c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^4-1/2/c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^4-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^4-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^4-3/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2*e^2+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*e^4+6/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d^2*e^2+2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3*e*b+6/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d^2*e^2+2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3*e*b-1/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e^4-1/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e^4-1/2/c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*e^4-1/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e^4-1/2/c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*e^4+2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d*e^3-2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^3+3/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e^2+1/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e^4-2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d*e^3+2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^3-3/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e^2+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d*e^3-3/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2*e^2+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*e^4+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d*e^3+2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3*e+1/5/c*e^4*x^5","B"
264,1,1211,280,0.037000," ","int((e*x^2+d)^3/(c*x^4+b*x^2+a),x)","-\frac{3 \sqrt{2}\, a b \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, a d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{3 \sqrt{2}\, b^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{2} d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, b \,d^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b \,d^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{e^{3} x^{3}}{3 c}+\frac{\sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, d^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b \,e^{3} x}{c^{2}}+\frac{3 d \,e^{2} x}{c}"," ",0,"1/3/c*e^3*x^3-e^3/c^2*b*x+3/c*d*e^2*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^3-1/2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3+3/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2-3/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e^3+3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d*e^2+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2+3/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e*b-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^3+1/2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3-3/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2+3/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e^3+3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d*e^2+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2+3/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e*b-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3","B"
265,1,695,204,0.028000," ","int((e*x^2+d)^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{e^{2} x}{c}"," ",0,"1/c*e^2*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2-2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^2-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2+2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^2-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2","B"
266,1,328,138,0.020000," ","int((e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-1/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d","B"
267,1,116,114,0.014000," ","int(1/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","A"
268,1,480,208,0.022000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{d e}}"," ",0,"e^2/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(a*e^2-b*d*e+c*d^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(a*e^2-b*d*e+c*d^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d","B"
269,1,1141,366,0.029000," ","int(1/(e*x^2+d)^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a \,c^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \,c^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} c \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} c \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \,c^{2} d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \,c^{2} d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{3} d^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{3} d^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{a \,e^{4} x}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d}+\frac{a \,e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{d e}\, d}-\frac{\sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b \,e^{3} x}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right)}-\frac{3 b \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{d e}}+\frac{\sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{c d \,e^{2} x}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right)}+\frac{5 c d \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right)^{2} \sqrt{d e}}"," ",0,"1/2*e^4/(a*e^2-b*d*e+c*d^2)^2/d*x/(e*x^2+d)*a-1/2*e^3/(a*e^2-b*d*e+c*d^2)^2*x/(e*x^2+d)*b+1/2*e^2/(a*e^2-b*d*e+c*d^2)^2*d*x/(e*x^2+d)*c+1/2*e^4/(a*e^2-b*d*e+c*d^2)^2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-3/2*e^3/(a*e^2-b*d*e+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+5/2*e^2/(a*e^2-b*d*e+c*d^2)^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c-1/2/(a*e^2-b*d*e+c*d^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2+1/(a*e^2-b*d*e+c*d^2)^2*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e+1/(a*e^2-b*d*e+c*d^2)^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+1/(a*e^2-b*d*e+c*d^2)^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-1/(a*e^2-b*d*e+c*d^2)^2*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2+1/2/(a*e^2-b*d*e+c*d^2)^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2-1/(a*e^2-b*d*e+c*d^2)^2*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e+1/(a*e^2-b*d*e+c*d^2)^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+1/(a*e^2-b*d*e+c*d^2)^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-1/(a*e^2-b*d*e+c*d^2)^2*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2","B"
270,1,1846,505,0.050000," ","int((e*x^2+d)^3/(c*x^4+b*x^2+a)^2,x)","\frac{2 \sqrt{2}\, a b \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a c d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} c \,d^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c \,d^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{3} e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b^{2} d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b c \,d^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c \,d^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \,d^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c \,d^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{\left(2 a^{2} c \,e^{3}-a \,b^{2} e^{3}+3 a b c d \,e^{2}-6 a \,c^{2} d^{2} e +b \,c^{2} d^{3}\right) x^{3}}{2 \left(4 a c -b^{2}\right) a c}+\frac{\left(a^{2} b \,e^{3}-6 a^{2} c d \,e^{2}+3 a b c \,d^{2} e +2 a \,c^{2} d^{3}-b^{2} c \,d^{3}\right) x}{2 \left(4 a c -b^{2}\right) a c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"-1/4/a/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^3+2*a/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^3-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3-3/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2+1/4/a/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^3+2*a/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^3-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3-3/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2-3*a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e^2+3/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^3-3*a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e^2+3/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^3+1/4/(4*a*c-b^2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3+3/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2-3/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3-1/4/(4*a*c-b^2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3-3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2+3/2/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3-3/2*a/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^3+3/2*a/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^3+(-1/2*(2*a^2*c*e^3-a*b^2*e^3+3*a*b*c*d*e^2-6*a*c^2*d^2*e+b*c^2*d^3)/a/c/(4*a*c-b^2)*x^3+1/2/c*(a^2*b*e^3-6*a^2*c*d*e^2+3*a*b*c*d^2*e+2*a*c^2*d^3-b^2*c*d^3)/(4*a*c-b^2)/a*x)/(c*x^4+b*x^2+a)","B"
271,1,1223,344,0.042000," ","int((e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, a c \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} c \,d^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c \,d^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, b c d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, b c d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c \,d^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c d e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{\left(a b \,e^{2}-4 a c d e +b c \,d^{2}\right) x^{3}}{2 \left(4 a c -b^{2}\right) a}-\frac{\left(2 a^{2} e^{2}-2 a b d e -2 a c \,d^{2}+b^{2} d^{2}\right) x}{2 \left(4 a c -b^{2}\right) a}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/a*(a*b*e^2-4*a*c*d*e+b*c*d^2)/(4*a*c-b^2)*x^3-1/2*(2*a^2*e^2-2*a*b*d*e-2*a*c*d^2+b^2*d^2)/a/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2-1/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e+1/4/a/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2-a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^2-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+2/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^2+1/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e-1/4/a/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2-a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^2-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^2+2/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2","B"
272,1,1761,251,0.085000," ","int((e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{4 \sqrt{2}\, a b \,c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 \sqrt{2}\, a b \,c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{12 \sqrt{2}\, a \,c^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{12 \sqrt{2}\, a \,c^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{4} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{3 \sqrt{2}\, b^{4} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{3 \sqrt{2}\, b^{3} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{3} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{8 \sqrt{2}\, b^{2} c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{8 \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, a \,c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b d x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{b d x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{e x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{e x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, d x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{\sqrt{-4 a c +b^{2}}\, d x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}"," ",0,"-1/4*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*d+1/2/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*e-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b*d-12*c^3/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*a-8*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+3/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d-2*c^2/(4*a*c-b^2)*a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-3/2*c/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+c^2/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+3/4*c/(4*a*c-b^2)/a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+4*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+3*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+1/4*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*d+1/2/(4*a*c-b^2)*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*e-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*b*d-12*c^3/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*a-8*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+3/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d+2*c^2/(4*a*c-b^2)*a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+3/2*c/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-c^2/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-3/4*c/(4*a*c-b^2)/a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+4*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+3*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e","B"
273,1,733,206,0.060000," ","int(1/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}"," ",0,"-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b+c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)-1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b^2+1/4*c/(4*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b-c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)+1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b^2-1/4*c/(4*a*c-b^2)/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
274,1,3841,571,0.064000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"e^4/(a*e^2-b*d*e+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)+1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^3*e^3+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c^3*d^3+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d*e^2+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d^2*e+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^3-1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c/a/(4*a*c-b^2)*x^3*b^3*d*e^2+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c^2/a/(4*a*c-b^2)*x^3*b^2*d^2*e+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)*x*b^3*c*d^2*e-1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^3-3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3+1/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2-1/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d^2*e+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d*e^2+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^3+4/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^3-3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2+5/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e+1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^2*e^3-1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c^3/(4*a*c-b^2)*x^3*d^2*e-1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c^2*a/(4*a*c-b^2)*x^3*e^3-3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e^3-7/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e^2+1/2/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2*e+4/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e^3-7/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^2*e-1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d*e^2+1/4/(a*e^2-b*d*e+c*d^2)^2/a/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d^3+5/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d^2*e-3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d*e^2-3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^4/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3+5/2/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^3-5/2/(a*e^2-b*d*e+c*d^2)^2*a/(4*a*c-b^2)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e^3-3/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b*e^3*c+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*c^2*d*e^2+1/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^2*c*d*e^2-5/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*c^2*d^2*e-1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)*x*b^4*d*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)*x*b^2*c^2*d^3+1/2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e-3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3-3/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^4/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^3-1/2/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d^2*e+3/4/(a*e^2-b*d*e+c*d^2)^2/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e^3+1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*b*d*e^2-1/2/(a*e^2-b*d*e+c*d^2)^2/(c*x^4+b*x^2+a)*c^3/a/(4*a*c-b^2)*x^3*b*d^3","B"
275,1,5709,951,0.084000," ","int(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
276,1,283,187,0.010000," ","int((e*x^2+d)^(5/2)*(c*x^4+b*x^2+a),x)","\frac{5 a \,d^{3} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{16 \sqrt{e}}-\frac{5 b \,d^{4} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{128 e^{\frac{3}{2}}}+\frac{3 c \,d^{5} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{256 e^{\frac{5}{2}}}+\frac{5 \sqrt{e \,x^{2}+d}\, a \,d^{2} x}{16}-\frac{5 \sqrt{e \,x^{2}+d}\, b \,d^{3} x}{128 e}+\frac{3 \sqrt{e \,x^{2}+d}\, c \,d^{4} x}{256 e^{2}}+\frac{5 \left(e \,x^{2}+d \right)^{\frac{3}{2}} a d x}{24}-\frac{5 \left(e \,x^{2}+d \right)^{\frac{3}{2}} b \,d^{2} x}{192 e}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} c \,d^{3} x}{128 e^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{7}{2}} c \,x^{3}}{10 e}+\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} a x}{6}-\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} b d x}{48 e}+\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} c \,d^{2} x}{160 e^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{7}{2}} b x}{8 e}-\frac{3 \left(e \,x^{2}+d \right)^{\frac{7}{2}} c d x}{80 e^{2}}"," ",0,"1/10*c*x^3*(e*x^2+d)^(7/2)/e-3/80*c*d/e^2*x*(e*x^2+d)^(7/2)+1/160*c*d^2/e^2*x*(e*x^2+d)^(5/2)+1/128*c*d^3/e^2*x*(e*x^2+d)^(3/2)+3/256*c*d^4/e^2*x*(e*x^2+d)^(1/2)+3/256*c*d^5/e^(5/2)*ln(x*e^(1/2)+(e*x^2+d)^(1/2))+1/8*b*x*(e*x^2+d)^(7/2)/e-1/48*b*d/e*x*(e*x^2+d)^(5/2)-5/192*b*d^2/e*x*(e*x^2+d)^(3/2)-5/128*b*d^3/e*x*(e*x^2+d)^(1/2)-5/128*b*d^4/e^(3/2)*ln(x*e^(1/2)+(e*x^2+d)^(1/2))+1/6*a*x*(e*x^2+d)^(5/2)+5/24*a*d*x*(e*x^2+d)^(3/2)+5/16*a*d^2*x*(e*x^2+d)^(1/2)+5/16*a*d^3/e^(1/2)*ln(x*e^(1/2)+(e*x^2+d)^(1/2))","A"
277,1,229,151,0.010000," ","int((e*x^2+d)^(3/2)*(c*x^4+b*x^2+a),x)","\frac{3 a \,d^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{8 \sqrt{e}}-\frac{b \,d^{3} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{16 e^{\frac{3}{2}}}+\frac{3 c \,d^{4} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{128 e^{\frac{5}{2}}}+\frac{3 \sqrt{e \,x^{2}+d}\, a d x}{8}-\frac{\sqrt{e \,x^{2}+d}\, b \,d^{2} x}{16 e}+\frac{3 \sqrt{e \,x^{2}+d}\, c \,d^{3} x}{128 e^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} c \,x^{3}}{8 e}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} a x}{4}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b d x}{24 e}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} c \,d^{2} x}{64 e^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} b x}{6 e}-\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} c d x}{16 e^{2}}"," ",0,"1/8*c*x^3*(e*x^2+d)^(5/2)/e-1/16*c*d/e^2*x*(e*x^2+d)^(5/2)+1/64*c*d^2/e^2*x*(e*x^2+d)^(3/2)+3/128*c*d^3/e^2*x*(e*x^2+d)^(1/2)+3/128*c*d^4/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/6*b*x*(e*x^2+d)^(5/2)/e-1/24*b*d/e*x*(e*x^2+d)^(3/2)-1/16*b*d^2/e*x*(e*x^2+d)^(1/2)-1/16*b*d^3/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/4*a*x*(e*x^2+d)^(3/2)+3/8*a*d*x*(e*x^2+d)^(1/2)+3/8*a*d^2/e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))","A"
278,1,175,112,0.010000," ","int((e*x^2+d)^(1/2)*(c*x^4+b*x^2+a),x)","\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} c \,x^{3}}{6 e}+\frac{a d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 \sqrt{e}}-\frac{b \,d^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{8 e^{\frac{3}{2}}}+\frac{c \,d^{3} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{16 e^{\frac{5}{2}}}+\frac{\sqrt{e \,x^{2}+d}\, a x}{2}-\frac{\sqrt{e \,x^{2}+d}\, b d x}{8 e}+\frac{\sqrt{e \,x^{2}+d}\, c \,d^{2} x}{16 e^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b x}{4 e}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} c d x}{8 e^{2}}"," ",0,"1/6*c*x^3*(e*x^2+d)^(3/2)/e-1/8*c*d/e^2*x*(e*x^2+d)^(3/2)+1/16*c*d^2/e^2*x*(e*x^2+d)^(1/2)+1/16*c*d^3/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/4*b*x*(e*x^2+d)^(3/2)/e-1/8*b*d/e*x*(e*x^2+d)^(1/2)-1/8*b*d^2/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/2*a*x*(e*x^2+d)^(1/2)+1/2*a*d/e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))","A"
279,1,122,81,0.009000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","\frac{\sqrt{e \,x^{2}+d}\, c \,x^{3}}{4 e}+\frac{a \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{\sqrt{e}}-\frac{b d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 e^{\frac{3}{2}}}+\frac{3 c \,d^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{8 e^{\frac{5}{2}}}+\frac{\sqrt{e \,x^{2}+d}\, b x}{2 e}-\frac{3 \sqrt{e \,x^{2}+d}\, c d x}{8 e^{2}}"," ",0,"1/4*c*x^3*(e*x^2+d)^(1/2)/e-3/8*c*d/e^2*x*(e*x^2+d)^(1/2)+3/8*c*d^2/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/2*b*x/e*(e*x^2+d)^(1/2)-1/2*b*d/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+a*ln(e^(1/2)*x+(e*x^2+d)^(1/2))/e^(1/2)","A"
280,1,112,75,0.009000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(3/2),x)","\frac{c \,x^{3}}{2 \sqrt{e \,x^{2}+d}\, e}+\frac{a x}{\sqrt{e \,x^{2}+d}\, d}-\frac{b x}{\sqrt{e \,x^{2}+d}\, e}+\frac{3 c d x}{2 \sqrt{e \,x^{2}+d}\, e^{2}}+\frac{b \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{e^{\frac{3}{2}}}-\frac{3 c d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 e^{\frac{5}{2}}}"," ",0,"1/2*c*x^3/e/(e*x^2+d)^(1/2)+3/2*c*d/e^2*x/(e*x^2+d)^(1/2)-3/2*c*d/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-b*x/e/(e*x^2+d)^(1/2)+b/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+a*x/d/(e*x^2+d)^(1/2)","A"
281,1,124,87,0.008000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(5/2),x)","-\frac{c \,x^{3}}{3 \left(e \,x^{2}+d \right)^{\frac{3}{2}} e}+\frac{a x}{3 \left(e \,x^{2}+d \right)^{\frac{3}{2}} d}-\frac{b x}{3 \left(e \,x^{2}+d \right)^{\frac{3}{2}} e}+\frac{2 a x}{3 \sqrt{e \,x^{2}+d}\, d^{2}}+\frac{b x}{3 \sqrt{e \,x^{2}+d}\, d e}-\frac{c x}{\sqrt{e \,x^{2}+d}\, e^{2}}+\frac{c \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{e^{\frac{5}{2}}}"," ",0,"-1/3*c*x^3/e/(e*x^2+d)^(3/2)-c/e^2*x/(e*x^2+d)^(1/2)+c/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/3*b/e*x/(e*x^2+d)^(3/2)+1/3*b/d/e*x/(e*x^2+d)^(1/2)+1/3*a*x/d/(e*x^2+d)^(3/2)+2/3*a/d^2*x/(e*x^2+d)^(1/2)","A"
282,1,66,76,0.005000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(7/2),x)","\frac{\left(8 a \,e^{2} x^{4}+2 b d e \,x^{4}+3 c \,d^{2} x^{4}+20 a d e \,x^{2}+5 b \,d^{2} x^{2}+15 a \,d^{2}\right) x}{15 \left(e \,x^{2}+d \right)^{\frac{5}{2}} d^{3}}"," ",0,"1/15*x*(8*a*e^2*x^4+2*b*d*e*x^4+3*c*d^2*x^4+20*a*d*e*x^2+5*b*d^2*x^2+15*a*d^2)/(e*x^2+d)^(5/2)/d^3","A"
283,1,100,112,0.004000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(9/2),x)","\frac{\left(48 a \,e^{3} x^{6}+8 b d \,e^{2} x^{6}+6 c \,d^{2} e \,x^{6}+168 a d \,e^{2} x^{4}+28 b \,d^{2} e \,x^{4}+21 c \,d^{3} x^{4}+210 a \,d^{2} e \,x^{2}+35 b \,d^{3} x^{2}+105 a \,d^{3}\right) x}{105 \left(e \,x^{2}+d \right)^{\frac{7}{2}} d^{4}}"," ",0,"1/105*x*(48*a*e^3*x^6+8*b*d*e^2*x^6+6*c*d^2*e*x^6+168*a*d*e^2*x^4+28*b*d^2*e*x^4+21*c*d^3*x^4+210*a*d^2*e*x^2+35*b*d^3*x^2+105*a*d^3)/(e*x^2+d)^(7/2)/d^4","A"
284,1,136,147,0.006000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(11/2),x)","\frac{\left(128 a \,e^{4} x^{8}+16 b d \,e^{3} x^{8}+8 c \,d^{2} e^{2} x^{8}+576 a d \,e^{3} x^{6}+72 b \,d^{2} e^{2} x^{6}+36 c \,d^{3} e \,x^{6}+1008 a \,d^{2} e^{2} x^{4}+126 b \,d^{3} e \,x^{4}+63 c \,d^{4} x^{4}+840 a \,d^{3} e \,x^{2}+105 b \,d^{4} x^{2}+315 a \,d^{4}\right) x}{315 \left(e \,x^{2}+d \right)^{\frac{9}{2}} d^{5}}"," ",0,"1/315*x*(128*a*e^4*x^8+16*b*d*e^3*x^8+8*c*d^2*e^2*x^8+576*a*d*e^3*x^6+72*b*d^2*e^2*x^6+36*c*d^3*e*x^6+1008*a*d^2*e^2*x^4+126*b*d^3*e*x^4+63*c*d^4*x^4+840*a*d^3*e*x^2+105*b*d^4*x^2+315*a*d^4)/(e*x^2+d)^(9/2)/d^5","A"
285,1,172,188,0.008000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^(13/2),x)","\frac{\left(1280 a \,e^{5} x^{10}+128 b d \,e^{4} x^{10}+48 c \,d^{2} e^{3} x^{10}+7040 a d \,e^{4} x^{8}+704 b \,d^{2} e^{3} x^{8}+264 c \,d^{3} e^{2} x^{8}+15840 a \,d^{2} e^{3} x^{6}+1584 b \,d^{3} e^{2} x^{6}+594 c \,d^{4} e \,x^{6}+18480 a \,d^{3} e^{2} x^{4}+1848 b \,d^{4} e \,x^{4}+693 c \,d^{5} x^{4}+11550 a \,d^{4} e \,x^{2}+1155 b \,d^{5} x^{2}+3465 a \,d^{5}\right) x}{3465 \left(e \,x^{2}+d \right)^{\frac{11}{2}} d^{6}}"," ",0,"1/3465*x*(1280*a*e^5*x^10+128*b*d*e^4*x^10+48*c*d^2*e^3*x^10+7040*a*d*e^4*x^8+704*b*d^2*e^3*x^8+264*c*d^3*e^2*x^8+15840*a*d^2*e^3*x^6+1584*b*d^3*e^2*x^6+594*c*d^4*e*x^6+18480*a*d^3*e^2*x^4+1848*b*d^4*e*x^4+693*c*d^5*x^4+11550*a*d^4*e*x^2+1155*b*d^5*x^2+3465*a*d^5)/(e*x^2+d)^(11/2)/d^6","A"
286,1,172,201,0.025000," ","int((5*x^2+7)^3*(x^4+3*x^2+2)^(1/2),x)","\frac{125 \sqrt{x^{4}+3 x^{2}+2}\, x^{7}}{9}+\frac{1700 \sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{21}+\frac{11446 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{63}+\frac{4258 \sqrt{x^{4}+3 x^{2}+2}\, x}{21}-\frac{2945 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{21 \sqrt{x^{4}+3 x^{2}+2}}+\frac{577 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{6 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"125/9*x^7*(x^4+3*x^2+2)^(1/2)+1700/21*x^5*(x^4+3*x^2+2)^(1/2)+11446/63*x^3*(x^4+3*x^2+2)^(1/2)+4258/21*x*(x^4+3*x^2+2)^(1/2)-2945/21*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+577/6*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
287,1,155,184,0.007000," ","int((5*x^2+7)^2*(x^4+3*x^2+2)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{7}+\frac{113 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{7}+\frac{557 \sqrt{x^{4}+3 x^{2}+2}\, x}{21}-\frac{472 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{21 \sqrt{x^{4}+3 x^{2}+2}}+\frac{31 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"25/7*(x^4+3*x^2+2)^(1/2)*x^5+113/7*(x^4+3*x^2+2)^(1/2)*x^3+557/21*(x^4+3*x^2+2)^(1/2)*x-472/21*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+31/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
288,1,137,169,0.008000," ","int((5*x^2+7)*(x^4+3*x^2+2)^(1/2),x)","\sqrt{x^{4}+3 x^{2}+2}\, x^{3}+\frac{10 \sqrt{x^{4}+3 x^{2}+2}\, x}{3}-\frac{11 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{x^{4}+3 x^{2}+2}}+\frac{5 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"(x^4+3*x^2+2)^(1/2)*x^3+10/3*(x^4+3*x^2+2)^(1/2)*x-11/3*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+5/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
289,1,121,161,0.004000," ","int((x^4+3*x^2+2)^(1/2),x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{3}-\frac{2 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{x^{4}+3 x^{2}+2}}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/3*(x^4+3*x^2+2)^(1/2)*x-2/3*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
290,1,138,210,0.035000," ","int((x^4+3*x^2+2)^(1/2)/(5*x^2+7),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{10 \sqrt{x^{4}+3 x^{2}+2}}-\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{50 \sqrt{x^{4}+3 x^{2}+2}}+\frac{6 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{175 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-3/50*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-1/10*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+6/175*I*2^(1/2)*(1+1/2*x^2)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
291,1,162,240,0.021000," ","int((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2,x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{70 x^{2}+98}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{140 \sqrt{x^{4}+3 x^{2}+2}}-\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{175 \sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{2450 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/14*x*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)-3/175*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+1/140*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-1/2450*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
292,1,186,264,0.023000," ","int((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^3,x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{28 \left(5 x^{2}+7\right)^{2}}+\frac{11 \sqrt{x^{4}+3 x^{2}+2}\, x}{2352 \left(5 x^{2}+7\right)}+\frac{11 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{23520 \sqrt{x^{4}+3 x^{2}+2}}-\frac{31 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{58800 \sqrt{x^{4}+3 x^{2}+2}}-\frac{1201 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{411600 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/28*x*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2+11/2352*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x-31/58800*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+11/23520*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-1201/411600*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
293,1,206,223,0.020000," ","int((5*x^2+7)^3*(x^4+3*x^2+2)^(3/2),x)","\frac{125 \sqrt{x^{4}+3 x^{2}+2}\, x^{11}}{13}+\frac{12075 \sqrt{x^{4}+3 x^{2}+2}\, x^{9}}{143}+\frac{131810 \sqrt{x^{4}+3 x^{2}+2}\, x^{7}}{429}+\frac{598324 \sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{1001}+\frac{10067363 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{15015}+\frac{2262081 \sqrt{x^{4}+3 x^{2}+2}\, x}{5005}-\frac{1171349 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{5005 \sqrt{x^{4}+3 x^{2}+2}}+\frac{10442 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{65 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"2262081/5005*(x^4+3*x^2+2)^(1/2)*x+10067363/15015*(x^4+3*x^2+2)^(1/2)*x^3+598324/1001*(x^4+3*x^2+2)^(1/2)*x^5+131810/429*(x^4+3*x^2+2)^(1/2)*x^7+125/13*x^11*(x^4+3*x^2+2)^(1/2)+12075/143*x^9*(x^4+3*x^2+2)^(1/2)-1171349/5005*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+10442/65*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
294,1,189,206,0.009000," ","int((5*x^2+7)^2*(x^4+3*x^2+2)^(3/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+2}\, x^{9}}{11}+\frac{1670 \sqrt{x^{4}+3 x^{2}+2}\, x^{7}}{99}+\frac{11492 \sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{231}+\frac{258044 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{3465}+\frac{23851 \sqrt{x^{4}+3 x^{2}+2}\, x}{385}-\frac{13879 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{385 \sqrt{x^{4}+3 x^{2}+2}}+\frac{371 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{15 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"25/11*(x^4+3*x^2+2)^(1/2)*x^9+1670/99*(x^4+3*x^2+2)^(1/2)*x^7+11492/231*(x^4+3*x^2+2)^(1/2)*x^5+258044/3465*(x^4+3*x^2+2)^(1/2)*x^3+23851/385*(x^4+3*x^2+2)^(1/2)*x-13879/385*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+371/15*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
295,1,172,191,0.005000," ","int((5*x^2+7)*(x^4+3*x^2+2)^(3/2),x)","\frac{5 \sqrt{x^{4}+3 x^{2}+2}\, x^{7}}{9}+\frac{71 \sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{21}+\frac{2417 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{315}+\frac{293 \sqrt{x^{4}+3 x^{2}+2}\, x}{35}-\frac{197 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{35 \sqrt{x^{4}+3 x^{2}+2}}+\frac{58 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{15 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"5/9*(x^4+3*x^2+2)^(1/2)*x^7+71/21*(x^4+3*x^2+2)^(1/2)*x^5+2417/315*(x^4+3*x^2+2)^(1/2)*x^3+293/35*(x^4+3*x^2+2)^(1/2)*x-197/35*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+58/15*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
296,1,155,184,0.005000," ","int((x^4+3*x^2+2)^(3/2),x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, x^{5}}{7}+\frac{24 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{35}+\frac{39 \sqrt{x^{4}+3 x^{2}+2}\, x}{35}-\frac{31 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{35 \sqrt{x^{4}+3 x^{2}+2}}+\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{5 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/7*(x^4+3*x^2+2)^(1/2)*x^5+24/35*(x^4+3*x^2+2)^(1/2)*x^3+39/35*(x^4+3*x^2+2)^(1/2)*x-31/35*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+3/5*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
297,1,170,238,0.016000," ","int((x^4+3*x^2+2)^(3/2)/(5*x^2+7),x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{25}+\frac{11 \sqrt{x^{4}+3 x^{2}+2}\, x}{75}-\frac{12 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{125 \sqrt{x^{4}+3 x^{2}+2}}-\frac{73 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{1875 \sqrt{x^{4}+3 x^{2}+2}}-\frac{36 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{4375 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/25*(x^4+3*x^2+2)^(1/2)*x^3+11/75*(x^4+3*x^2+2)^(1/2)*x-73/1875*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-12/125*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-36/4375*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
298,1,177,248,0.022000," ","int((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^2,x)","-\frac{3 \sqrt{x^{4}+3 x^{2}+2}\, x}{175 \left(5 x^{2}+7\right)}+\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{75}-\frac{9 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{350 \sqrt{x^{4}+3 x^{2}+2}}-\frac{13 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2625 \sqrt{x^{4}+3 x^{2}+2}}+\frac{9 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{6125 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-3/175*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x+1/75*(x^4+3*x^2+2)^(1/2)*x-13/2625*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-9/350*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+9/6125*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
299,1,186,262,0.022000," ","int((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^3,x)","-\frac{3 \sqrt{x^{4}+3 x^{2}+2}\, x}{350 \left(5 x^{2}+7\right)^{2}}+\frac{17 \sqrt{x^{4}+3 x^{2}+2}\, x}{9800 \left(5 x^{2}+7\right)}-\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{784 \sqrt{x^{4}+3 x^{2}+2}}-\frac{29 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{9800 \sqrt{x^{4}+3 x^{2}+2}}+\frac{141 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{68600 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-3/350*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2*x+17/9800*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x-29/9800*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-3/784*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+141/68600*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
300,1,138,179,0.018000," ","int((5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x)","25 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}+75 \sqrt{x^{4}+3 x^{2}+2}\, x -\frac{193 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}+\frac{135 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"25*(x^4+3*x^2+2)^(1/2)*x^3+75*(x^4+3*x^2+2)^(1/2)*x-193/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+135/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
301,1,121,162,0.007000," ","int((5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+2}\, x}{3}-\frac{97 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{6 \sqrt{x^{4}+3 x^{2}+2}}+\frac{10 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"25/3*(x^4+3*x^2+2)^(1/2)*x-97/6*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+10*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
302,1,106,147,0.004000," ","int((5*x^2+7)/(x^4+3*x^2+2)^(1/2),x)","-\frac{7 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}+\frac{5 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"5/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-7/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))","C"
303,1,46,63,0.004000," ","int(1/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))","C"
304,1,47,133,0.014000," ","int(1/(5*x^2+7)/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{7 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-1/7*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
305,1,162,240,0.020000," ","int(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x)","-\frac{25 \sqrt{x^{4}+3 x^{2}+2}\, x}{84 \left(5 x^{2}+7\right)}-\frac{5 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{168 \sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{84 \sqrt{x^{4}+3 x^{2}+2}}-\frac{13 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{588 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-25/84*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x-1/84*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-5/168*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-13/588*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
306,1,186,264,0.021000," ","int(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x)","-\frac{25 \sqrt{x^{4}+3 x^{2}+2}\, x}{168 \left(5 x^{2}+7\right)^{2}}-\frac{325 \sqrt{x^{4}+3 x^{2}+2}\, x}{4704 \left(5 x^{2}+7\right)}-\frac{65 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{9408 \sqrt{x^{4}+3 x^{2}+2}}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{4704 \sqrt{x^{4}+3 x^{2}+2}}-\frac{505 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{32928 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-25/168*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2*x-325/4704*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x+1/4704*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-65/9408*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-505/32928*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
307,1,274,201,0.036000," ","int((5*x^2+7)^5/(x^4+3*x^2+2)^(3/2),x)","625 \sqrt{x^{4}+3 x^{2}+2}\, x^{3}+\frac{5000 \sqrt{x^{4}+3 x^{2}+2}\, x}{3}-\frac{15383 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{6 \sqrt{x^{4}+3 x^{2}+2}}-\frac{6250 \left(\frac{17}{2} x^{3}+9 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}+\frac{7679 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}-\frac{43750 \left(-\frac{9}{2} x^{3}-5 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{122500 \left(\frac{5}{2} x^{3}+3 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{171500 \left(-\frac{3}{2} x^{3}-2 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{120050 \left(x^{3}+\frac{3}{2} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{33614 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-6250*(17/2*x^3+9*x)/(x^4+3*x^2+2)^(1/2)+625*(x^4+3*x^2+2)^(1/2)*x^3+5000/3*(x^4+3*x^2+2)^(1/2)*x+7679/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-15383/6*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-43750*(-9/2*x^3-5*x)/(x^4+3*x^2+2)^(1/2)-122500*(5/2*x^3+3*x)/(x^4+3*x^2+2)^(1/2)-171500*(-3/2*x^3-2*x)/(x^4+3*x^2+2)^(1/2)-120050*(x^3+3/2*x)/(x^4+3*x^2+2)^(1/2)-33614*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)","C"
308,1,234,184,0.009000," ","int((5*x^2+7)^4/(x^4+3*x^2+2)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+2}\, x}{3}-\frac{1067 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{x^{4}+3 x^{2}+2}}-\frac{1250 \left(-\frac{9}{2} x^{3}-5 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}+\frac{637 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}-\frac{7000 \left(\frac{5}{2} x^{3}+3 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{14700 \left(-\frac{3}{2} x^{3}-2 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{13720 \left(x^{3}+\frac{3}{2} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{4802 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-1250*(-9/2*x^3-5*x)/(x^4+3*x^2+2)^(1/2)+625/3*(x^4+3*x^2+2)^(1/2)*x+637/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-1067/3*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-7000*(5/2*x^3+3*x)/(x^4+3*x^2+2)^(1/2)-14700*(-3/2*x^3-2*x)/(x^4+3*x^2+2)^(1/2)-13720*(x^3+3/2*x)/(x^4+3*x^2+2)^(1/2)-4802*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)","C"
309,1,196,169,0.008000," ","int((5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x)","-\frac{169 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}-\frac{250 \left(\frac{5}{2} x^{3}+3 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}+\frac{261 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}-\frac{1050 \left(-\frac{3}{2} x^{3}-2 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{1470 \left(x^{3}+\frac{3}{2} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{686 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-250*(5/2*x^3+3*x)/(x^4+3*x^2+2)^(1/2)-169/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+261/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-1050*(-3/2*x^3-2*x)/(x^4+3*x^2+2)^(1/2)-1470*(x^3+3/2*x)/(x^4+3*x^2+2)^(1/2)-686*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)","C"
310,1,173,169,0.008000," ","int((5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x)","-\frac{6 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{50 \left(-\frac{3}{2} x^{3}-2 x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{17 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}-\frac{140 \left(x^{3}+\frac{3}{2} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{98 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-50*(-3/2*x^3-2*x)/(x^4+3*x^2+2)^(1/2)-6*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-17/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-140*(x^3+3/2*x)/(x^4+3*x^2+2)^(1/2)-98*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)","C"
311,1,150,167,0.006000," ","int((5*x^2+7)/(x^4+3*x^2+2)^(3/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}-\frac{10 \left(x^{3}+\frac{3}{2} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}-\frac{14 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-10*(x^3+3/2*x)/(x^4+3*x^2+2)^(1/2)-1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-1/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-14*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)","C"
312,1,129,169,0.005000," ","int(1/(x^4+3*x^2+2)^(3/2),x)","\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{2 \left(-\frac{3}{4} x^{3}-\frac{5}{4} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}-\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{4 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-2*(-3/4*x^3-5/4*x)/(x^4+3*x^2+2)^(1/2)+I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-3/4*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))","C"
313,1,161,205,0.019000," ","int(1/(5*x^2+7)/(x^4+3*x^2+2)^(3/2),x)","\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{6 \sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{12 \sqrt{x^{4}+3 x^{2}+2}}+\frac{25 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{42 \sqrt{x^{4}+3 x^{2}+2}}-\frac{2 \left(-\frac{1}{6} x^{3}-\frac{5}{12} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-2*(-1/6*x^3-5/12*x)/(x^4+3*x^2+2)^(1/2)-1/12*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+1/6*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+25/42*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
314,1,185,262,0.024000," ","int(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+2}\, x}{504 \left(5 x^{2}+7\right)}+\frac{31 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{112 \sqrt{x^{4}+3 x^{2}+2}}+\frac{13 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{168 \sqrt{x^{4}+3 x^{2}+2}}+\frac{75 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{392 \sqrt{x^{4}+3 x^{2}+2}}-\frac{2 \left(-\frac{11}{72} x^{3}-\frac{5}{18} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-2*(-11/72*x^3-5/18*x)/(x^4+3*x^2+2)^(1/2)+625/504*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x+13/168*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+31/112*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+75/392*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
315,1,209,286,0.025000," ","int(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+2}\, x}{1008 \left(5 x^{2}+7\right)^{2}}+\frac{41875 \sqrt{x^{4}+3 x^{2}+2}\, x}{84672 \left(5 x^{2}+7\right)}+\frac{5797 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{56448 \sqrt{x^{4}+3 x^{2}+2}}-\frac{53 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{28224 \sqrt{x^{4}+3 x^{2}+2}}+\frac{38525 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{197568 \sqrt{x^{4}+3 x^{2}+2}}-\frac{2 \left(-\frac{23}{432} x^{3}-\frac{25}{216} x \right)}{\sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-2*(-23/432*x^3-25/216*x)/(x^4+3*x^2+2)^(1/2)+625/1008*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2*x+41875/84672*(x^4+3*x^2+2)^(1/2)/(5*x^2+7)*x-53/28224*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+5797/56448*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))+38525/197568*I*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
316,1,193,102,0.025000," ","int((5*x^2+7)^4*(-x^4+x^2+2)^(1/2),x)","\frac{625 \sqrt{-x^{4}+x^{2}+2}\, x^{9}}{11}+\frac{12625 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{33}+\frac{20050 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{21}+\frac{166072 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{231}-\frac{518647 \sqrt{-x^{4}+x^{2}+2}\, x}{231}+\frac{1073278 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{231 \sqrt{-x^{4}+x^{2}+2}}-\frac{3764813 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{462 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"166072/231*x^3*(-x^4+x^2+2)^(1/2)-518647/231*x*(-x^4+x^2+2)^(1/2)+20050/21*x^5*(-x^4+x^2+2)^(1/2)+12625/33*x^7*(-x^4+x^2+2)^(1/2)+625/11*x^9*(-x^4+x^2+2)^(1/2)-3764813/462*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+1073278/231*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","A"
317,1,176,85,0.009000," ","int((5*x^2+7)^3*(-x^4+x^2+2)^(1/2),x)","\frac{125 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{9}+\frac{4600 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{63}+\frac{7466 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{63}-\frac{4994 \sqrt{-x^{4}+x^{2}+2}\, x}{63}+\frac{26603 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{63 \sqrt{-x^{4}+x^{2}+2}}-\frac{79411 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{126 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"125/9*(-x^4+x^2+2)^(1/2)*x^7+4600/63*(-x^4+x^2+2)^(1/2)*x^5+7466/63*(-x^4+x^2+2)^(1/2)*x^3-4994/63*(-x^4+x^2+2)^(1/2)*x+26603/63*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-79411/126*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
318,1,159,68,0.008000," ","int((5*x^2+7)^2*(-x^4+x^2+2)^(1/2),x)","\frac{25 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{7}+\frac{93 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{7}+\frac{125 \sqrt{-x^{4}+x^{2}+2}\, x}{21}+\frac{904 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{21 \sqrt{-x^{4}+x^{2}+2}}-\frac{2045 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{42 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"25/7*(-x^4+x^2+2)^(1/2)*x^5+93/7*(-x^4+x^2+2)^(1/2)*x^3+125/21*(-x^4+x^2+2)^(1/2)*x+904/21*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-2045/42*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
319,1,141,50,0.006000," ","int((5*x^2+7)*(-x^4+x^2+2)^(1/2),x)","\sqrt{-x^{4}+x^{2}+2}\, x^{3}+2 \sqrt{-x^{4}+x^{2}+2}\, x +\frac{5 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{\sqrt{-x^{4}+x^{2}+2}}-\frac{7 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{2 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"(-x^4+x^2+2)^(1/2)*x^3+2*(-x^4+x^2+2)^(1/2)*x+5*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-7/2*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
320,1,125,44,0.004000," ","int((-x^4+x^2+2)^(1/2),x)","\frac{\sqrt{-x^{4}+x^{2}+2}\, x}{3}+\frac{2 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{3 \sqrt{-x^{4}+x^{2}+2}}-\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{6 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"1/3*(-x^4+x^2+2)^(1/2)*x+2/3*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-1/6*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
321,1,141,47,0.019000," ","int((-x^4+x^2+2)^(1/2)/(5*x^2+7),x)","-\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{10 \sqrt{-x^{4}+x^{2}+2}}+\frac{17 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{50 \sqrt{-x^{4}+x^{2}+2}}-\frac{34 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{175 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"17/50*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-1/10*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))-34/175*2^(1/2)*(1-1/2*x^2)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
322,1,165,71,0.022000," ","int((-x^4+x^2+2)^(1/2)/(5*x^2+7)^2,x)","\frac{\sqrt{-x^{4}+x^{2}+2}\, x}{70 x^{2}+98}+\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{140 \sqrt{-x^{4}+x^{2}+2}}-\frac{3 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{175 \sqrt{-x^{4}+x^{2}+2}}+\frac{99 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{2450 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"1/14*x*(-x^4+x^2+2)^(1/2)/(5*x^2+7)-3/175*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+1/140*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+99/2450*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
323,1,189,95,0.020000," ","int((-x^4+x^2+2)^(1/2)/(5*x^2+7)^3,x)","\frac{\sqrt{-x^{4}+x^{2}+2}\, x}{28 \left(5 x^{2}+7\right)^{2}}-\frac{31 \sqrt{-x^{4}+x^{2}+2}\, x}{13328 \left(5 x^{2}+7\right)}-\frac{31 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{133280 \sqrt{-x^{4}+x^{2}+2}}-\frac{269 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{333200 \sqrt{-x^{4}+x^{2}+2}}+\frac{16601 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{2332400 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"1/28*x*(-x^4+x^2+2)^(1/2)/(5*x^2+7)^2-31/13328*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x-269/333200*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-31/133280*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+16601/2332400*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","A"
324,1,227,124,0.023000," ","int((5*x^2+7)^4*(-x^4+x^2+2)^(3/2),x)","-\frac{125 \sqrt{-x^{4}+x^{2}+2}\, x^{13}}{3}-\frac{8500 \sqrt{-x^{4}+x^{2}+2}\, x^{11}}{39}-\frac{84775 \sqrt{-x^{4}+x^{2}+2}\, x^{9}}{429}+\frac{432290 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{429}+\frac{833561 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{273}+\frac{43271392 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{15015}-\frac{12639493 \sqrt{-x^{4}+x^{2}+2}\, x}{5005}+\frac{36673503 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{5005 \sqrt{-x^{4}+x^{2}+2}}-\frac{62070711 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{5005 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"43271392/15015*(-x^4+x^2+2)^(1/2)*x^3-12639493/5005*(-x^4+x^2+2)^(1/2)*x+833561/273*(-x^4+x^2+2)^(1/2)*x^5+432290/429*(-x^4+x^2+2)^(1/2)*x^7-84775/429*(-x^4+x^2+2)^(1/2)*x^9-8500/39*x^11*(-x^4+x^2+2)^(1/2)-125/3*x^13*(-x^4+x^2+2)^(1/2)-62070711/5005*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+36673503/5005*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","A"
325,1,210,107,0.007000," ","int((5*x^2+7)^3*(-x^4+x^2+2)^(3/2),x)","-\frac{125 \sqrt{-x^{4}+x^{2}+2}\, x^{11}}{13}-\frac{5075 \sqrt{-x^{4}+x^{2}+2}\, x^{9}}{143}+\frac{5890 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{429}+\frac{65248 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{273}+\frac{5757461 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{15015}-\frac{436307 \sqrt{-x^{4}+x^{2}+2}\, x}{15015}+\frac{10736597 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{15015 \sqrt{-x^{4}+x^{2}+2}}-\frac{15536264 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{15015 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"5757461/15015*(-x^4+x^2+2)^(1/2)*x^3-436307/15015*(-x^4+x^2+2)^(1/2)*x+65248/273*(-x^4+x^2+2)^(1/2)*x^5+5890/429*(-x^4+x^2+2)^(1/2)*x^7-5075/143*(-x^4+x^2+2)^(1/2)*x^9-125/13*(-x^4+x^2+2)^(1/2)*x^11-15536264/15015*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+10736597/15015*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","A"
326,1,193,90,0.009000," ","int((5*x^2+7)^2*(-x^4+x^2+2)^(3/2),x)","-\frac{25 \sqrt{-x^{4}+x^{2}+2}\, x^{9}}{11}-\frac{470 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{99}+\frac{112 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{9}+\frac{21404 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{495}+\frac{10627 \sqrt{-x^{4}+x^{2}+2}\, x}{495}+\frac{37883 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{495 \sqrt{-x^{4}+x^{2}+2}}-\frac{42971 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{495 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-25/11*(-x^4+x^2+2)^(1/2)*x^9-470/99*(-x^4+x^2+2)^(1/2)*x^7+112/9*(-x^4+x^2+2)^(1/2)*x^5+21404/495*(-x^4+x^2+2)^(1/2)*x^3+10627/495*(-x^4+x^2+2)^(1/2)*x+37883/495*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-42971/495*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
327,1,176,75,0.007000," ","int((5*x^2+7)*(-x^4+x^2+2)^(3/2),x)","-\frac{5 \sqrt{-x^{4}+x^{2}+2}\, x^{7}}{9}-\frac{13 \sqrt{-x^{4}+x^{2}+2}\, x^{5}}{63}+\frac{1259 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{315}+\frac{1567 \sqrt{-x^{4}+x^{2}+2}\, x}{315}+\frac{2843 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{315 \sqrt{-x^{4}+x^{2}+2}}-\frac{2216 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{315 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-5/9*(-x^4+x^2+2)^(1/2)*x^7-13/63*(-x^4+x^2+2)^(1/2)*x^5+1259/315*(-x^4+x^2+2)^(1/2)*x^3+1567/315*(-x^4+x^2+2)^(1/2)*x+2843/315*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-2216/315*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
328,1,159,68,0.004000," ","int((-x^4+x^2+2)^(3/2),x)","-\frac{\sqrt{-x^{4}+x^{2}+2}\, x^{5}}{7}+\frac{8 \sqrt{-x^{4}+x^{2}+2}\, x^{3}}{35}+\frac{29 \sqrt{-x^{4}+x^{2}+2}\, x}{35}+\frac{41 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{35 \sqrt{-x^{4}+x^{2}+2}}-\frac{17 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{35 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-1/7*(-x^4+x^2+2)^(1/2)*x^5+8/35*(-x^4+x^2+2)^(1/2)*x^3+29/35*(-x^4+x^2+2)^(1/2)*x+41/35*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-17/35*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
329,1,173,69,0.017000," ","int((-x^4+x^2+2)^(3/2)/(5*x^2+7),x)","-\frac{\sqrt{-x^{4}+x^{2}+2}\, x^{3}}{25}+\frac{13 \sqrt{-x^{4}+x^{2}+2}\, x}{75}+\frac{46 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{375 \sqrt{-x^{4}+x^{2}+2}}-\frac{89 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{625 \sqrt{-x^{4}+x^{2}+2}}+\frac{1156 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{4375 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-1/25*(-x^4+x^2+2)^(1/2)*x^3+13/75*(-x^4+x^2+2)^(1/2)*x-89/625*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+46/375*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+1156/4375*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
330,1,180,86,0.020000," ","int((-x^4+x^2+2)^(3/2)/(5*x^2+7)^2,x)","-\frac{17 \sqrt{-x^{4}+x^{2}+2}\, x}{175 \left(5 x^{2}+7\right)}-\frac{\sqrt{-x^{4}+x^{2}+2}\, x}{75}-\frac{97 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{1050 \sqrt{-x^{4}+x^{2}+2}}+\frac{229 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{875 \sqrt{-x^{4}+x^{2}+2}}-\frac{1241 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{6125 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-17/175*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x-1/75*(-x^4+x^2+2)^(1/2)*x+229/875*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-97/1050*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))-1241/6125*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
331,1,189,95,0.022000," ","int((-x^4+x^2+2)^(3/2)/(5*x^2+7)^3,x)","-\frac{17 \sqrt{-x^{4}+x^{2}+2}\, x}{350 \left(5 x^{2}+7\right)^{2}}+\frac{563 \sqrt{-x^{4}+x^{2}+2}\, x}{9800 \left(5 x^{2}+7\right)}+\frac{191 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{19600 \sqrt{-x^{4}+x^{2}+2}}-\frac{1251 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{49000 \sqrt{-x^{4}+x^{2}+2}}+\frac{9879 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{343000 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-17/350*(-x^4+x^2+2)^(1/2)/(5*x^2+7)^2*x+563/9800*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x-1251/49000*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+191/19600*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+9879/343000*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","A"
332,1,142,63,0.018000," ","int((5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x)","-25 \sqrt{-x^{4}+x^{2}+2}\, x^{3}-\frac{625 \sqrt{-x^{4}+x^{2}+2}\, x}{3}+\frac{2279 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{6 \sqrt{-x^{4}+x^{2}+2}}-\frac{3905 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{6 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-25*(-x^4+x^2+2)^(1/2)*x^3-625/3*(-x^4+x^2+2)^(1/2)*x+2279/6*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-3905/6*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
333,1,125,46,0.009000," ","int((5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x)","-\frac{25 \sqrt{-x^{4}+x^{2}+2}\, x}{3}+\frac{197 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{6 \sqrt{-x^{4}+x^{2}+2}}-\frac{130 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{3 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-25/3*(-x^4+x^2+2)^(1/2)*x+197/6*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-130/3*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
334,1,110,31,0.005000," ","int((5*x^2+7)/(-x^4+x^2+2)^(1/2),x)","\frac{7 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{2 \sqrt{-x^{4}+x^{2}+2}}-\frac{5 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{2 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-5/2*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+7/2*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","B"
335,1,47,13,0.004000," ","int(1/(-x^4+x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{2 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"1/2*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","B"
336,1,48,16,0.015000," ","int(1/(5*x^2+7)/(-x^4+x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{7 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"1/7*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
337,1,165,71,0.020000," ","int(1/(5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x)","-\frac{25 \sqrt{-x^{4}+x^{2}+2}\, x}{476 \left(5 x^{2}+7\right)}-\frac{5 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{952 \sqrt{-x^{4}+x^{2}+2}}-\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{476 \sqrt{-x^{4}+x^{2}+2}}+\frac{167 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{3332 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-25/476*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x-1/476*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-5/952*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+167/3332*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
338,1,189,95,0.021000," ","int(1/(5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x)","-\frac{25 \sqrt{-x^{4}+x^{2}+2}\, x}{952 \left(5 x^{2}+7\right)^{2}}-\frac{12525 \sqrt{-x^{4}+x^{2}+2}\, x}{453152 \left(5 x^{2}+7\right)}-\frac{2505 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{906304 \sqrt{-x^{4}+x^{2}+2}}-\frac{263 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{453152 \sqrt{-x^{4}+x^{2}+2}}+\frac{58915 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{3172064 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"-25/952*(-x^4+x^2+2)^(1/2)/(5*x^2+7)^2*x-12525/453152*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x-263/453152*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-2505/906304*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))+58915/3172064*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","A"
339,1,280,85,0.037000," ","int((5*x^2+7)^5/(-x^4+x^2+2)^(3/2),x)","625 \sqrt{-x^{4}+x^{2}+2}\, x^{3}+\frac{27500 \sqrt{-x^{4}+x^{2}+2}\, x}{3}-\frac{799361 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{18 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{53125}{9} x^{3}+\frac{43750}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{3482293 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{153125}{9} x^{3}+\frac{218750}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{306250}{9} x^{3}+\frac{122500}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{85750}{9} x^{3}+\frac{343000}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{120050}{9} x^{3}-\frac{60025}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{16807}{18} x^{3}+\frac{84035}{18} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"6250*(17/18*x^3+7/9*x)/(-x^4+x^2+2)^(1/2)+625*(-x^4+x^2+2)^(1/2)*x^3+27500/3*(-x^4+x^2+2)^(1/2)*x-799361/18*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+3482293/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+43750*(7/18*x^3+5/9*x)/(-x^4+x^2+2)^(1/2)+122500*(5/18*x^3+1/9*x)/(-x^4+x^2+2)^(1/2)+171500*(1/18*x^3+2/9*x)/(-x^4+x^2+2)^(1/2)+120050*(1/9*x^3-1/18*x)/(-x^4+x^2+2)^(1/2)+33614*(5/36*x-1/36*x^3)/(-x^4+x^2+2)^(1/2)","B"
340,1,240,68,0.008000," ","int((5*x^2+7)^4/(-x^4+x^2+2)^(3/2),x)","\frac{625 \sqrt{-x^{4}+x^{2}+2}\, x}{3}-\frac{17369 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{9 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{4375}{9} x^{3}+\frac{6250}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{165239 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{17500}{9} x^{3}+\frac{7000}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{2450}{3} x^{3}+\frac{9800}{3} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{13720}{9} x^{3}-\frac{6860}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{2401}{18} x^{3}+\frac{12005}{18} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"1250*(7/18*x^3+5/9*x)/(-x^4+x^2+2)^(1/2)+625/3*(-x^4+x^2+2)^(1/2)*x-17369/9*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+165239/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+7000*(5/18*x^3+1/9*x)/(-x^4+x^2+2)^(1/2)+14700*(1/18*x^3+2/9*x)/(-x^4+x^2+2)^(1/2)+13720*(1/9*x^3-1/18*x)/(-x^4+x^2+2)^(1/2)+4802*(-1/36*x^3+5/36*x)/(-x^4+x^2+2)^(1/2)","B"
341,1,202,53,0.008000," ","int((5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x)","-\frac{929 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{18 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{625}{9} x^{3}+\frac{250}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{7147 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{175}{3} x^{3}+\frac{700}{3} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{490}{3} x^{3}-\frac{245}{3} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{343}{18} x^{3}+\frac{1715}{18} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"250*(5/18*x^3+1/9*x)/(-x^4+x^2+2)^(1/2)-929/18*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+7147/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+1050*(1/18*x^3+2/9*x)/(-x^4+x^2+2)^(1/2)+1470*(1/9*x^3-1/18*x)/(-x^4+x^2+2)^(1/2)+686*(-1/36*x^3+5/36*x)/(-x^4+x^2+2)^(1/2)","B"
342,1,179,53,0.008000," ","int((5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x)","\frac{34 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{9 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{25}{9} x^{3}+\frac{100}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{281 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{140}{9} x^{3}-\frac{70}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{49}{18} x^{3}+\frac{245}{18} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"50*(1/18*x^3+2/9*x)/(-x^4+x^2+2)^(1/2)+34/9*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+281/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+140*(1/9*x^3-1/18*x)/(-x^4+x^2+2)^(1/2)+98*(-1/36*x^3+5/36*x)/(-x^4+x^2+2)^(1/2)","B"
343,1,156,53,0.007000," ","int((5*x^2+7)/(-x^4+x^2+2)^(3/2),x)","\frac{19 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{18 \sqrt{-x^{4}+x^{2}+2}}+\frac{\frac{10}{9} x^{3}-\frac{5}{9} x}{\sqrt{-x^{4}+x^{2}+2}}+\frac{13 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{7}{18} x^{3}+\frac{35}{18} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"10*(1/9*x^3-1/18*x)/(-x^4+x^2+2)^(1/2)+19/18*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+13/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))+14*(-1/36*x^3+5/36*x)/(-x^4+x^2+2)^(1/2)","B"
344,1,133,53,0.005000," ","int(1/(-x^4+x^2+2)^(3/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{9 \sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{1}{18} x^{3}+\frac{5}{18} x}{\sqrt{-x^{4}+x^{2}+2}}-\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)\right)}{36 \sqrt{-x^{4}+x^{2}+2}}"," ",0,"2*(-1/36*x^3+5/36*x)/(-x^4+x^2+2)^(1/2)+1/9*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-1/36*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*(EllipticF(1/2*2^(1/2)*x,I*2^(1/2))-EllipticE(1/2*2^(1/2)*x,I*2^(1/2)))","B"
345,1,164,69,0.015000," ","int(1/(5*x^2+7)/(-x^4+x^2+2)^(3/2),x)","\frac{4 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{153 \sqrt{-x^{4}+x^{2}+2}}+\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{204 \sqrt{-x^{4}+x^{2}+2}}-\frac{25 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{238 \sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{8}{153} x^{3}+\frac{35}{306} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"2*(-4/153*x^3+35/612*x)/(-x^4+x^2+2)^(1/2)+1/204*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+4/153*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))-25/238*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
346,1,188,93,0.023000," ","int(1/(5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x)","\frac{625 \sqrt{-x^{4}+x^{2}+2}\, x}{16184 \left(5 x^{2}+7\right)}+\frac{5143 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{291312 \sqrt{-x^{4}+x^{2}+2}}+\frac{89 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{48552 \sqrt{-x^{4}+x^{2}+2}}-\frac{10825 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{113288 \sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{287}{10404} x^{3}+\frac{145}{2601} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"2*(-287/20808*x^3+145/5202*x)/(-x^4+x^2+2)^(1/2)+625/16184*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x+89/48552*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+5143/291312*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))-10825/113288*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","B"
347,1,212,117,0.025000," ","int(1/(5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x)","\frac{625 \sqrt{-x^{4}+x^{2}+2}\, x}{32368 \left(5 x^{2}+7\right)^{2}}+\frac{645625 \sqrt{-x^{4}+x^{2}+2}\, x}{15407168 \left(5 x^{2}+7\right)}+\frac{3086453 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticE \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{277329024 \sqrt{-x^{4}+x^{2}+2}}+\frac{60409 \sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)}{46221504 \sqrt{-x^{4}+x^{2}+2}}-\frac{6898575 \sqrt{2}\, \sqrt{-\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, x}{2}, -\frac{10}{7}, i \sqrt{2}\right)}{107850176 \sqrt{-x^{4}+x^{2}+2}}+\frac{-\frac{4909}{353736} x^{3}+\frac{4915}{176868} x}{\sqrt{-x^{4}+x^{2}+2}}"," ",0,"2*(-4909/707472*x^3+4915/353736*x)/(-x^4+x^2+2)^(1/2)+625/32368*(-x^4+x^2+2)^(1/2)/(5*x^2+7)^2*x+645625/15407168*(-x^4+x^2+2)^(1/2)/(5*x^2+7)*x+60409/46221504*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*2^(1/2))+3086453/277329024*2^(1/2)*(-2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticE(1/2*2^(1/2)*x,I*2^(1/2))-6898575/107850176*2^(1/2)*(-1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+x^2+2)^(1/2)*EllipticPi(1/2*2^(1/2)*x,-10/7,I*2^(1/2))","A"
348,1,292,262,0.167000," ","int((5*x^2+7)^4*(x^4+3*x^2+4)^(1/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+4}\, x^{9}}{11}+\frac{40375 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{99}+\frac{3650 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{3}+\frac{189898 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{99}+\frac{55327 \sqrt{x^{4}+3 x^{2}+4}\, x}{33}+\frac{382496 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{33 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{1653280 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{33 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"625/11*x^9*(x^4+3*x^2+4)^(1/2)+40375/99*x^7*(x^4+3*x^2+4)^(1/2)+189898/99*x^3*(x^4+3*x^2+4)^(1/2)+55327/33*x*(x^4+3*x^2+4)^(1/2)+382496/33/(-6+2*I*7^(1/2))^(1/2)*(1-(-3/8+1/8*I*7^(1/2))*x^2)^(1/2)*(1-(-3/8-1/8*I*7^(1/2))*x^2)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*x*(-6+2*I*7^(1/2))^(1/2),1/4*(2+6*I*7^(1/2))^(1/2))-1653280/33/(-6+2*I*7^(1/2))^(1/2)*(1-(-3/8+1/8*I*7^(1/2))*x^2)^(1/2)*(1-(-3/8-1/8*I*7^(1/2))*x^2)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*x*(-6+2*I*7^(1/2))^(1/2),1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*x*(-6+2*I*7^(1/2))^(1/2),1/4*(2+6*I*7^(1/2))^(1/2)))+3650/3*x^5*(x^4+3*x^2+4)^(1/2)","C"
349,1,275,245,0.010000," ","int((5*x^2+7)^3*(x^4+3*x^2+4)^(1/2),x)","\frac{125 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{9}+\frac{1700 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{21}+\frac{12146 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{63}+\frac{5008 \sqrt{x^{4}+3 x^{2}+4}\, x}{21}+\frac{35120 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{21 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{150944 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{21 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"125/9*(x^4+3*x^2+4)^(1/2)*x^7+1700/21*(x^4+3*x^2+4)^(1/2)*x^5+12146/63*(x^4+3*x^2+4)^(1/2)*x^3+5008/21*(x^4+3*x^2+4)^(1/2)*x+35120/21/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-150944/21/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
350,1,258,228,0.009000," ","int((5*x^2+7)^2*(x^4+3*x^2+4)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{7}+\frac{113 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{7}+\frac{219 \sqrt{x^{4}+3 x^{2}+4}\, x}{7}+\frac{1984 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{10208 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"25/7*(x^4+3*x^2+4)^(1/2)*x^5+113/7*(x^4+3*x^2+4)^(1/2)*x^3+219/7*(x^4+3*x^2+4)^(1/2)*x+1984/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-10208/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
351,1,240,213,0.006000," ","int((5*x^2+7)*(x^4+3*x^2+4)^(1/2),x)","\sqrt{x^{4}+3 x^{2}+4}\, x^{3}+\frac{10 \sqrt{x^{4}+3 x^{2}+4}\, x}{3}+\frac{176 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{3 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{288 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"(x^4+3*x^2+4)^(1/2)*x^3+10/3*(x^4+3*x^2+4)^(1/2)*x+176/3/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-288/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
352,1,224,205,0.004000," ","int((x^4+3*x^2+4)^(1/2),x)","\frac{\sqrt{x^{4}+3 x^{2}+4}\, x}{3}+\frac{32 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{3 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{32 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"1/3*(x^4+3*x^2+4)^(1/2)*x+32/3/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-32/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
353,1,386,300,0.118000," ","int((x^4+3*x^2+4)^(1/2)/(5*x^2+7),x)","\frac{32 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{5 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{32 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{25 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{32 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{5 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{44 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{175 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"32/25/(-6+2*I*7^(1/2))^(1/2)*(1+3/8*x^2-1/8*I*x^2*7^(1/2))^(1/2)*(1+3/8*x^2+1/8*I*x^2*7^(1/2))^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-32/5/(-6+2*I*7^(1/2))^(1/2)*(1+3/8*x^2-1/8*I*x^2*7^(1/2))^(1/2)*(1+3/8*x^2+1/8*I*x^2*7^(1/2))^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+32/5/(-6+2*I*7^(1/2))^(1/2)*(1+3/8*x^2-1/8*I*x^2*7^(1/2))^(1/2)*(1+3/8*x^2+1/8*I*x^2*7^(1/2))^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+44/175/(-3/8+1/8*I*7^(1/2))^(1/2)*(1+3/8*x^2-1/8*I*x^2*7^(1/2))^(1/2)*(1+3/8*x^2+1/8*I*x^2*7^(1/2))^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
354,1,410,324,0.025000," ","int((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2,x)","\frac{\sqrt{x^{4}+3 x^{2}+4}\, x}{70 x^{2}+98}-\frac{16 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{35 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{2 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{25 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{16 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{35 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{51 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{2450 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"1/14*x*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)+2/25/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+16/35/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-16/35/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+51/2450/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
355,1,434,348,0.029000," ","int((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^3,x)","\frac{\sqrt{x^{4}+3 x^{2}+4}\, x}{28 \left(5 x^{2}+7\right)^{2}}+\frac{139 \sqrt{x^{4}+3 x^{2}+4}\, x}{17248 \left(5 x^{2}+7\right)}-\frac{139 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{2695 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{51 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{15400 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{139 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{2695 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{14999 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{3018400 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"1/28*x*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2+139/17248*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x-51/15400/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+139/2695/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-139/2695/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+14999/3018400/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
356,1,326,284,0.041000," ","int((5*x^2+7)^4*(x^4+3*x^2+4)^(3/2),x)","\frac{125 \sqrt{x^{4}+3 x^{2}+4}\, x^{13}}{3}+\frac{5500 \sqrt{x^{4}+3 x^{2}+4}\, x^{11}}{13}+\frac{841525 \sqrt{x^{4}+3 x^{2}+4}\, x^{9}}{429}+\frac{6863530 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{1287}+\frac{356027 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{39}+\frac{64070384 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{6435}+\frac{15015343 \sqrt{x^{4}+3 x^{2}+4}\, x}{2145}+\frac{89363792 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{2145 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{405282752 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{2145 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"15015343/2145*(x^4+3*x^2+4)^(1/2)*x+64070384/6435*(x^4+3*x^2+4)^(1/2)*x^3+6863530/1287*(x^4+3*x^2+4)^(1/2)*x^7+356027/39*(x^4+3*x^2+4)^(1/2)*x^5+5500/13*x^11*(x^4+3*x^2+4)^(1/2)+125/3*x^13*(x^4+3*x^2+4)^(1/2)+841525/429*(x^4+3*x^2+4)^(1/2)*x^9-405282752/2145/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))+89363792/2145/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))","C"
357,1,309,267,0.008000," ","int((5*x^2+7)^3*(x^4+3*x^2+4)^(3/2),x)","\frac{125 \sqrt{x^{4}+3 x^{2}+4}\, x^{11}}{13}+\frac{12075 \sqrt{x^{4}+3 x^{2}+4}\, x^{9}}{143}+\frac{48520 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{143}+\frac{71434 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{91}+\frac{5528301 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{5005}+\frac{4865781 \sqrt{x^{4}+3 x^{2}+4}\, x}{5005}+\frac{32017264 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{5005 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{144821184 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{5005 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"4865781/5005*(x^4+3*x^2+4)^(1/2)*x+5528301/5005*(x^4+3*x^2+4)^(1/2)*x^3+48520/143*(x^4+3*x^2+4)^(1/2)*x^7+71434/91*(x^4+3*x^2+4)^(1/2)*x^5+125/13*(x^4+3*x^2+4)^(1/2)*x^11+12075/143*(x^4+3*x^2+4)^(1/2)*x^9-144821184/5005/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))+32017264/5005/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))","C"
358,1,292,250,0.009000," ","int((5*x^2+7)^2*(x^4+3*x^2+4)^(3/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+4}\, x^{9}}{11}+\frac{1670 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{99}+\frac{1222 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{21}+\frac{391024 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{3465}+\frac{50691 \sqrt{x^{4}+3 x^{2}+4}\, x}{385}+\frac{396304 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{385 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{5611072 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{1155 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"25/11*(x^4+3*x^2+4)^(1/2)*x^9+1670/99*(x^4+3*x^2+4)^(1/2)*x^7+1222/21*(x^4+3*x^2+4)^(1/2)*x^5+391024/3465*(x^4+3*x^2+4)^(1/2)*x^3+50691/385*(x^4+3*x^2+4)^(1/2)*x+396304/385/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-5611072/1155/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
359,1,275,235,0.008000," ","int((5*x^2+7)*(x^4+3*x^2+4)^(3/2),x)","\frac{5 \sqrt{x^{4}+3 x^{2}+4}\, x^{7}}{9}+\frac{71 \sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{21}+\frac{3187 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{315}+\frac{583 \sqrt{x^{4}+3 x^{2}+4}\, x}{35}+\frac{6352 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{35 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{89536 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{105 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"5/9*(x^4+3*x^2+4)^(1/2)*x^7+71/21*(x^4+3*x^2+4)^(1/2)*x^5+3187/315*(x^4+3*x^2+4)^(1/2)*x^3+583/35*(x^4+3*x^2+4)^(1/2)*x+6352/35/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-89536/105/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
360,1,258,228,0.004000," ","int((x^4+3*x^2+4)^(3/2),x)","\frac{\sqrt{x^{4}+3 x^{2}+4}\, x^{5}}{7}+\frac{24 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{35}+\frac{69 \sqrt{x^{4}+3 x^{2}+4}\, x}{35}+\frac{1136 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{35 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{4416 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{35 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"1/7*(x^4+3*x^2+4)^(1/2)*x^5+24/35*(x^4+3*x^2+4)^(1/2)*x^3+69/35*(x^4+3*x^2+4)^(1/2)*x+1136/35/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-4416/35/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
361,1,418,322,0.021000," ","int((x^4+3*x^2+4)^(3/2)/(5*x^2+7),x)","\frac{\sqrt{x^{4}+3 x^{2}+4}\, x^{3}}{25}+\frac{11 \sqrt{x^{4}+3 x^{2}+4}\, x}{75}+\frac{3008 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{125 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{9424 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{1875 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{3008 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{125 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{1936 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{4375 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"1/25*(x^4+3*x^2+4)^(1/2)*x^3+11/75*(x^4+3*x^2+4)^(1/2)*x+9424/1875/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-3008/125/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+3008/125/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+1936/4375/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
362,1,425,339,0.028000," ","int((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^2,x)","\frac{22 \sqrt{x^{4}+3 x^{2}+4}\, x}{175 \left(5 x^{2}+7\right)}+\frac{\sqrt{x^{4}+3 x^{2}+4}\, x}{75}+\frac{128 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{175 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{232 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{375 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{128 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{175 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{286 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{6125 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"22/175*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x+1/75*(x^4+3*x^2+4)^(1/2)*x+232/375/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-128/175/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+128/175/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+286/6125/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
363,1,434,348,0.027000," ","int((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^3,x)","\frac{11 \sqrt{x^{4}+3 x^{2}+4}\, x}{175 \left(5 x^{2}+7\right)^{2}}+\frac{167 \sqrt{x^{4}+3 x^{2}+4}\, x}{9800 \left(5 x^{2}+7\right)}+\frac{36 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{245 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{17 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{350 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{36 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{245 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{1347 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{68600 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"11/175*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2*x+167/9800*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x+17/350/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-36/245/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+36/245/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+1347/68600/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
364,1,241,223,0.031000," ","int((5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x)","25 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}+75 \sqrt{x^{4}+3 x^{2}+4}\, x +\frac{172 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{480 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"25*(x^4+3*x^2+4)^(1/2)*x^3+75*(x^4+3*x^2+4)^(1/2)*x+172/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+480/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
365,1,224,206,0.008000," ","int((5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+4}\, x}{3}+\frac{188 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{3 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{640 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"25/3*(x^4+3*x^2+4)^(1/2)*x+188/3/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-640/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
366,1,209,191,0.005000," ","int((5*x^2+7)/(x^4+3*x^2+4)^(1/2),x)","\frac{28 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{160 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"-160/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))+28/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))","C"
367,1,85,84,0.003000," ","int(1/(x^4+3*x^2+4)^(1/2),x)","\frac{4 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{\sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"4/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))","C"
368,1,107,194,0.018000," ","int(1/(5*x^2+7)/(x^4+3*x^2+4)^(1/2),x)","\frac{\sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{7 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"1/7/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
369,1,410,324,0.024000," ","int(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+4}\, x}{616 \left(5 x^{2}+7\right)}-\frac{20 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{77 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{\sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{22 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{20 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{77 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{37 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{4312 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"25/616*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x-1/22/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+20/77/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-20/77/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+37/4312/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
370,1,434,348,0.025000," ","int(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x)","\frac{25 \sqrt{x^{4}+3 x^{2}+4}\, x}{1232 \left(5 x^{2}+7\right)^{2}}+\frac{2775 \sqrt{x^{4}+3 x^{2}+4}\, x}{758912 \left(5 x^{2}+7\right)}-\frac{555 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{23716 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{23 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{27104 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{555 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{23716 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{3285 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{5312384 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}"," ",0,"25/1232*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2*x+2775/758912*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x-23/27104/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+555/23716/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-555/23716/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-3285/5312384/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
371,1,379,245,0.054000," ","int((5*x^2+7)^5/(x^4+3*x^2+4)^(3/2),x)","625 \sqrt{x^{4}+3 x^{2}+4}\, x^{3}+\frac{5000 \sqrt{x^{4}+3 x^{2}+4}\, x}{3}-\frac{505532 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{21 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{6250 \left(\frac{31}{14} x^{3}+\frac{18}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}+\frac{1766232 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{43750 \left(-\frac{9}{14} x^{3}+\frac{2}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{122500 \left(-\frac{1}{14} x^{3}-\frac{6}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{171500 \left(\frac{3}{14} x^{3}+\frac{4}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{120050 \left(-\frac{1}{7} x^{3}-\frac{3}{14} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{33614 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-6250*(31/14*x^3+18/7*x)/(x^4+3*x^2+4)^(1/2)+625*(x^4+3*x^2+4)^(1/2)*x^3+5000/3*(x^4+3*x^2+4)^(1/2)*x-505532/21/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+1766232/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))-43750*(-9/14*x^3+2/7*x)/(x^4+3*x^2+4)^(1/2)-122500*(-1/14*x^3-6/7*x)/(x^4+3*x^2+4)^(1/2)-171500*(3/14*x^3+4/7*x)/(x^4+3*x^2+4)^(1/2)-120050*(-1/7*x^3-3/14*x)/(x^4+3*x^2+4)^(1/2)-33614*(1/56*x+3/56*x^3)/(x^4+3*x^2+4)^(1/2)","C"
372,1,339,228,0.009000," ","int((5*x^2+7)^4/(x^4+3*x^2+4)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+4}\, x}{3}-\frac{27736 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{21 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{1250 \left(-\frac{9}{14} x^{3}+\frac{2}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{116184 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{7000 \left(-\frac{1}{14} x^{3}-\frac{6}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{14700 \left(\frac{3}{14} x^{3}+\frac{4}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{13720 \left(-\frac{1}{7} x^{3}-\frac{3}{14} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{4802 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-1250*(-9/14*x^3+2/7*x)/(x^4+3*x^2+4)^(1/2)+625/3*(x^4+3*x^2+4)^(1/2)*x-27736/21/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-116184/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))-7000*(-1/14*x^3-6/7*x)/(x^4+3*x^2+4)^(1/2)-14700*(3/14*x^3+4/7*x)/(x^4+3*x^2+4)^(1/2)-13720*(-1/7*x^3-3/14*x)/(x^4+3*x^2+4)^(1/2)-4802*(3/56*x^3+1/56*x)/(x^4+3*x^2+4)^(1/2)","C"
373,1,301,213,0.008000," ","int((5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x)","\frac{4724 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{250 \left(-\frac{1}{14} x^{3}-\frac{6}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{35592 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{1050 \left(\frac{3}{14} x^{3}+\frac{4}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{1470 \left(-\frac{1}{7} x^{3}-\frac{3}{14} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{686 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-250*(-1/14*x^3-6/7*x)/(x^4+3*x^2+4)^(1/2)+4724/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-35592/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))-1050*(3/14*x^3+4/7*x)/(x^4+3*x^2+4)^(1/2)-1470*(-1/7*x^3-3/14*x)/(x^4+3*x^2+4)^(1/2)-686*(3/56*x^3+1/56*x)/(x^4+3*x^2+4)^(1/2)","C"
374,1,278,213,0.008000," ","int((5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x)","\frac{352 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{50 \left(\frac{3}{14} x^{3}+\frac{4}{7} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}+\frac{904 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{140 \left(-\frac{1}{7} x^{3}-\frac{3}{14} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{98 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-50*(3/14*x^3+4/7*x)/(x^4+3*x^2+4)^(1/2)+352/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+904/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))-140*(-1/7*x^3-3/14*x)/(x^4+3*x^2+4)^(1/2)-98*(3/56*x^3+1/56*x)/(x^4+3*x^2+4)^(1/2)","C"
375,1,255,213,0.007000," ","int((5*x^2+7)/(x^4+3*x^2+4)^(3/2),x)","-\frac{4 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{10 \left(-\frac{1}{7} x^{3}-\frac{3}{14} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}+\frac{152 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{14 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-10*(-1/7*x^3-3/14*x)/(x^4+3*x^2+4)^(1/2)-4/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+152/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))-14*(3/56*x^3+1/56*x)/(x^4+3*x^2+4)^(1/2)","C"
376,1,232,213,0.005000," ","int(1/(x^4+3*x^2+4)^(3/2),x)","\frac{8 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{2 \left(\frac{3}{56} x^{3}+\frac{1}{56} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}-\frac{24 \sqrt{-\left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{8}-\frac{i \sqrt{7}}{8}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)+\EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)\right)}{7 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}"," ",0,"-2*(3/56*x^3+1/56*x)/(x^4+3*x^2+4)^(1/2)+8/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-24/7/(-6+2*I*7^(1/2))^(1/2)*(-(-3/8+1/8*I*7^(1/2))*x^2+1)^(1/2)*(-(-3/8-1/8*I*7^(1/2))*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*(EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2)))","C"
377,1,409,322,0.023000," ","int(1/(5*x^2+7)/(x^4+3*x^2+4)^(3/2),x)","\frac{32 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{77 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{\sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{77 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{32 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{77 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{25 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{308 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{2 \left(\frac{1}{154} x^{3}+\frac{13}{616} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-2*(1/154*x^3+13/616*x)/(x^4+3*x^2+4)^(1/2)-1/77/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-32/77/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+32/77/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+25/308/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
378,1,433,346,0.029000," ","int(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+4}\, x}{27104 \left(5 x^{2}+7\right)}-\frac{199 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{847 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{349 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{6776 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{199 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{847 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{575 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{189728 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{2 \left(-\frac{37}{27104} x^{3}-\frac{3}{3388} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"-2*(-37/27104*x^3-3/3388*x)/(x^4+3*x^2+4)^(1/2)+625/27104*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x-349/6776/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+199/847/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-199/847/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+575/189728/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
379,1,457,370,0.030000," ","int(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x)","\frac{625 \sqrt{x^{4}+3 x^{2}+4}\, x}{54208 \left(5 x^{2}+7\right)^{2}}+\frac{51875 \sqrt{x^{4}+3 x^{2}+4}\, x}{33392128 \left(5 x^{2}+7\right)}-\frac{18159 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticE \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{1043504 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}+\frac{1173 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{1192576 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}}+\frac{18159 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticF \left(\frac{\sqrt{-6+2 i \sqrt{7}}\, x}{4}, \frac{\sqrt{2+6 i \sqrt{7}}}{4}\right)}{1043504 \sqrt{-6+2 i \sqrt{7}}\, \sqrt{x^{4}+3 x^{2}+4}\, \left(i \sqrt{7}+3\right)}-\frac{529425 \sqrt{\frac{3 x^{2}}{8}-\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \sqrt{\frac{3 x^{2}}{8}+\frac{i \sqrt{7}\, x^{2}}{8}+1}\, \EllipticPi \left(\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, x , -\frac{5}{7 \left(-\frac{3}{8}+\frac{i \sqrt{7}}{8}\right)}, \frac{\sqrt{-\frac{3}{8}-\frac{i \sqrt{7}}{8}}}{\sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}}\right)}{233744896 \sqrt{-\frac{3}{8}+\frac{i \sqrt{7}}{8}}\, \sqrt{x^{4}+3 x^{2}+4}}-\frac{2 \left(-\frac{139}{1192576} x^{3}-\frac{137}{298144} x \right)}{\sqrt{x^{4}+3 x^{2}+4}}"," ",0,"625/54208*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2*x+51875/33392128*(x^4+3*x^2+4)^(1/2)/(5*x^2+7)*x-2*(-139/1192576*x^3-137/298144*x)/(x^4+3*x^2+4)^(1/2)+1173/1192576/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))+18159/1043504/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticF(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-18159/1043504/(-6+2*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)/(I*7^(1/2)+3)*EllipticE(1/4*(-6+2*I*7^(1/2))^(1/2)*x,1/4*(2+6*I*7^(1/2))^(1/2))-529425/233744896/(-3/8+1/8*I*7^(1/2))^(1/2)*(3/8*x^2-1/8*I*7^(1/2)*x^2+1)^(1/2)*(3/8*x^2+1/8*I*7^(1/2)*x^2+1)^(1/2)/(x^4+3*x^2+4)^(1/2)*EllipticPi((-3/8+1/8*I*7^(1/2))^(1/2)*x,-5/7/(-3/8+1/8*I*7^(1/2)),(-3/8-1/8*I*7^(1/2))^(1/2)/(-3/8+1/8*I*7^(1/2))^(1/2))","C"
380,1,1186,455,0.022000," ","int((e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{3 \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a \,d^{2} e}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, d^{3} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+3 \left(\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) d \,e^{2}+\left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{15 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{\left(-\frac{3 a}{5 c}+\frac{8 b^{2}}{15 c^{2}}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{15 c^{2}}\right) e^{3}"," ",0,"e^3*(1/5/c*x^3*(c*x^4+b*x^2+a)^(1/2)-4/15*b/c^2*x*(c*x^4+b*x^2+a)^(1/2)+1/15*b/c^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(-3/5*a/c+8/15*b^2/c^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))+3*d*e^2*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*x-1/12/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))-3/2*d^2*e*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","B"
381,1,756,348,0.008000," ","int((e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a d e}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, d^{2} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\left(\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) e^{2}"," ",0,"e^2*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*x-1/12/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))-d*e*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","B"
382,1,362,283,0.005000," ","int((e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a e}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, d \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}"," ",0,"-1/2*e*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
383,1,200,377,0.036000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d}"," ",0,"1/d*2^(1/2)/(-b/a+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2*b*x^2/a-1/2/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2*b*x^2/a+1/2/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
384,1,1279,681,0.036000," ","int(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) d}+\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) d}+\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, a \,e^{2} \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d^{2}}-\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, b e \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d}-\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{8 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{3 \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, c \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, e^{2} x}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(e \,x^{2}+d \right) d}"," ",0,"1/2*e^2*x*(c*x^4+b*x^2+a)^(1/2)/d/(a*e^2-b*d*e+c*d^2)/(e*x^2+d)-1/8*c/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/2/(a*e^2-b*d*e+c*d^2)/d^2*e^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a-1/(a*e^2-b*d*e+c*d^2)/d*e*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*b+3/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*c","A"
385,1,1195,477,0.023000," ","int((e*x^2+d)^3/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{3 \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a \,d^{2} e}{2 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, d^{3} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}+3 \left(-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) d \,e^{2}+\left(-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{15 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{\left(\frac{3 a}{5 c}+\frac{8 b^{2}}{15 c^{2}}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}-\frac{4 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, b x}{15 c^{2}}\right) e^{3}"," ",0,"e^3*(-1/5/c*x^3*(-c*x^4+b*x^2+a)^(1/2)-4/15*b/c^2*x*(-c*x^4+b*x^2+a)^(1/2)+1/15*b/c^2*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(3/5*a/c+8/15*b^2/c^2)*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))+3*d*e^2*(-1/3*(-c*x^4+b*x^2+a)^(1/2)/c*x+1/12/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/3*b/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))-3/2*d^2*e*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d^3*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","B"
386,1,761,382,0.009000," ","int((e*x^2+d)^2/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a d e}{\sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, d^{2} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}+\left(-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) e^{2}"," ",0,"e^2*(-1/3*(-c*x^4+b*x^2+a)^(1/2)/c*x+1/12/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/3*b/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))-d*e*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d^2*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
387,1,364,319,0.006000," ","int((e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a e}{2 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, d \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}"," ",0,"-1/2*e*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*d*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
388,1,201,165,0.038000," ","int(1/(e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, d}"," ",0,"1/d*2^(1/2)/(-1/a*b+1/a*(4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*b*x^2-1/2/a*x^2*(4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*b*x^2+1/2/a*x^2*(4*a*c+b^2)^(1/2))^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2))","A"
389,1,1293,613,0.036000," ","int(1/(e*x^2+d)^2/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) d}-\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) d}+\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, a \,e^{2} \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, d^{2}}-\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, b e \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}}\right)}{\left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, d}+\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{4 a c +b^{2}}\, x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{8 \left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}-\frac{3 \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, c \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-b d e -c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}+\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, e^{2} x}{2 \left(a \,e^{2}-b d e -c \,d^{2}\right) \left(e \,x^{2}+d \right) d}"," ",0,"1/2*e^2/(a*e^2-b*d*e-c*d^2)/d*x*(-c*x^4+b*x^2+a)^(1/2)/(e*x^2+d)+1/8*c/(a*e^2-b*d*e-c*d^2)*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/4*c*e/(a*e^2-b*d*e-c*d^2)/d*a*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/4*c*e/(a*e^2-b*d*e-c*d^2)/d*a*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/2/(a*e^2-b*d*e-c*d^2)/d^2*e^2*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2))*a-1/(a*e^2-b*d*e-c*d^2)/d*e*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2))*b-3/2/(a*e^2-b*d*e-c*d^2)*2^(1/2)/(-1/a*b+(4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2))*c","B"
390,1,355,558,0.033000," ","int((e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x)","\frac{\sqrt{\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a e}{\sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}+\frac{\sqrt{\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, d \EllipticF \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{2 \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}"," ",0,"e*a/(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(4+2*(-b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4-2*(b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2-a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*x*(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/2*d/(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(4+2*(-b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4-2*(b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2-a)^(1/2)*EllipticF(1/2*x*(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
391,1,198,172,0.033000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x)","\frac{\sqrt{-\frac{b \,x^{2}}{2 a}+\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{-\frac{b \,x^{2}}{2 a}-\frac{\sqrt{4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\sqrt{-\frac{-b +\sqrt{4 a c +b^{2}}}{2 a}}\, x , \frac{2 a e}{\left(-b +\sqrt{4 a c +b^{2}}\right) d}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{4 a c +b^{2}}}{a}}}{2 \sqrt{-\frac{-b +\sqrt{4 a c +b^{2}}}{2 a}}}\right)}{\sqrt{\frac{b}{2 a}-\frac{\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}\, d}"," ",0,"1/d/(1/2/a*b-1/2*(4*a*c+b^2)^(1/2)/a)^(1/2)*(1-1/2/a*b*x^2+1/2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(1-1/2/a*b*x^2-1/2*(4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2-a)^(1/2)*EllipticPi((-1/2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,2/(-b+(4*a*c+b^2)^(1/2))*a/d*e,1/2*2^(1/2)*((b+(4*a*c+b^2)^(1/2))/a)^(1/2)/(-1/2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2))","A"
392,1,357,293,0.035000," ","int((e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x)","\frac{\sqrt{\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{-\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a e}{\sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right)}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}-a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{-\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, d \EllipticF \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{2 \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right)}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}-a}}"," ",0,"e*a/(-2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4+2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4-2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(-c*x^4+b*x^2-a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*(-2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*x*(-2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/2*d/(-2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4+2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4-2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(-c*x^4+b*x^2-a)^(1/2)*EllipticF(1/2*x*(-2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
393,1,199,390,0.033000," ","int(1/(e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x)","\frac{\sqrt{-\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{-\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\sqrt{-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 a}}\, x , \frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}}{2 \sqrt{-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 a}}}\right)}{\sqrt{\frac{b}{2 a}-\frac{\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{-c \,x^{4}+b \,x^{2}-a}\, d}"," ",0,"1/d/(1/2/a*b-1/2*(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1-1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(1-1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(-c*x^4+b*x^2-a)^(1/2)*EllipticPi((-1/2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,1/2*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(-1/2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
394,1,380,241,0.011000," ","int((e*x^2+d)^3/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, d^{3} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}+\frac{3 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right) d^{2} e}{2 \sqrt{x^{4}+3 x^{2}+2}}+3 \left(\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{3}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{\sqrt{x^{4}+3 x^{2}+2}}\right) d \,e^{2}+\left(\frac{\sqrt{x^{4}+3 x^{2}+2}\, x^{3}}{5}-\frac{4 \sqrt{x^{4}+3 x^{2}+2}\, x}{5}-\frac{4 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{5 \sqrt{x^{4}+3 x^{2}+2}}+\frac{9 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{5 \sqrt{x^{4}+3 x^{2}+2}}\right) e^{3}"," ",0,"e^3*(1/5*(x^4+3*x^2+2)^(1/2)*x^3-4/5*(x^4+3*x^2+2)^(1/2)*x-4/5*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+9/5*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2))))+3*d*e^2*(1/3*(x^4+3*x^2+2)^(1/2)*x+1/3*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2))))+3/2*I*d^2*e*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-1/2*I*d^3*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))","C"
395,1,235,188,0.010000," ","int((e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, d^{2} \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right) d e}{\sqrt{x^{4}+3 x^{2}+2}}+\left(\frac{\sqrt{x^{4}+3 x^{2}+2}\, x}{3}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{x^{4}+3 x^{2}+2}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{\sqrt{x^{4}+3 x^{2}+2}}\right) e^{2}"," ",0,"e^2*(1/3*(x^4+3*x^2+2)^(1/2)*x+1/3*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2))))+I*d*e*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-1/2*I*d^2*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))","C"
396,1,108,149,0.005000," ","int((e*x^2+d)/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, d \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right) e}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/2*I*e*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-EllipticE(1/2*I*2^(1/2)*x,2^(1/2)))-1/2*I*d*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))","C"
397,1,55,153,0.025000," ","int(1/(e*x^2+d)/(x^4+3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 e}{d}, \sqrt{2}\right)}{\sqrt{x^{4}+3 x^{2}+2}\, d}"," ",0,"-I/d*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,2*e/d,2^(1/2))","C"
398,1,443,354,0.031000," ","int(1/(e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x)","\frac{\sqrt{x^{4}+3 x^{2}+2}\, e^{2} x}{2 \left(d^{2}-3 d e +2 e^{2}\right) \left(e \,x^{2}+d \right) d}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, e \EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{4 \left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}\, d}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, e \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{4 \left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}\, d}+\frac{3 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, e \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 e}{d}, \sqrt{2}\right)}{\left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}\, d}-\frac{i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, e^{2} \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 e}{d}, \sqrt{2}\right)}{\left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}\, d^{2}}+\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{4 \left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}}-\frac{3 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{2 e}{d}, \sqrt{2}\right)}{2 \left(d^{2}-3 d e +2 e^{2}\right) \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"1/2*e^2*x*(x^4+3*x^2+2)^(1/2)/d/(d^2-3*d*e+2*e^2)/(e*x^2+d)+1/4*I/(d^2-3*d*e+2*e^2)*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-1/4*I*e/(d^2-3*d*e+2*e^2)/d*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))+1/4*I*e/(d^2-3*d*e+2*e^2)/d*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticE(1/2*I*2^(1/2)*x,2^(1/2))-3/2*I/(d^2-3*d*e+2*e^2)*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,2/d*e,2^(1/2))+3*I/(d^2-3*d*e+2*e^2)/d*e*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,2/d*e,2^(1/2))-I/(d^2-3*d*e+2*e^2)/d^2*e^2*2^(1/2)*(1/2*x^2+1)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,2/d*e,2^(1/2))","C"
399,0,0,26,0.096000," ","int((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x)","\int \left(e \,x^{2}+c \right)^{q} \left(b \,x^{4}+c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x)","F"
400,0,0,472,0.088000," ","int((e*x^2+c)^3*(b*x^4+c*x^2+a)^p,x)","\int \left(e \,x^{2}+c \right)^{3} \left(b \,x^{4}+c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)^3*(b*x^4+c*x^2+a)^p,x)","F"
401,0,0,332,0.086000," ","int((e*x^2+c)^2*(b*x^4+c*x^2+a)^p,x)","\int \left(e \,x^{2}+c \right)^{2} \left(b \,x^{4}+c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)^2*(b*x^4+c*x^2+a)^p,x)","F"
402,0,0,248,0.027000," ","int((e*x^2+c)*(b*x^4+c*x^2+a)^p,x)","\int \left(e \,x^{2}+c \right) \left(b \,x^{4}+c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x^2+c)*(b*x^4+c*x^2+a)^p,x)","F"
403,0,0,121,0.015000," ","int((b*x^4+c*x^2+a)^p,x)","\int \left(b \,x^{4}+c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((b*x^4+c*x^2+a)^p,x)","F"
404,0,0,26,0.093000," ","int((b*x^4+c*x^2+a)^p/(e*x^2+c),x)","\int \frac{\left(b \,x^{4}+c \,x^{2}+a \right)^{p}}{e \,x^{2}+c}\, dx"," ",0,"int((b*x^4+c*x^2+a)^p/(e*x^2+c),x)","F"
405,0,0,26,0.115000," ","int((b*x^4+c*x^2+a)^p/(e*x^2+c)^2,x)","\int \frac{\left(b \,x^{4}+c \,x^{2}+a \right)^{p}}{\left(e \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+c*x^2+a)^p/(e*x^2+c)^2,x)","F"
406,1,251,426,0.021000," ","int((g*x+f)/(e*x+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, g \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e}+\frac{\left(-d g +e f \right) \left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}}\right)}{e^{2}}"," ",0,"g/e/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+(-d*g+e*f)/e^2*(-1/2/(c*d^4/e^4+a)^(1/2)*arctanh(1/2*(2*c*x^2*d^2/e^2+2*a)/(c*d^4/e^4+a)^(1/2)/(c*x^4+a)^(1/2))+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*e*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
407,1,247,182,0.020000," ","int((g*x+f)/(e*x+d)/(c*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, g \EllipticF \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}\, e}+\frac{\left(-d g +e f \right) \left(\frac{\sqrt{\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, x , -\frac{\sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{\frac{\sqrt{c}}{\sqrt{a}}}}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{-\frac{\sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}-a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}-2 a}{2 \sqrt{-a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}-a}}\right)}{2 \sqrt{-a +\frac{c \,d^{4}}{e^{4}}}}\right)}{e^{2}}"," ",0,"g/e/(-1/a^(1/2)*c^(1/2))^(1/2)*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticF((-1/a^(1/2)*c^(1/2))^(1/2)*x,I)+(-d*g+e*f)/e^2*(-1/2/(c*d^4/e^4-a)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2-2*a)/(c*d^4/e^4-a)^(1/2)/(c*x^4-a)^(1/2))+1/(-1/a^(1/2)*c^(1/2))^(1/2)/d*e*(1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4-a)^(1/2)*EllipticPi((-1/a^(1/2)*c^(1/2))^(1/2)*x,-e^2*a^(1/2)/d^2/c^(1/2),(1/a^(1/2)*c^(1/2))^(1/2)/(-1/a^(1/2)*c^(1/2))^(1/2)))","A"
408,1,327,47,0.166000," ","int((1+x-3^(1/2))/(1+x+3^(1/2))/(-4+x^4+4*x^2*3^(1/2))^(1/2),x)","\frac{\sqrt{-\left(\frac{\sqrt{3}}{2}-1\right) x^{2}+1}\, \sqrt{-\left(1+\frac{\sqrt{3}}{2}\right) x^{2}+1}\, \EllipticF \left(\left(\frac{i \sqrt{3}}{2}-\frac{i}{2}\right) x , i \sqrt{1+4 \sqrt{3}\, \left(1+\frac{\sqrt{3}}{2}\right)}\right)}{\left(\frac{i \sqrt{3}}{2}-\frac{i}{2}\right) \sqrt{x^{4}+4 \sqrt{3}\, x^{2}-4}}-2 \sqrt{3}\, \left(-\frac{\sqrt{-\left(\frac{\sqrt{3}}{2}-1\right) x^{2}+1}\, \sqrt{-\left(1+\frac{\sqrt{3}}{2}\right) x^{2}+1}\, \EllipticPi \left(\sqrt{\frac{\sqrt{3}}{2}-1}\, x , \frac{1}{\left(\frac{\sqrt{3}}{2}-1\right) \left(-1-\sqrt{3}\right)^{2}}, \frac{\sqrt{1+\frac{\sqrt{3}}{2}}}{\sqrt{\frac{\sqrt{3}}{2}-1}}\right)}{\sqrt{\frac{\sqrt{3}}{2}-1}\, \left(-1-\sqrt{3}\right) \sqrt{x^{4}+4 \sqrt{3}\, x^{2}-4}}-\frac{\arctanh \left(\frac{4 \sqrt{3}\, x^{2}+2 \left(-1-\sqrt{3}\right)^{2} x^{2}+4 \sqrt{3}\, \left(-1-\sqrt{3}\right)^{2}-8}{2 \sqrt{\left(-1-\sqrt{3}\right)^{4}+4 \sqrt{3}\, \left(-1-\sqrt{3}\right)^{2}-4}\, \sqrt{x^{4}+4 \sqrt{3}\, x^{2}-4}}\right)}{2 \sqrt{\left(-1-\sqrt{3}\right)^{4}+4 \sqrt{3}\, \left(-1-\sqrt{3}\right)^{2}-4}}\right)"," ",0,"1/(1/2*I*3^(1/2)-1/2*I)*(1-(1/2*3^(1/2)-1)*x^2)^(1/2)*(1-(1+1/2*3^(1/2))*x^2)^(1/2)/(-4+x^4+4*x^2*3^(1/2))^(1/2)*EllipticF(x*(1/2*I*3^(1/2)-1/2*I),I*(1+4*3^(1/2)*(1+1/2*3^(1/2)))^(1/2))-2*3^(1/2)*(-1/2/((-1-3^(1/2))^4+4*3^(1/2)*(-1-3^(1/2))^2-4)^(1/2)*arctanh(1/2*(4*3^(1/2)*(-1-3^(1/2))^2-8+4*x^2*3^(1/2)+2*x^2*(-1-3^(1/2))^2)/((-1-3^(1/2))^4+4*3^(1/2)*(-1-3^(1/2))^2-4)^(1/2)/(-4+x^4+4*x^2*3^(1/2))^(1/2))-1/(1/2*3^(1/2)-1)^(1/2)/(-1-3^(1/2))*(1-(1/2*3^(1/2)-1)*x^2)^(1/2)*(1-(1+1/2*3^(1/2))*x^2)^(1/2)/(-4+x^4+4*x^2*3^(1/2))^(1/2)*EllipticPi((1/2*3^(1/2)-1)^(1/2)*x,1/(1/2*3^(1/2)-1)/(-1-3^(1/2))^2,(1+1/2*3^(1/2))^(1/2)/(1/2*3^(1/2)-1)^(1/2)))","C"
409,1,311,45,0.161000," ","int((1+x+3^(1/2))/(1+x-3^(1/2))/(-4+x^4-4*3^(1/2)*x^2)^(1/2),x)","\frac{\sqrt{-\left(-1-\frac{\sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{3}}{2}+1\right) x^{2}+1}\, \EllipticF \left(\left(\frac{i}{2}+\frac{i \sqrt{3}}{2}\right) x , i \sqrt{1-4 \sqrt{3}\, \left(-\frac{\sqrt{3}}{2}+1\right)}\right)}{\left(\frac{i}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{x^{4}-4 \sqrt{3}\, x^{2}-4}}+2 \sqrt{3}\, \left(-\frac{\sqrt{-\left(-1-\frac{\sqrt{3}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{3}}{2}+1\right) x^{2}+1}\, \EllipticPi \left(\sqrt{-1-\frac{\sqrt{3}}{2}}\, x , \frac{1}{\left(-1-\frac{\sqrt{3}}{2}\right) \left(\sqrt{3}-1\right)^{2}}, \frac{\sqrt{-\frac{\sqrt{3}}{2}+1}}{\sqrt{-1-\frac{\sqrt{3}}{2}}}\right)}{\sqrt{-1-\frac{\sqrt{3}}{2}}\, \left(\sqrt{3}-1\right) \sqrt{x^{4}-4 \sqrt{3}\, x^{2}-4}}-\frac{\arctanh \left(\frac{-4 \sqrt{3}\, x^{2}+2 \left(\sqrt{3}-1\right)^{2} x^{2}-4 \sqrt{3}\, \left(\sqrt{3}-1\right)^{2}-8}{2 \sqrt{\left(\sqrt{3}-1\right)^{4}-4 \sqrt{3}\, \left(\sqrt{3}-1\right)^{2}-4}\, \sqrt{x^{4}-4 \sqrt{3}\, x^{2}-4}}\right)}{2 \sqrt{\left(\sqrt{3}-1\right)^{4}-4 \sqrt{3}\, \left(\sqrt{3}-1\right)^{2}-4}}\right)"," ",0,"1/(1/2*I+1/2*I*3^(1/2))*(1-(-1-1/2*3^(1/2))*x^2)^(1/2)*(1-(-1/2*3^(1/2)+1)*x^2)^(1/2)/(-4+x^4-4*3^(1/2)*x^2)^(1/2)*EllipticF(x*(1/2*I+1/2*I*3^(1/2)),I*(1-4*3^(1/2)*(-1/2*3^(1/2)+1))^(1/2))+2*3^(1/2)*(-1/2/((3^(1/2)-1)^4-4*3^(1/2)*(3^(1/2)-1)^2-4)^(1/2)*arctanh(1/2*(-4*3^(1/2)*(3^(1/2)-1)^2-8-4*3^(1/2)*x^2+2*x^2*(3^(1/2)-1)^2)/((3^(1/2)-1)^4-4*3^(1/2)*(3^(1/2)-1)^2-4)^(1/2)/(-4+x^4-4*3^(1/2)*x^2)^(1/2))-1/(-1-1/2*3^(1/2))^(1/2)/(3^(1/2)-1)*(1-(-1-1/2*3^(1/2))*x^2)^(1/2)*(1-(-1/2*3^(1/2)+1)*x^2)^(1/2)/(-4+x^4-4*3^(1/2)*x^2)^(1/2)*EllipticPi((-1-1/2*3^(1/2))^(1/2)*x,1/(-1-1/2*3^(1/2))/(3^(1/2)-1)^2,(-1/2*3^(1/2)+1)^(1/2)/(-1-1/2*3^(1/2))^(1/2)))","C"
410,1,336,52,0.161000," ","int((1+2*x-3^(1/2))/(1+2*x+3^(1/2))/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2),x)","\frac{\sqrt{-\left(2 \sqrt{3}-4\right) x^{2}+1}\, \sqrt{-\left(4+2 \sqrt{3}\right) x^{2}+1}\, \EllipticF \left(\left(i \sqrt{3}-i\right) x , i \sqrt{1+\sqrt{3}\, \left(4+2 \sqrt{3}\right)}\right)}{\left(i \sqrt{3}-i\right) \sqrt{4 x^{4}+4 \sqrt{3}\, x^{2}-1}}-2 \sqrt{3}\, \left(-\frac{\sqrt{-\left(2 \sqrt{3}-4\right) x^{2}+1}\, \sqrt{-\left(4+2 \sqrt{3}\right) x^{2}+1}\, \EllipticPi \left(\sqrt{2 \sqrt{3}-4}\, x , \frac{1}{\left(2 \sqrt{3}-4\right) \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{2}}, \frac{\sqrt{4+2 \sqrt{3}}}{\sqrt{2 \sqrt{3}-4}}\right)}{2 \sqrt{2 \sqrt{3}-4}\, \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right) \sqrt{4 x^{4}+4 \sqrt{3}\, x^{2}-1}}-\frac{\arctanh \left(\frac{4 \sqrt{3}\, x^{2}+8 \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{2} x^{2}+4 \sqrt{3}\, \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{2}-2}{2 \sqrt{4 \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{4}+4 \sqrt{3}\, \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{2}-1}\, \sqrt{4 x^{4}+4 \sqrt{3}\, x^{2}-1}}\right)}{4 \sqrt{4 \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{4}+4 \sqrt{3}\, \left(-\frac{1}{2}-\frac{\sqrt{3}}{2}\right)^{2}-1}}\right)"," ",0,"1/(I*3^(1/2)-I)*(1-(2*3^(1/2)-4)*x^2)^(1/2)*(1-(4+2*3^(1/2))*x^2)^(1/2)/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2)*EllipticF(x*(I*3^(1/2)-I),I*(1+3^(1/2)*(4+2*3^(1/2)))^(1/2))-2*3^(1/2)*(-1/4/(4*(-1/2-1/2*3^(1/2))^4+4*3^(1/2)*(-1/2-1/2*3^(1/2))^2-1)^(1/2)*arctanh(1/2*(4*3^(1/2)*(-1/2-1/2*3^(1/2))^2-2+4*3^(1/2)*x^2+8*x^2*(-1/2-1/2*3^(1/2))^2)/(4*(-1/2-1/2*3^(1/2))^4+4*3^(1/2)*(-1/2-1/2*3^(1/2))^2-1)^(1/2)/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2))-1/2/(2*3^(1/2)-4)^(1/2)/(-1/2-1/2*3^(1/2))*(1-(2*3^(1/2)-4)*x^2)^(1/2)*(1-(4+2*3^(1/2))*x^2)^(1/2)/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2)*EllipticPi((2*3^(1/2)-4)^(1/2)*x,1/(2*3^(1/2)-4)/(-1/2-1/2*3^(1/2))^2,(4+2*3^(1/2))^(1/2)/(2*3^(1/2)-4)^(1/2)))","C"
411,1,337,50,0.154000," ","int((1+2*x+3^(1/2))/(1+2*x-3^(1/2))/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2),x)","\frac{\sqrt{-\left(-4-2 \sqrt{3}\right) x^{2}+1}\, \sqrt{-\left(-2 \sqrt{3}+4\right) x^{2}+1}\, \EllipticF \left(\left(i+i \sqrt{3}\right) x , i \sqrt{1-\sqrt{3}\, \left(-2 \sqrt{3}+4\right)}\right)}{\left(i+i \sqrt{3}\right) \sqrt{4 x^{4}-4 \sqrt{3}\, x^{2}-1}}+2 \sqrt{3}\, \left(-\frac{\sqrt{-\left(-4-2 \sqrt{3}\right) x^{2}+1}\, \sqrt{-\left(-2 \sqrt{3}+4\right) x^{2}+1}\, \EllipticPi \left(\sqrt{-4-2 \sqrt{3}}\, x , \frac{1}{\left(-4-2 \sqrt{3}\right) \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{2}}, \frac{\sqrt{-2 \sqrt{3}+4}}{\sqrt{-4-2 \sqrt{3}}}\right)}{2 \sqrt{-4-2 \sqrt{3}}\, \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right) \sqrt{4 x^{4}-4 \sqrt{3}\, x^{2}-1}}-\frac{\arctanh \left(\frac{-4 \sqrt{3}\, x^{2}+8 \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{2} x^{2}-4 \sqrt{3}\, \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{2}-2}{2 \sqrt{4 \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{4}-4 \sqrt{3}\, \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{2}-1}\, \sqrt{4 x^{4}-4 \sqrt{3}\, x^{2}-1}}\right)}{4 \sqrt{4 \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{4}-4 \sqrt{3}\, \left(\frac{\sqrt{3}}{2}-\frac{1}{2}\right)^{2}-1}}\right)"," ",0,"1/(I+I*3^(1/2))*(1-(-4-2*3^(1/2))*x^2)^(1/2)*(1-(-2*3^(1/2)+4)*x^2)^(1/2)/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2)*EllipticF(x*(I+I*3^(1/2)),I*(1-3^(1/2)*(-2*3^(1/2)+4))^(1/2))+2*3^(1/2)*(-1/4/(4*(1/2*3^(1/2)-1/2)^4-4*3^(1/2)*(1/2*3^(1/2)-1/2)^2-1)^(1/2)*arctanh(1/2*(-4*3^(1/2)*(1/2*3^(1/2)-1/2)^2-2-4*3^(1/2)*x^2+8*x^2*(1/2*3^(1/2)-1/2)^2)/(4*(1/2*3^(1/2)-1/2)^4-4*3^(1/2)*(1/2*3^(1/2)-1/2)^2-1)^(1/2)/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2))-1/2/(-4-2*3^(1/2))^(1/2)/(1/2*3^(1/2)-1/2)*(1-(-4-2*3^(1/2))*x^2)^(1/2)*(1-(-2*3^(1/2)+4)*x^2)^(1/2)/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2)*EllipticPi((-4-2*3^(1/2))^(1/2)*x,1/(-4-2*3^(1/2))/(1/2*3^(1/2)-1/2)^2,(-2*3^(1/2)+4)^(1/2)/(-4-2*3^(1/2))^(1/2)))","C"
412,1,437,525,0.025000," ","int((g*x+f)/(e*x+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, g \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, e}+\frac{\left(-d g +e f \right) \left(\frac{\sqrt{2}\, \sqrt{-\frac{\left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{2 a}+1}\, \sqrt{\frac{\left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{2 a}+1}\, e \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{2 a \,e^{2}}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d^{2}}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d}-\frac{\arctanh \left(\frac{b \,x^{2}+\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a +\frac{b \,d^{2}}{e^{2}}}{2 \sqrt{a +\frac{b \,d^{2}}{e^{2}}+\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}\right)}{2 \sqrt{a +\frac{b \,d^{2}}{e^{2}}+\frac{c \,d^{4}}{e^{4}}}}\right)}{e^{2}}"," ",0,"1/4*g/e*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+(-d*g+e*f)/e^2*(-1/2/(c*d^4/e^4+b*d^2/e^2+a)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+b*x^2+b*d^2/e^2+2*a)/(c*d^4/e^4+b*d^2/e^2+a)^(1/2)/(c*x^4+b*x^2+a)^(1/2))+2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/d*e*(1-1/2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(1+1/2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,2/(-b+(-4*a*c+b^2)^(1/2))*a/d^2*e^2,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","A"
413,1,439,531,0.024000," ","int((g*x+f)/(e*x+d)/(c*x^4+b*x^2-a)^(1/2),x)","\frac{\sqrt{\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, g \EllipticF \left(\frac{\sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{2 \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right)}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}\, e}+\frac{\left(-d g +e f \right) \left(\frac{\sqrt{\frac{\left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{2 a}+1}\, \sqrt{-\frac{\left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{2 a}+1}\, e \EllipticPi \left(\sqrt{-\frac{-b +\sqrt{4 a c +b^{2}}}{2 a}}\, x , -\frac{2 a \,e^{2}}{\left(-b +\sqrt{4 a c +b^{2}}\right) d^{2}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{4 a c +b^{2}}}{a}}}{2 \sqrt{-\frac{-b +\sqrt{4 a c +b^{2}}}{2 a}}}\right)}{\sqrt{-\frac{-b +\sqrt{4 a c +b^{2}}}{2 a}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}\, d}-\frac{\arctanh \left(\frac{b \,x^{2}+\frac{2 c \,d^{2} x^{2}}{e^{2}}-2 a +\frac{b \,d^{2}}{e^{2}}}{2 \sqrt{-a +\frac{b \,d^{2}}{e^{2}}+\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}\right)}{2 \sqrt{-a +\frac{b \,d^{2}}{e^{2}}+\frac{c \,d^{4}}{e^{4}}}}\right)}{e^{2}}"," ",0,"1/2*g/e/(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(-2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2-a)^(1/2)*EllipticF(1/2*(-2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+(-d*g+e*f)/e^2*(-1/2/(c*d^4/e^4+b*d^2/e^2-a)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+b*x^2+b*d^2/e^2-2*a)/(c*d^4/e^4+b*d^2/e^2-a)^(1/2)/(c*x^4+b*x^2-a)^(1/2))+1/(-1/2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)/d*e*(1+1/2*(-b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(1-1/2*(b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2-a)^(1/2)*EllipticPi((-1/2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(4*a*c+b^2)^(1/2))*a/d^2*e^2,1/2*2^(1/2)*((b+(4*a*c+b^2)^(1/2))/a)^(1/2)/(-1/2*(-b+(4*a*c+b^2)^(1/2))/a)^(1/2)))","A"