1,1,193,94,0.067000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^3,x)","\frac{\left(a x -1\right) \left(6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +8 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-15 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{24 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} \sqrt{a^{2}}}"," ",0,"1/24*(a*x-1)*(6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+8*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+24*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-15*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^4/(a^2)^(1/2)","B"
2,1,173,74,0.046000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2,x)","\frac{\left(a x -1\right) \left(3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+6 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{3} \sqrt{a^{2}}}"," ",0,"1/6*(a*x-1)*(3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+6*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^3/(a^2)^(1/2)","B"
3,1,152,53,0.046000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x,x)","\frac{\left(a x -1\right) \left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} \sqrt{a^{2}}}"," ",0,"1/2*(a*x-1)*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^2/(a^2)^(1/2)","B"
4,1,97,32,0.040000," ","int(1/((a*x-1)/(a*x+1))^(1/2),x)","\frac{\left(a x -1\right) \left(\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"(a*x-1)*(((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
5,1,131,20,0.049000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x,x)","\frac{\left(a x -1\right) \left(\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}+a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"(a*x-1)*(((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)+a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","B"
6,1,220,22,0.051000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^2,x)","\frac{\left(a x -1\right) \left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x \sqrt{a^{2}}}"," ",0,"(a*x-1)*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/x/(a^2)^(1/2)","B"
7,1,260,32,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^3,x)","\frac{\left(a x -1\right) \left(2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{2} \sqrt{a^{2}}}"," ",0,"1/2*(a*x-1)*(2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/x^2/(a^2)^(1/2)","B"
8,1,284,63,0.057000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^4,x)","-\frac{\left(a x -1\right) \left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-6 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+3 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} \sqrt{a^{2}}}"," ",0,"-1/6*(a*x-1)*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+3*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/x^3/(a^2)^(1/2)","B"
9,1,308,74,0.059000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^5,x)","-\frac{\left(a x -1\right) \left(-24 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+9 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+24 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-24 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+15 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+8 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{24 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} \sqrt{a^{2}}}"," ",0,"-1/24*(a*x-1)*(-24*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+9*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+24*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-24*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+15*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+8*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/x^4/(a^2)^(1/2)","B"
10,1,39,39,0.035000," ","int((a*x+1)/(a*x-1)*x^3,x)","\frac{x^{4}}{4}+\frac{2 x^{3}}{3 a}+\frac{x^{2}}{a^{2}}+\frac{2 x}{a^{3}}+\frac{2 \ln \left(a x -1\right)}{a^{4}}"," ",0,"1/4*x^4+2/3*x^3/a+x^2/a^2+2*x/a^3+2/a^4*ln(a*x-1)","A"
11,1,31,31,0.036000," ","int((a*x+1)/(a*x-1)*x^2,x)","\frac{x^{3}}{3}+\frac{x^{2}}{a}+\frac{2 x}{a^{2}}+\frac{2 \ln \left(a x -1\right)}{a^{3}}"," ",0,"1/3*x^3+x^2/a+2*x/a^2+2/a^3*ln(a*x-1)","A"
12,1,24,24,0.035000," ","int((a*x+1)/(a*x-1)*x,x)","\frac{x^{2}}{2}+\frac{2 x}{a}+\frac{2 \ln \left(a x -1\right)}{a^{2}}"," ",0,"1/2*x^2+2*x/a+2/a^2*ln(a*x-1)","A"
13,1,14,14,0.034000," ","int((a*x+1)/(a*x-1),x)","x +\frac{2 \ln \left(a x -1\right)}{a}"," ",0,"x+2/a*ln(a*x-1)","A"
14,1,14,14,0.040000," ","int((a*x+1)/(a*x-1)/x,x)","-\ln \left(x \right)+2 \ln \left(a x -1\right)"," ",0,"-ln(x)+2*ln(a*x-1)","A"
15,1,19,19,0.041000," ","int((a*x+1)/(a*x-1)/x^2,x)","\frac{1}{x}-2 a \ln \left(x \right)+2 a \ln \left(a x -1\right)"," ",0,"1/x-2*a*ln(x)+2*a*ln(a*x-1)","A"
16,1,31,31,0.040000," ","int((a*x+1)/(a*x-1)/x^3,x)","\frac{1}{2 x^{2}}+\frac{2 a}{x}-2 a^{2} \ln \left(x \right)+2 a^{2} \ln \left(a x -1\right)"," ",0,"1/2/x^2+2*a/x-2*a^2*ln(x)+2*a^2*ln(a*x-1)","A"
17,1,38,38,0.042000," ","int((a*x+1)/(a*x-1)/x^4,x)","\frac{1}{3 x^{3}}+\frac{a}{x^{2}}+\frac{2 a^{2}}{x}-2 a^{3} \ln \left(x \right)+2 a^{3} \ln \left(a x -1\right)"," ",0,"1/3/x^3+a/x^2+2*a^2/x-2*a^3*ln(x)+2*a^3*ln(a*x-1)","A"
18,1,471,100,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^2,x)","\frac{9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-18 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-4 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +42 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+42 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +18 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-10 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-84 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -84 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +42 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+42 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{6 a^{3} \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/6/a^3*(9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-18*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+42*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+42*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+18*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-10*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-84*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-84*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+42*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+42*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
19,1,421,80,0.055000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x,x)","-\frac{-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-10 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-10 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+4 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+20 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+20 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-10 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -10 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{2 a^{2} \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/2/a^2*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-10*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-10*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+4*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+20*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+20*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-10*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-10*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
20,1,248,56,0.049000," ","int(1/((a*x-1)/(a*x+1))^(3/2),x)","-\frac{-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-3 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-3 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{a \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/a*(-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-3*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-3*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
21,1,363,42,0.055000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/x,x)","\frac{\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}+\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}+a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(1/2)*(a^2)^(1/2)+arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)+a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
22,1,593,47,0.057000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/x^2,x)","\frac{-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+5 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-\sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -7 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-6 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +3 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}}{\sqrt{a^{2}}\, x \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+5*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-7*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-6*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+3*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/(a^2)^(1/2)/x/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
23,1,641,79,0.056000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/x^3,x)","\frac{-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+21 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+9 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-6 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-11 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-24 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-18 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-12 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-4 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+12 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+12 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+9 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}}{2 \sqrt{a^{2}}\, x^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/2*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+21*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+9*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-11*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-24*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-18*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-12*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+12*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+12*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+9*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/(a^2)^(1/2)/x^2/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
24,1,666,81,0.062000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/x^4,x)","\frac{-30 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+93 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+33 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+30 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-30 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-30 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-51 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-96 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-66 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)-60 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-12 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+60 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+14 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+33 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+33 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+30 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-30 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-30 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+5 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}}{6 \sqrt{a^{2}}\, x^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/6*(-30*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+93*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+33*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+30*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-30*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-30*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-51*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-96*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-66*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))-60*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-12*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+60*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+14*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+33*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+33*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+30*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-30*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-30*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+5*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/(a^2)^(1/2)/x^3/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
25,1,52,53,0.042000," ","int(1/(a*x-1)^2*(a*x+1)^2*x^3,x)","\frac{x^{4}}{4}+\frac{4 x^{3}}{3 a}+\frac{4 x^{2}}{a^{2}}+\frac{12 x}{a^{3}}+\frac{16 \ln \left(a x -1\right)}{a^{4}}-\frac{4}{a^{4} \left(a x -1\right)}"," ",0,"1/4*x^4+4/3*x^3/a+4*x^2/a^2+12*x/a^3+16/a^4*ln(a*x-1)-4/a^4/(a*x-1)","A"
26,1,44,45,0.040000," ","int(1/(a*x-1)^2*(a*x+1)^2*x^2,x)","\frac{x^{3}}{3}+\frac{2 x^{2}}{a}+\frac{8 x}{a^{2}}+\frac{12 \ln \left(a x -1\right)}{a^{3}}-\frac{4}{a^{3} \left(a x -1\right)}"," ",0,"1/3*x^3+2*x^2/a+8*x/a^2+12/a^3*ln(a*x-1)-4/a^3/(a*x-1)","A"
27,1,36,37,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2*x,x)","\frac{x^{2}}{2}+\frac{4 x}{a}+\frac{8 \ln \left(a x -1\right)}{a^{2}}-\frac{4}{a^{2} \left(a x -1\right)}"," ",0,"1/2*x^2+4*x/a+8/a^2*ln(a*x-1)-4/a^2/(a*x-1)","A"
28,1,26,27,0.039000," ","int(1/(a*x-1)^2*(a*x+1)^2,x)","x +\frac{4 \ln \left(a x -1\right)}{a}-\frac{4}{a \left(a x -1\right)}"," ",0,"x+4/a*ln(a*x-1)-4/a/(a*x-1)","A"
29,1,13,13,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2/x,x)","\ln \left(x \right)-\frac{4}{a x -1}"," ",0,"ln(x)-4/(a*x-1)","A"
30,1,31,32,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2/x^2,x)","-\frac{1}{x}+4 a \ln \left(x \right)-\frac{4 a}{a x -1}-4 a \ln \left(a x -1\right)"," ",0,"-1/x+4*a*ln(x)-4*a/(a*x-1)-4*a*ln(a*x-1)","A"
31,1,43,44,0.040000," ","int(1/(a*x-1)^2*(a*x+1)^2/x^3,x)","-\frac{1}{2 x^{2}}-\frac{4 a}{x}+8 a^{2} \ln \left(x \right)-\frac{4 a^{2}}{a x -1}-8 a^{2} \ln \left(a x -1\right)"," ",0,"-1/2/x^2-4*a/x+8*a^2*ln(x)-4*a^2/(a*x-1)-8*a^2*ln(a*x-1)","A"
32,1,51,52,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2/x^4,x)","-\frac{1}{3 x^{3}}-\frac{2 a}{x^{2}}-\frac{8 a^{2}}{x}+12 a^{3} \ln \left(x \right)-\frac{4 a^{3}}{a x -1}-12 a^{3} \ln \left(a x -1\right)"," ",0,"-1/3/x^3-2*a/x^2-8*a^2/x+12*a^3*ln(x)-4*a^3/(a*x-1)-12*a^3*ln(a*x-1)","A"
33,1,193,94,0.051000," ","int(x^3*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -8 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-15 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right)}{24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} \sqrt{a^{2}}}"," ",0,"1/24*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-8*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-15*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-24*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^4/(a^2)^(1/2)","B"
34,1,173,74,0.052000," ","int(x^2*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+6 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{3} \sqrt{a^{2}}}"," ",0,"-1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+6*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a^3/(a^2)^(1/2)","B"
35,1,152,54,0.046000," ","int(x*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} \sqrt{a^{2}}}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a^2/(a^2)^(1/2)","B"
36,1,98,33,0.042000," ","int(((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
37,1,133,18,0.051000," ","int(((a*x-1)/(a*x+1))^(1/2)/x,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}-a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)-a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","B"
38,1,220,23,0.052000," ","int(((a*x-1)/(a*x+1))^(1/2)/x^2,x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, x \sqrt{a^{2}}}"," ",0,"((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)*(a*x+1))^(1/2)/x/(a^2)^(1/2)","B"
39,1,260,34,0.054000," ","int(((a*x-1)/(a*x+1))^(1/2)/x^3,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{2} \sqrt{a^{2}}}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/x^2/(a^2)^(1/2)","B"
40,1,284,64,0.059000," ","int(((a*x-1)/(a*x+1))^(1/2)/x^4,x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+6 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-3 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} \sqrt{a^{2}}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-3*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/x^3/(a^2)^(1/2)","B"
41,1,308,74,0.066000," ","int(((a*x-1)/(a*x+1))^(1/2)/x^5,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-24 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-9 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+24 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+24 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-15 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+8 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} \sqrt{a^{2}}}"," ",0,"-1/24*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-24*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-9*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+24*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+24*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-15*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+8*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/x^4/(a^2)^(1/2)","B"
42,1,39,38,0.035000," ","int(x^3/(a*x+1)*(a*x-1),x)","-\frac{2 x}{a^{3}}+\frac{x^{2}}{a^{2}}-\frac{2 x^{3}}{3 a}+\frac{x^{4}}{4}+\frac{2 \ln \left(a x +1\right)}{a^{4}}"," ",0,"-2*x/a^3+x^2/a^2-2/3*x^3/a+1/4*x^4+2*ln(a*x+1)/a^4","A"
43,1,32,31,0.035000," ","int(x^2/(a*x+1)*(a*x-1),x)","\frac{2 x}{a^{2}}-\frac{x^{2}}{a}+\frac{x^{3}}{3}-\frac{2 \ln \left(a x +1\right)}{a^{3}}"," ",0,"2*x/a^2-x^2/a+1/3*x^3-2/a^3*ln(a*x+1)","A"
44,1,24,23,0.034000," ","int(x/(a*x+1)*(a*x-1),x)","-\frac{2 x}{a}+\frac{x^{2}}{2}+\frac{2 \ln \left(a x +1\right)}{a^{2}}"," ",0,"-2*x/a+1/2*x^2+2/a^2*ln(a*x+1)","A"
45,1,14,13,0.032000," ","int((a*x-1)/(a*x+1),x)","x -\frac{2 \ln \left(a x +1\right)}{a}"," ",0,"x-2*ln(a*x+1)/a","A"
46,1,14,13,0.038000," ","int(1/(a*x+1)*(a*x-1)/x,x)","-\ln \left(x \right)+2 \ln \left(a x +1\right)"," ",0,"-ln(x)+2*ln(a*x+1)","A"
47,1,19,18,0.044000," ","int(1/(a*x+1)*(a*x-1)/x^2,x)","\frac{1}{x}+2 a \ln \left(x \right)-2 a \ln \left(a x +1\right)"," ",0,"1/x+2*a*ln(x)-2*a*ln(a*x+1)","A"
48,1,31,30,0.044000," ","int(1/(a*x+1)*(a*x-1)/x^3,x)","\frac{1}{2 x^{2}}-\frac{2 a}{x}-2 a^{2} \ln \left(x \right)+2 a^{2} \ln \left(a x +1\right)"," ",0,"1/2/x^2-2*a/x-2*a^2*ln(x)+2*a^2*ln(a*x+1)","A"
49,1,39,38,0.042000," ","int(1/(a*x+1)*(a*x-1)/x^4,x)","\frac{1}{3 x^{3}}-\frac{a}{x^{2}}+\frac{2 a^{2}}{x}+2 a^{3} \ln \left(x \right)-2 a^{3} \ln \left(a x +1\right)"," ",0,"1/3/x^3-a/x^2+2*a^2/x+2*a^3*ln(x)-2*a^3*ln(a*x+1)","A"
50,1,539,118,0.058000," ","int(x^3*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+21 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-8 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +42 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-21 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-16 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -72 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+72 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+21 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -42 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+8 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-144 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +144 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-21 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -72 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+72 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{8 a^{4} \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"1/8*(2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+21*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-8*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+42*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-21*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-16*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-72*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+72*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+21*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-42*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+8*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-144*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+144*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-21*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-72*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+72*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a^4*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
51,1,471,98,0.057000," ","int(x^2*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+18 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-4 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -42 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+42 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -18 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+10 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-84 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +84 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -42 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+42 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 a^{3} \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/6*(9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+18*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-42*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+42*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-18*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+10*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-84*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+84*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-42*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+42*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a^3*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
52,1,421,78,0.054000," ","int(x*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-10 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+10 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+4 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-20 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+20 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-10 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +10 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a^{2} \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"1/2*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-10*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+10*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+4*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-20*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+20*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-10*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+10*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a^2*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
53,1,248,54,0.050000," ","int(((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+3 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+3 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \sqrt{a^{2}}\, \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-(-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+3*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+3*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
54,1,369,42,0.053000," ","int(((a*x-1)/(a*x+1))^(3/2)/x,x)","\frac{\left(-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}+a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\sqrt{a^{2}}\, \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"(-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)+a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
55,1,592,49,0.056000," ","int(((a*x-1)/(a*x+1))^(3/2)/x^2,x)","-\frac{\left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+\sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-5 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -7 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-6 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -3 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\sqrt{a^{2}}\, x \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-5*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-7*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-6*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-3*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
56,1,642,75,0.057000," ","int(((a*x-1)/(a*x+1))^(3/2)/x^3,x)","\frac{\left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+6 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-21 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-9 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+4 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+12 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+11 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-24 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-18 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+12 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-12 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-9 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-6 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 \sqrt{a^{2}}\, x^{2} \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"1/2*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-21*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-9*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+12*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+11*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-24*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-18*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+12*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-12*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-9*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-6*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x^2/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
57,1,666,84,0.061000," ","int(((a*x-1)/(a*x+1))^(3/2)/x^4,x)","-\frac{\left(-30 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-93 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}-33 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+30 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+30 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-30 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+51 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-96 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-66 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+60 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+12 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+60 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+14 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-33 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-33 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+30 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+30 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-30 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-5 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 \sqrt{a^{2}}\, x^{3} \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-1/6*(-30*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-93*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5-33*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+30*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+30*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-30*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+51*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-96*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-66*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+60*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+12*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+60*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+14*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-33*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-33*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+30*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+30*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-30*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-5*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x^3/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
58,1,690,115,0.062000," ","int(((a*x-1)/(a*x+1))^(3/2)/x^5,x)","\frac{\left(-56 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{7} a^{7}+56 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-163 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}-51 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{6} a^{6}+56 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+56 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{6} a^{6}-56 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+91 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-158 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}-102 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+112 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+16 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{4} a^{4}+112 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-112 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+22 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-51 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-51 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+56 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+56 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-56 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-7 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{8 \sqrt{a^{2}}\, x^{4} \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"1/8*(-56*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^7*a^7+56*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5-163*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6-51*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^6*a^6+56*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+56*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^6*a^6-56*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+91*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-158*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5-102*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+112*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+16*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^4*a^4+112*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-112*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+22*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-51*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-51*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+56*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+56*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-56*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-7*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x^4/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
59,0,0,211,0.133000," ","int(1/((a*x-1)/(a*x+1))^(1/4)*x^4,x)","\int \frac{x^{4}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)*x^4,x)","F"
60,0,0,180,0.081000," ","int(1/((a*x-1)/(a*x+1))^(1/4)*x^3,x)","\int \frac{x^{3}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)*x^3,x)","F"
61,0,0,149,0.080000," ","int(1/((a*x-1)/(a*x+1))^(1/4)*x^2,x)","\int \frac{x^{2}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)*x^2,x)","F"
62,0,0,118,0.079000," ","int(1/((a*x-1)/(a*x+1))^(1/4)*x,x)","\int \frac{x}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)*x,x)","F"
63,0,0,84,0.079000," ","int(1/((a*x-1)/(a*x+1))^(1/4),x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4),x)","F"
64,0,0,242,0.089000," ","int(1/((a*x-1)/(a*x+1))^(1/4)/x,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}} x}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)/x,x)","F"
65,0,0,219,0.107000," ","int(1/((a*x-1)/(a*x+1))^(1/4)/x^2,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}} x^{2}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)/x^2,x)","F"
66,0,0,258,0.092000," ","int(1/((a*x-1)/(a*x+1))^(1/4)/x^3,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}} x^{3}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)/x^3,x)","F"
67,0,0,289,0.094000," ","int(1/((a*x-1)/(a*x+1))^(1/4)/x^4,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}} x^{4}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)/x^4,x)","F"
68,0,0,211,0.120000," ","int(1/((a*x-1)/(a*x+1))^(3/4)*x^4,x)","\int \frac{x^{4}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)*x^4,x)","F"
69,0,0,180,0.084000," ","int(1/((a*x-1)/(a*x+1))^(3/4)*x^3,x)","\int \frac{x^{3}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)*x^3,x)","F"
70,0,0,149,0.082000," ","int(1/((a*x-1)/(a*x+1))^(3/4)*x^2,x)","\int \frac{x^{2}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)*x^2,x)","F"
71,0,0,118,0.080000," ","int(1/((a*x-1)/(a*x+1))^(3/4)*x,x)","\int \frac{x}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)*x,x)","F"
72,0,0,86,0.077000," ","int(1/((a*x-1)/(a*x+1))^(3/4),x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4),x)","F"
73,0,0,242,0.075000," ","int(1/((a*x-1)/(a*x+1))^(3/4)/x,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}} x}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)/x,x)","F"
74,0,0,219,0.104000," ","int(1/((a*x-1)/(a*x+1))^(3/4)/x^2,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}} x^{2}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)/x^2,x)","F"
75,0,0,258,0.090000," ","int(1/((a*x-1)/(a*x+1))^(3/4)/x^3,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}} x^{3}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)/x^3,x)","F"
76,0,0,289,0.092000," ","int(1/((a*x-1)/(a*x+1))^(3/4)/x^4,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}} x^{4}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)/x^4,x)","F"
77,0,0,239,0.362000," ","int(1/((a*x-1)/(a*x+1))^(5/4)*x^4,x)","\int \frac{x^{4}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)*x^4,x)","F"
78,0,0,208,0.360000," ","int(1/((a*x-1)/(a*x+1))^(5/4)*x^3,x)","\int \frac{x^{3}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)*x^3,x)","F"
79,0,0,177,0.362000," ","int(1/((a*x-1)/(a*x+1))^(5/4)*x^2,x)","\int \frac{x^{2}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)*x^2,x)","F"
80,0,0,146,0.373000," ","int(1/((a*x-1)/(a*x+1))^(5/4)*x,x)","\int \frac{x}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)*x,x)","F"
81,0,0,114,0.365000," ","int(1/((a*x-1)/(a*x+1))^(5/4),x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4),x)","F"
82,0,0,269,0.089000," ","int(1/((a*x-1)/(a*x+1))^(5/4)/x,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}} x}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)/x,x)","F"
83,0,0,246,0.375000," ","int(1/((a*x-1)/(a*x+1))^(5/4)/x^2,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}} x^{2}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)/x^2,x)","F"
84,0,0,286,0.371000," ","int(1/((a*x-1)/(a*x+1))^(5/4)/x^3,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}} x^{3}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)/x^3,x)","F"
85,0,0,314,0.367000," ","int(1/((a*x-1)/(a*x+1))^(5/4)/x^4,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}} x^{4}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)/x^4,x)","F"
86,0,0,211,0.088000," ","int(x^4*((a*x-1)/(a*x+1))^(1/4),x)","\int x^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(x^4*((a*x-1)/(a*x+1))^(1/4),x)","F"
87,0,0,180,0.082000," ","int(x^3*((a*x-1)/(a*x+1))^(1/4),x)","\int x^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(x^3*((a*x-1)/(a*x+1))^(1/4),x)","F"
88,0,0,149,0.079000," ","int(x^2*((a*x-1)/(a*x+1))^(1/4),x)","\int x^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(x^2*((a*x-1)/(a*x+1))^(1/4),x)","F"
89,0,0,118,0.080000," ","int(x*((a*x-1)/(a*x+1))^(1/4),x)","\int x \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(x*((a*x-1)/(a*x+1))^(1/4),x)","F"
90,0,0,85,0.077000," ","int(((a*x-1)/(a*x+1))^(1/4),x)","\int \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(1/4),x)","F"
91,0,0,244,0.074000," ","int(((a*x-1)/(a*x+1))^(1/4)/x,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}{x}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(1/4)/x,x)","F"
92,0,0,220,0.093000," ","int(((a*x-1)/(a*x+1))^(1/4)/x^2,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}{x^{2}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(1/4)/x^2,x)","F"
93,0,0,258,0.092000," ","int(((a*x-1)/(a*x+1))^(1/4)/x^3,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}{x^{3}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(1/4)/x^3,x)","F"
94,0,0,289,0.095000," ","int(((a*x-1)/(a*x+1))^(1/4)/x^4,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}{x^{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(1/4)/x^4,x)","F"
95,0,0,211,0.089000," ","int(x^4*((a*x-1)/(a*x+1))^(3/4),x)","\int x^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(x^4*((a*x-1)/(a*x+1))^(3/4),x)","F"
96,0,0,180,0.082000," ","int(x^3*((a*x-1)/(a*x+1))^(3/4),x)","\int x^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(x^3*((a*x-1)/(a*x+1))^(3/4),x)","F"
97,0,0,149,0.082000," ","int(x^2*((a*x-1)/(a*x+1))^(3/4),x)","\int x^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(x^2*((a*x-1)/(a*x+1))^(3/4),x)","F"
98,0,0,118,0.078000," ","int(x*((a*x-1)/(a*x+1))^(3/4),x)","\int x \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(x*((a*x-1)/(a*x+1))^(3/4),x)","F"
99,0,0,86,0.078000," ","int(((a*x-1)/(a*x+1))^(3/4),x)","\int \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(3/4),x)","F"
100,0,0,244,0.074000," ","int(((a*x-1)/(a*x+1))^(3/4)/x,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}{x}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(3/4)/x,x)","F"
101,0,0,220,0.092000," ","int(((a*x-1)/(a*x+1))^(3/4)/x^2,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}{x^{2}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(3/4)/x^2,x)","F"
102,0,0,258,0.087000," ","int(((a*x-1)/(a*x+1))^(3/4)/x^3,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}{x^{3}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(3/4)/x^3,x)","F"
103,0,0,289,0.092000," ","int(((a*x-1)/(a*x+1))^(3/4)/x^4,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}{x^{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(3/4)/x^4,x)","F"
104,0,0,239,0.362000," ","int(x^4*((a*x-1)/(a*x+1))^(5/4),x)","\int x^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(x^4*((a*x-1)/(a*x+1))^(5/4),x)","F"
105,0,0,208,0.363000," ","int(x^3*((a*x-1)/(a*x+1))^(5/4),x)","\int x^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(x^3*((a*x-1)/(a*x+1))^(5/4),x)","F"
106,0,0,177,0.365000," ","int(x^2*((a*x-1)/(a*x+1))^(5/4),x)","\int x^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(x^2*((a*x-1)/(a*x+1))^(5/4),x)","F"
107,0,0,146,0.364000," ","int(x*((a*x-1)/(a*x+1))^(5/4),x)","\int x \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(x*((a*x-1)/(a*x+1))^(5/4),x)","F"
108,0,0,114,0.374000," ","int(((a*x-1)/(a*x+1))^(5/4),x)","\int \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(5/4),x)","F"
109,0,0,267,0.084000," ","int(((a*x-1)/(a*x+1))^(5/4)/x,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}{x}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(5/4)/x,x)","F"
110,0,0,246,0.375000," ","int(((a*x-1)/(a*x+1))^(5/4)/x^2,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}{x^{2}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(5/4)/x^2,x)","F"
111,0,0,286,0.367000," ","int(((a*x-1)/(a*x+1))^(5/4)/x^3,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}{x^{3}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(5/4)/x^3,x)","F"
112,0,0,314,0.371000," ","int(((a*x-1)/(a*x+1))^(5/4)/x^4,x)","\int \frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}{x^{4}}\, dx"," ",0,"int(((a*x-1)/(a*x+1))^(5/4)/x^4,x)","F"
113,1,2891,223,4.641000," ","int(1/((-1+x)/(1+x))^(1/6)*x^2,x)","\text{output too large to display}"," ",0,"1/54*(18*x^2+21*x+22)*(-1+x)/((-1+x)/(1+x))^(1/6)+(19/162*RootOf(_Z^2-_Z+1)*ln(-(1+4*x+6*x^2+x^4+4*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6))/(1+x)^4)-19/162*ln((-2-8*x-12*x^2-2*x^4-8*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4)*RootOf(_Z^2-_Z+1)+19/162*ln((-2-8*x-12*x^2-2*x^4-8*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
114,1,2886,202,4.202000," ","int(1/((-1+x)/(1+x))^(1/6)*x,x)","\text{output too large to display}"," ",0,"1/6*(4+3*x)*(-1+x)/((-1+x)/(1+x))^(1/6)+(1/18*RootOf(_Z^2-_Z+1)*ln(-(1+4*x+6*x^2+x^4+4*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6))/(1+x)^4)-1/18*ln((-2-8*x-12*x^2-2*x^4-8*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4)*RootOf(_Z^2-_Z+1)+1/18*ln((-2-8*x-12*x^2-2*x^4-8*x^3+6*RootOf(_Z^2-_Z+1)*x^2+RootOf(_Z^2-_Z+1)+RootOf(_Z^2-_Z+1)*x^4+4*RootOf(_Z^2-_Z+1)*x^3+4*RootOf(_Z^2-_Z+1)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+18*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+12*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+6*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(_Z^2-_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
115,1,1700,180,4.095000," ","int(1/((-1+x)/(1+x))^(1/6),x)","\frac{-1+x}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{6}}}+\frac{\left(\frac{\ln \left(\frac{-2-8 x -12 x^{2}-2 x^{4}-8 x^{3}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{5}{6}}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{3}-18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{2}-18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x -6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}\, x^{2}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-12 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}\, x -12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-18 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} x -3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{3}-9 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{2}-9 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x -12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x -3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{4}-12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{3}-18 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{2}-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-4 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}}}{\left(1+x \right)^{4}}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \ln \left(\frac{-1-4 x -6 x^{2}-x^{4}-4 x^{3}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{5}{6}}-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}}-6 \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}}-6 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x +6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{3}+18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{2}+18 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)-3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} x -6 \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}\, x^{2}+3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{3}-12 \sqrt{x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1}\, x +9 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x^{2}+9 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}} x +12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x +3 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{4}+12 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{3}+18 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{6}} x^{2}-12 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{2}-2 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{4}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x^{3}-8 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) x -6 \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right)+6 \RootOf \left(\textit{\_Z}^{2}+\textit{\_Z} +1\right) \left(x^{6}+4 x^{5}+5 x^{4}-5 x^{2}-4 x -1\right)^{\frac{1}{3}}}{\left(1+x \right)^{4}}\right)}{3}\right) \left(\left(-1+x \right) \left(1+x \right)^{5}\right)^{\frac{1}{6}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{6}} \left(1+x \right)}"," ",0,"(-1+x)/((-1+x)/(1+x))^(1/6)+(1/3*ln((-2-8*x-12*x^2-6*RootOf(_Z^2+_Z+1)*x^2-RootOf(_Z^2+_Z+1)*x^4-4*RootOf(_Z^2+_Z+1)*x^3-4*RootOf(_Z^2+_Z+1)*x-2*x^4-8*x^3-RootOf(_Z^2+_Z+1)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^2+_Z+1)*x-6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3-18*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2-18*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x-6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^2+_Z+1)*x^4-12*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^2+_Z+1)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^2+_Z+1)*x^2-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^2+_Z+1)*x-6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^2+_Z+1)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^2+_Z+1)-6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4)+1/3*RootOf(_Z^2+_Z+1)*ln((-1-4*x-6*x^2-12*RootOf(_Z^2+_Z+1)*x^2-2*RootOf(_Z^2+_Z+1)*x^4-8*RootOf(_Z^2+_Z+1)*x^3-8*RootOf(_Z^2+_Z+1)*x-x^4-4*x^3-2*RootOf(_Z^2+_Z+1)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^2+_Z+1)*x+6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3+18*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+18*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^2+_Z+1)+6*RootOf(_Z^2+_Z+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^3-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x^2+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
116,1,2320,320,14.615000," ","int(1/((-1+x)/(1+x))^(1/6)/x,x)","\text{Expression too large to display}"," ",0,"-3*ln(-(18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)+3*(-(1-x)/(1+x))^(5/6)*x+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+3*(-(1-x)/(1+x))^(5/6)+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)+6*(-(1-x)/(1+x))^(1/2)*x+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)*x+6*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*x+6*(-(1-x)/(1+x))^(1/2)+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)+3*(-(1-x)/(1+x))^(1/6)*x+RootOf(_Z^2+1)*x+3*(-(1-x)/(1+x))^(1/6))/x)*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)+3*RootOf(9*_Z^2+3*_Z+1)*ln(9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-3*(-(1-x)/(1+x))^(5/6)*x+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)*x-3*(-(1-x)/(1+x))^(5/6)+6*(-(1-x)/(1+x))^(2/3)*x-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+6*(-(1-x)/(1+x))^(2/3)-6*(-(1-x)/(1+x))^(1/2)*x+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)*x-6*(-(1-x)/(1+x))^(1/2)+3*(-(1-x)/(1+x))^(1/3)*x-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)+3*(-(1-x)/(1+x))^(1/3)+3*RootOf(9*_Z^2+3*_Z+1)-1)-3*ln(-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-3*(-(1-x)/(1+x))^(5/6)*x-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)*x-3*(-(1-x)/(1+x))^(5/6)+3*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+3*(-(1-x)/(1+x))^(2/3)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)*x-3*(-(1-x)/(1+x))^(1/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)-3*(-(1-x)/(1+x))^(1/3)+3*(-(1-x)/(1+x))^(1/6)*x-3*RootOf(9*_Z^2+3*_Z+1)+3*(-(1-x)/(1+x))^(1/6)-2)*RootOf(9*_Z^2+3*_Z+1)+RootOf(_Z^2+1)*ln(-(9*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x+9*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)+3*(-(1-x)/(1+x))^(5/6)*x+6*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)*x-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)*x-18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+3*(-(1-x)/(1+x))^(5/6)+6*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)-18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)-6*(-(1-x)/(1+x))^(1/2)*x-3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)*x+3*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*x-6*(-(1-x)/(1+x))^(1/2)-3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)-RootOf(_Z^2+1)*x)/x)-ln(-(18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)+3*(-(1-x)/(1+x))^(5/6)*x+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+3*(-(1-x)/(1+x))^(5/6)+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(2/3)+18*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)+6*(-(1-x)/(1+x))^(1/2)*x+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)*x+6*RootOf(_Z^2+1)*RootOf(9*_Z^2+3*_Z+1)*x+6*(-(1-x)/(1+x))^(1/2)+3*RootOf(_Z^2+1)*(-(1-x)/(1+x))^(1/3)+3*(-(1-x)/(1+x))^(1/6)*x+RootOf(_Z^2+1)*x+3*(-(1-x)/(1+x))^(1/6))/x)*RootOf(_Z^2+1)-ln(-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-3*(-(1-x)/(1+x))^(5/6)*x-9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(2/3)+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)*x-3*(-(1-x)/(1+x))^(5/6)+3*(-(1-x)/(1+x))^(2/3)*x+18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/2)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)*x+3*(-(1-x)/(1+x))^(2/3)-18*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/3)+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)*x-3*(-(1-x)/(1+x))^(1/3)*x+9*RootOf(9*_Z^2+3*_Z+1)*(-(1-x)/(1+x))^(1/6)-3*(-(1-x)/(1+x))^(1/3)+3*(-(1-x)/(1+x))^(1/6)*x-3*RootOf(9*_Z^2+3*_Z+1)+3*(-(1-x)/(1+x))^(1/6)-2)","C"
117,1,3474,181,7.821000," ","int(1/((-1+x)/(1+x))^(1/6)/x^2,x)","\text{output too large to display}"," ",0,"(-1+x)/x/((-1+x)/(1+x))^(1/6)+(1/1594323*ln(-(-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-12*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4+39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x)*RootOf(_Z^4-6561*_Z^2+43046721)^3-1/243*ln(-(-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-12*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4+39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x)*RootOf(_Z^4-6561*_Z^2+43046721)+1/243*RootOf(_Z^4-6561*_Z^2+43046721)*ln(-(-RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-4*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-6*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3-6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5-26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4-39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-4*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-RootOf(_Z^4-6561*_Z^2+43046721)^3*x-26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-6561*RootOf(_Z^4-6561*_Z^2+43046721)*x-1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x-1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3-9565938*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3-486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4-19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3+118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2+1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
118,1,2997,200,20.934000," ","int(1/((-1+x)/(1+x))^(1/6)/x^3,x)","\text{output too large to display}"," ",0,"1/6*(-1+x)*(4*x+3)/x^2/((-1+x)/(1+x))^(1/6)+(-1/18*RootOf(_Z^2+1)*ln(-(-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*x^2+4*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2+RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x+RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^5+4*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^4+6*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^3-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^2+1)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2+729*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^2-18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x+729*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x+3*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+324*RootOf(_Z^2+1)*x^2+81*RootOf(_Z^2+1)*x+324*RootOf(_Z^2+1)*x^4+486*RootOf(_Z^2+1)*x^3+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+81*RootOf(_Z^2+1)*x^5+3*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-486*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*x^4-12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^2+1)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x+12*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*x^3+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*x^2+12*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+3*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-486*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)+243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)-486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x)/(1+x)^4/x)-1/1458*ln(-(8*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2+2*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x+2*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^5+8*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^4+12*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^3+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2-729*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^2+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x-729*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x-324*RootOf(_Z^2+1)*x^2-81*RootOf(_Z^2+1)*x-324*RootOf(_Z^2+1)*x^4-486*RootOf(_Z^2+1)*x^3+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-81*RootOf(_Z^2+1)*x^5+6*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3+6*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4/x)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)+1/18*ln(-(8*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2+2*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x+2*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^5+8*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^4+12*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^3+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^2-729*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^2+1)*x^2+18*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x-729*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*x-324*RootOf(_Z^2+1)*x^2-81*RootOf(_Z^2+1)*x-324*RootOf(_Z^2+1)*x^4-486*RootOf(_Z^2+1)*x^3+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-81*RootOf(_Z^2+1)*x^5+6*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*x^3+6*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(-81*_Z*RootOf(_Z^2+1)+_Z^2-6561)-243*RootOf(_Z^2+1)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2)/(1+x)^4/x)*RootOf(_Z^2+1))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
119,1,3484,221,7.217000," ","int(1/((-1+x)/(1+x))^(1/6)/x^4,x)","\text{output too large to display}"," ",0,"1/54*(-1+x)*(22*x^2+21*x+18)/x^3/((-1+x)/(1+x))^(1/6)+(19/86093442*ln(-(-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-12*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4+39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x)*RootOf(_Z^4-6561*_Z^2+43046721)^3-19/13122*ln(-(-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-12*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4+39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-8*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-2*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2+6561*RootOf(_Z^4-6561*_Z^2+43046721)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2-3188646*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x^2-6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4+19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x+9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x)*RootOf(_Z^4-6561*_Z^2+43046721)-19/13122*RootOf(_Z^4-6561*_Z^2+43046721)*ln((-RootOf(_Z^4-6561*_Z^2+43046721)^3*x^5-4*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^4-6*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3-6561*RootOf(_Z^4-6561*_Z^2+43046721)*x^5-26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^4-39366*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-4*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-RootOf(_Z^4-6561*_Z^2+43046721)^3*x-26244*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-6561*RootOf(_Z^4-6561*_Z^2+43046721)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)-1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(5/6)+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3-19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)+486*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3+39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2+6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x+1594323*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^4+6377292*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^3+9565938*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*x^2+6*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x-3*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^3+486*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x^2-243*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^4-19683*RootOf(_Z^4-6561*_Z^2+43046721)*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(2/3)*x+972*RootOf(_Z^4-6561*_Z^2+43046721)^2*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/2)*x-9*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)^3*x+39366*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^3-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^3+118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x^2-1458*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x^2+118098*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/3)*RootOf(_Z^4-6561*_Z^2+43046721)*x-972*(x^6+4*x^5+5*x^4-5*x^2-4*x-1)^(1/6)*RootOf(_Z^4-6561*_Z^2+43046721)^2*x)/(1+x)^4/x))/((-1+x)/(1+x))^(1/6)*((-1+x)*(1+x)^5)^(1/6)/(1+x)","C"
120,1,408,121,0.701000," ","int(1/((-1+x)/(1+x))^(1/3)*x^2,x)","\frac{\left(9 x^{2}+12 x +14\right) \left(-1+x \right)}{27 \left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}+\frac{\left(-\frac{22 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +x^{2}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{1+x}\right)}{81}+\frac{22 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 x^{2}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+4 x +2}{1+x}\right)}{81}\right) \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}} \left(1+x \right)}"," ",0,"1/27*(9*x^2+12*x+14)*(-1+x)/((-1+x)/(1+x))^(1/3)+(-22/81*ln(-(4*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x+4*RootOf(_Z^2-_Z+1)^2*x-4*RootOf(_Z^2-_Z+1)*x^2-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)+3*(x^3+x^2-x-1)^(1/3)*x-2*RootOf(_Z^2-_Z+1)*x+x^2+3*(x^3+x^2-x-1)^(1/3)+2*RootOf(_Z^2-_Z+1)-1)/(1+x))+22/81*RootOf(_Z^2-_Z+1)*ln((2*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)+2*RootOf(_Z^2-_Z+1)^2*x-5*RootOf(_Z^2-_Z+1)*x^2-3*(x^3+x^2-x-1)^(2/3)+3*(x^3+x^2-x-1)^(1/3)*x-6*RootOf(_Z^2-_Z+1)*x+2*x^2+3*(x^3+x^2-x-1)^(1/3)-RootOf(_Z^2-_Z+1)+4*x+2)/(1+x)))/((-1+x)/(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(1+x)","C"
121,1,403,100,0.584000," ","int(1/((-1+x)/(1+x))^(1/3)*x,x)","\frac{\left(5+3 x \right) \left(-1+x \right)}{6 \left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}+\frac{\left(-\frac{2 \ln \left(-\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +x^{2}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-1}{1+x}\right)}{9}+\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +2 x^{2}+3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+4 x +2}{1+x}\right)}{9}\right) \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}} \left(1+x \right)}"," ",0,"1/6*(5+3*x)*(-1+x)/((-1+x)/(1+x))^(1/3)+(-2/9*ln(-(4*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x+4*RootOf(_Z^2-_Z+1)^2*x-4*RootOf(_Z^2-_Z+1)*x^2-3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)+3*(x^3+x^2-x-1)^(1/3)*x-2*RootOf(_Z^2-_Z+1)*x+x^2+3*(x^3+x^2-x-1)^(1/3)+2*RootOf(_Z^2-_Z+1)-1)/(1+x))+2/9*RootOf(_Z^2-_Z+1)*ln((2*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)+2*RootOf(_Z^2-_Z+1)^2*x-5*RootOf(_Z^2-_Z+1)*x^2-3*(x^3+x^2-x-1)^(2/3)+3*(x^3+x^2-x-1)^(1/3)*x-6*RootOf(_Z^2-_Z+1)*x+2*x^2+3*(x^3+x^2-x-1)^(1/3)-RootOf(_Z^2-_Z+1)+4*x+2)/(1+x)))/((-1+x)/(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(1+x)","C"
122,1,605,78,0.544000," ","int(1/((-1+x)/(1+x))^(1/3),x)","\frac{-1+x}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}+\frac{\left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -2 x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+2}{1+x}\right)}{3}-\frac{2 \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2 x -1}{1+x}\right) \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{3}+\frac{2 \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -x^{2}-3 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-2 x -1}{1+x}\right)}{3}\right) \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}} \left(1+x \right)}"," ",0,"(-1+x)/((-1+x)/(1+x))^(1/3)+(2/3*RootOf(_Z^2-_Z+1)*ln(-(-2*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x-2*RootOf(_Z^2-_Z+1)^2*x+5*RootOf(_Z^2-_Z+1)*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)+4*RootOf(_Z^2-_Z+1)*x-2*x^2-RootOf(_Z^2-_Z+1)+2)/(1+x))-2/3*ln((2*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x+2*RootOf(_Z^2-_Z+1)^2*x+RootOf(_Z^2-_Z+1)*x^2-3*(x^3+x^2-x-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)-3*(x^3+x^2-x-1)^(1/3)*x-x^2-3*(x^3+x^2-x-1)^(1/3)-RootOf(_Z^2-_Z+1)-2*x-1)/(1+x))*RootOf(_Z^2-_Z+1)+2/3*ln((2*RootOf(_Z^2-_Z+1)^2*x^2+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)*x+2*RootOf(_Z^2-_Z+1)^2*x+RootOf(_Z^2-_Z+1)*x^2-3*(x^3+x^2-x-1)^(2/3)+3*RootOf(_Z^2-_Z+1)*(x^3+x^2-x-1)^(1/3)-3*(x^3+x^2-x-1)^(1/3)*x-x^2-3*(x^3+x^2-x-1)^(1/3)-RootOf(_Z^2-_Z+1)-2*x-1)/(1+x)))/((-1+x)/(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(1+x)","C"
123,1,1038,122,0.923000," ","int(1/((-1+x)/(1+x))^(1/3)/x,x)","3 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(\frac{945 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+1890 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -168 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x^{2}+945 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-336 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -168 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} x^{2}+3060 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +1353 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-168 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}-1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-1062 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -304 x^{2}+168 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}+1353 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+32 x -304}{x}\right)-3 \ln \left(-\frac{945 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+1890 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -147 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x^{2}+945 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-294 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -147 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} x^{2}-3060 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +537 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-147 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}+1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+978 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -11 x^{2}+147 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}+537 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-18 x -11}{x}\right) \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+\ln \left(-\frac{945 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+1890 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -147 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x^{2}+945 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-294 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}} x -147 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}} x^{2}-3060 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x +537 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}-147 \left(-\frac{1-x}{1+x}\right)^{\frac{2}{3}}-945 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}+1224 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+978 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -11 x^{2}+147 \left(-\frac{1-x}{1+x}\right)^{\frac{1}{3}}+537 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-18 x -11}{x}\right)"," ",0,"3*RootOf(9*_Z^2-3*_Z+1)*ln((945*(-(1-x)/(1+x))^(2/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+1890*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-168*(-(1-x)/(1+x))^(2/3)*x^2+945*(-(1-x)/(1+x))^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2-1224*RootOf(9*_Z^2-3*_Z+1)^2*x^2+945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)-336*(-(1-x)/(1+x))^(2/3)*x-168*(-(1-x)/(1+x))^(1/3)*x^2+3060*RootOf(9*_Z^2-3*_Z+1)^2*x+1353*RootOf(9*_Z^2-3*_Z+1)*x^2-168*(-(1-x)/(1+x))^(2/3)-945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(1/3)-1224*RootOf(9*_Z^2-3*_Z+1)^2-1062*RootOf(9*_Z^2-3*_Z+1)*x-304*x^2+168*(-(1-x)/(1+x))^(1/3)+1353*RootOf(9*_Z^2-3*_Z+1)+32*x-304)/x)-3*ln(-(945*(-(1-x)/(1+x))^(2/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+1890*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-147*(-(1-x)/(1+x))^(2/3)*x^2+945*(-(1-x)/(1+x))^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+1224*RootOf(9*_Z^2-3*_Z+1)^2*x^2+945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)-294*(-(1-x)/(1+x))^(2/3)*x-147*(-(1-x)/(1+x))^(1/3)*x^2-3060*RootOf(9*_Z^2-3*_Z+1)^2*x+537*RootOf(9*_Z^2-3*_Z+1)*x^2-147*(-(1-x)/(1+x))^(2/3)-945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(1/3)+1224*RootOf(9*_Z^2-3*_Z+1)^2+978*RootOf(9*_Z^2-3*_Z+1)*x-11*x^2+147*(-(1-x)/(1+x))^(1/3)+537*RootOf(9*_Z^2-3*_Z+1)-18*x-11)/x)*RootOf(9*_Z^2-3*_Z+1)+ln(-(945*(-(1-x)/(1+x))^(2/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+1890*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)*x-147*(-(1-x)/(1+x))^(2/3)*x^2+945*(-(1-x)/(1+x))^(1/3)*RootOf(9*_Z^2-3*_Z+1)*x^2+1224*RootOf(9*_Z^2-3*_Z+1)^2*x^2+945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(2/3)-294*(-(1-x)/(1+x))^(2/3)*x-147*(-(1-x)/(1+x))^(1/3)*x^2-3060*RootOf(9*_Z^2-3*_Z+1)^2*x+537*RootOf(9*_Z^2-3*_Z+1)*x^2-147*(-(1-x)/(1+x))^(2/3)-945*RootOf(9*_Z^2-3*_Z+1)*(-(1-x)/(1+x))^(1/3)+1224*RootOf(9*_Z^2-3*_Z+1)^2+978*RootOf(9*_Z^2-3*_Z+1)*x-11*x^2+147*(-(1-x)/(1+x))^(1/3)+537*RootOf(9*_Z^2-3*_Z+1)-18*x-11)/x)","C"
124,1,501,81,0.791000," ","int(1/((-1+x)/(1+x))^(1/3)/x^2,x)","\frac{-1+x}{x \left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}+\frac{\left(-\frac{2 \ln \left(\frac{8 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-45 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -8 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x -30 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}-216 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-45 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-81 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -16 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}-54 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -27 x^{2}-81 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-24 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-36 x -9}{x \left(1+x \right)}\right)}{3}+\frac{2 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+72 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +2 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x -27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+135 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+72 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-81 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +4 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}+6 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -36 x^{2}-81 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+33 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-216 x -180}{x \left(1+x \right)}\right)}{9}\right) \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}} \left(1+x \right)}"," ",0,"(-1+x)/x/((-1+x)/(1+x))^(1/3)+(-2/3*ln((8*RootOf(_Z^2-3*_Z+9)^2*x^2+27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)-45*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x-8*RootOf(_Z^2-3*_Z+9)^2*x-30*RootOf(_Z^2-3*_Z+9)*x^2-216*(x^3+x^2-x-1)^(2/3)-45*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)-81*(x^3+x^2-x-1)^(1/3)*x-16*RootOf(_Z^2-3*_Z+9)^2-54*RootOf(_Z^2-3*_Z+9)*x-27*x^2-81*(x^3+x^2-x-1)^(1/3)-24*RootOf(_Z^2-3*_Z+9)-36*x-9)/x/(1+x))+2/9*RootOf(_Z^2-3*_Z+9)*ln(-(-2*RootOf(_Z^2-3*_Z+9)^2*x^2+27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)+72*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x+2*RootOf(_Z^2-3*_Z+9)^2*x-27*RootOf(_Z^2-3*_Z+9)*x^2+135*(x^3+x^2-x-1)^(2/3)+72*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)-81*(x^3+x^2-x-1)^(1/3)*x+4*RootOf(_Z^2-3*_Z+9)^2+6*RootOf(_Z^2-3*_Z+9)*x-36*x^2-81*(x^3+x^2-x-1)^(1/3)+33*RootOf(_Z^2-3*_Z+9)-216*x-180)/x/(1+x)))/((-1+x)/(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(1+x)","C"
125,1,738,100,0.650000," ","int(1/((-1+x)/(1+x))^(1/3)/x^3,x)","\frac{\left(-1+x \right) \left(5 x +3\right)}{6 x^{2} \left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}+\frac{\left(\frac{2 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \ln \left(\frac{-10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x +69 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}-216 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+216 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}+36 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -108 x^{2}+216 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-33 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-144 x -36}{x \left(1+x \right)}\right)}{27}-\frac{2 \ln \left(-\frac{10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x +9 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+135 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-135 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}+96 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -9 x^{2}-135 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+87 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-54 x -45}{x \left(1+x \right)}\right) \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)}{27}+\frac{2 \ln \left(-\frac{10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -10 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x +9 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+135 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-135 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}+96 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -9 x^{2}-135 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+87 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-54 x -45}{x \left(1+x \right)}\right)}{9}\right) \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}} \left(1+x \right)}"," ",0,"1/6*(-1+x)*(5*x+3)/x^2/((-1+x)/(1+x))^(1/3)+(2/27*RootOf(_Z^2-3*_Z+9)*ln((-10*RootOf(_Z^2-3*_Z+9)^2*x^2+27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x+10*RootOf(_Z^2-3*_Z+9)^2*x+69*RootOf(_Z^2-3*_Z+9)*x^2-216*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)+216*(x^3+x^2-x-1)^(1/3)*x+20*RootOf(_Z^2-3*_Z+9)^2+36*RootOf(_Z^2-3*_Z+9)*x-108*x^2+216*(x^3+x^2-x-1)^(1/3)-33*RootOf(_Z^2-3*_Z+9)-144*x-36)/x/(1+x))-2/27*ln(-(10*RootOf(_Z^2-3*_Z+9)^2*x^2+27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x-10*RootOf(_Z^2-3*_Z+9)^2*x+9*RootOf(_Z^2-3*_Z+9)*x^2+135*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)-135*(x^3+x^2-x-1)^(1/3)*x-20*RootOf(_Z^2-3*_Z+9)^2+96*RootOf(_Z^2-3*_Z+9)*x-9*x^2-135*(x^3+x^2-x-1)^(1/3)+87*RootOf(_Z^2-3*_Z+9)-54*x-45)/x/(1+x))*RootOf(_Z^2-3*_Z+9)+2/9*ln(-(10*RootOf(_Z^2-3*_Z+9)^2*x^2+27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x-10*RootOf(_Z^2-3*_Z+9)^2*x+9*RootOf(_Z^2-3*_Z+9)*x^2+135*(x^3+x^2-x-1)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)-135*(x^3+x^2-x-1)^(1/3)*x-20*RootOf(_Z^2-3*_Z+9)^2+96*RootOf(_Z^2-3*_Z+9)*x-9*x^2-135*(x^3+x^2-x-1)^(1/3)+87*RootOf(_Z^2-3*_Z+9)-54*x-45)/x/(1+x)))/((-1+x)/(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(1+x)","C"
126,0,0,351,0.147000," ","int(1/((a*x-1)/(a*x+1))^(1/8)*x^2,x)","\int \frac{x^{2}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)*x^2,x)","F"
127,0,0,320,0.092000," ","int(1/((a*x-1)/(a*x+1))^(1/8)*x,x)","\int \frac{x}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)*x,x)","F"
128,0,0,288,0.093000," ","int(1/((a*x-1)/(a*x+1))^(1/8),x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8),x)","F"
129,0,0,736,0.109000," ","int(1/((a*x-1)/(a*x+1))^(1/8)/x,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}} x}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)/x,x)","F"
130,0,0,528,0.263000," ","int(1/((a*x-1)/(a*x+1))^(1/8)/x^2,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}} x^{2}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)/x^2,x)","F"
131,0,0,575,0.124000," ","int(1/((a*x-1)/(a*x+1))^(1/8)/x^3,x)","\int \frac{1}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}} x^{3}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)/x^3,x)","F"
132,1,201,47,0.513000," ","int(1/(a*x-1)^2*(a*x+1)^2*x^m,x)","-\frac{\left(-a \right)^{-m} \left(\frac{x^{m} \left(-a \right)^{m} \left(a^{2} m \,x^{2}+a m x +2 a x -m^{2}-3 m -2\right)}{\left(1+m \right) m \left(-a x +1\right)}+x^{m} \left(-a \right)^{m} \left(2+m \right) \Phi \left(a x , 1, m\right)\right)}{a}+\frac{2 \left(-a \right)^{-m} \left(-\frac{x^{m} \left(-a \right)^{m} \left(a x -m -1\right)}{m \left(-a x +1\right)}-x^{m} \left(-a \right)^{m} \left(1+m \right) \Phi \left(a x , 1, m\right)\right)}{a}-\frac{\left(-a \right)^{-m} \left(\frac{x^{m} \left(-a \right)^{m} \left(-1-m \right)}{\left(1+m \right) \left(-a x +1\right)}+x^{m} \left(-a \right)^{m} m \Phi \left(a x , 1, m\right)\right)}{a}"," ",0,"-(-a)^(-m)/a*(x^m*(-a)^m*(a^2*m*x^2+a*m*x+2*a*x-m^2-3*m-2)/(1+m)/m/(-a*x+1)+x^m*(-a)^m*(2+m)*LerchPhi(a*x,1,m))+2*(-a)^(-m)/a*(-x^m*(-a)^m*(a*x-m-1)/m/(-a*x+1)-x^m*(-a)^m*(1+m)*LerchPhi(a*x,1,m))-(-a)^(-m)/a*(1/(1+m)*x^m*(-a)^m*(-1-m)/(-a*x+1)+x^m*(-a)^m*m*LerchPhi(a*x,1,m))","C"
133,0,0,127,0.051000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^m,x)","\int \frac{x^{m}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/2)*x^m,x)","F"
134,1,106,37,0.413000," ","int((a*x+1)/(a*x-1)*x^m,x)","\frac{\left(-a \right)^{-m} \left(-\frac{x^{m} \left(-a \right)^{m} \left(-1-m \right)}{\left(1+m \right) m}-x^{m} \left(-a \right)^{m} \Phi \left(a x , 1, m\right)\right)}{a}-\frac{\left(-a \right)^{-m} \left(-\frac{x^{m} \left(-a \right)^{m} \left(a m x +m +1\right)}{\left(1+m \right) m}+x^{m} \left(-a \right)^{m} \Phi \left(a x , 1, m\right)\right)}{a}"," ",0,"(-a)^(-m)/a*(-1/(1+m)*x^m*(-a)^m*(-1-m)/m-x^m*(-a)^m*LerchPhi(a*x,1,m))-(-a)^(-m)/a*(-x^m*(-a)^m*(a*m*x+m+1)/(1+m)/m+x^m*(-a)^m*LerchPhi(a*x,1,m))","C"
135,0,0,62,0.047000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^m,x)","\int \frac{x^{m}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*x^m,x)","F"
136,0,0,63,0.044000," ","int(x^m*((a*x-1)/(a*x+1))^(1/2),x)","\int x^{m} \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int(x^m*((a*x-1)/(a*x+1))^(1/2),x)","F"
137,1,93,38,0.388000," ","int(x^m/(a*x+1)*(a*x-1),x)","a^{-1-m} \left(\frac{x^{m} a^{m} \left(a m x -m -1\right)}{\left(1+m \right) m}+x^{m} a^{m} \Phi \left(-a x , 1, m\right)\right)-a^{-1-m} \left(\frac{x^{m} a^{m}}{m}+\frac{x^{m} a^{m} \left(-1-m \right) \Phi \left(-a x , 1, m\right)}{1+m}\right)"," ",0,"a^(-1-m)*(x^m*a^m*(a*m*x-m-1)/(1+m)/m+x^m*a^m*LerchPhi(-a*x,1,m))-a^(-1-m)*(x^m*a^m/m+1/(1+m)*x^m*a^m*(-1-m)*LerchPhi(-a*x,1,m))","C"
138,0,0,126,0.047000," ","int(x^m*((a*x-1)/(a*x+1))^(3/2),x)","\int x^{m} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*((a*x-1)/(a*x+1))^(3/2),x)","F"
139,0,0,37,0.042000," ","int(1/((a*x-1)/(a*x+1))^(5/4)*x^m,x)","\int \frac{x^{m}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(5/4)*x^m,x)","F"
140,0,0,37,0.044000," ","int(1/((a*x-1)/(a*x+1))^(3/4)*x^m,x)","\int \frac{x^{m}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/4)*x^m,x)","F"
141,0,0,37,0.044000," ","int(1/((a*x-1)/(a*x+1))^(1/4)*x^m,x)","\int \frac{x^{m}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/4)*x^m,x)","F"
142,0,0,37,0.043000," ","int(x^m*((a*x-1)/(a*x+1))^(1/4),x)","\int x^{m} \left(\frac{a x -1}{a x +1}\right)^{\frac{1}{4}}\, dx"," ",0,"int(x^m*((a*x-1)/(a*x+1))^(1/4),x)","F"
143,0,0,37,0.046000," ","int(x^m*((a*x-1)/(a*x+1))^(3/4),x)","\int x^{m} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{4}}\, dx"," ",0,"int(x^m*((a*x-1)/(a*x+1))^(3/4),x)","F"
144,0,0,37,0.043000," ","int(x^m*((a*x-1)/(a*x+1))^(5/4),x)","\int x^{m} \left(\frac{a x -1}{a x +1}\right)^{\frac{5}{4}}\, dx"," ",0,"int(x^m*((a*x-1)/(a*x+1))^(5/4),x)","F"
145,0,0,30,0.039000," ","int(1/((-1+x)/(1+x))^(1/3)*x^m,x)","\int \frac{x^{m}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/((-1+x)/(1+x))^(1/3)*x^m,x)","F"
146,0,0,30,0.043000," ","int(1/((-1+x)/(1+x))^(1/6)*x^m,x)","\int \frac{x^{m}}{\left(\frac{-1+x}{1+x}\right)^{\frac{1}{6}}}\, dx"," ",0,"int(1/((-1+x)/(1+x))^(1/6)*x^m,x)","F"
147,0,0,37,0.041000," ","int(1/((a*x-1)/(a*x+1))^(1/8)*x^m,x)","\int \frac{x^{m}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{1}{8}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/8)*x^m,x)","F"
148,0,0,41,0.074000," ","int(exp(n*arccoth(a*x))*x^m,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x^{m}\, dx"," ",0,"int(exp(n*arccoth(a*x))*x^m,x)","F"
149,0,0,154,0.059000," ","int(exp(n*arccoth(a*x))*x^2,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x^{2}\, dx"," ",0,"int(exp(n*arccoth(a*x))*x^2,x)","F"
150,0,0,110,0.055000," ","int(exp(n*arccoth(a*x))*x,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x\, dx"," ",0,"int(exp(n*arccoth(a*x))*x,x)","F"
151,0,0,72,0.049000," ","int(exp(n*arccoth(a*x)),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}\, dx"," ",0,"int(exp(n*arccoth(a*x)),x)","F"
152,0,0,115,0.050000," ","int(exp(n*arccoth(a*x))/x,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x,x)","F"
153,0,0,60,0.055000," ","int(exp(n*arccoth(a*x))/x^2,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x^{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x^2,x)","F"
154,0,0,98,0.063000," ","int(exp(n*arccoth(a*x))/x^3,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x^{3}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x^3,x)","F"
155,0,0,143,0.064000," ","int(exp(n*arccoth(a*x))/x^4,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x^{4}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x^4,x)","F"
156,0,0,159,0.071000," ","int(exp(n*arccoth(a*x))/x^5,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x^{5}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x^5,x)","F"
157,0,0,133,0.349000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^p,x)","\int \frac{\left(-a c x +c \right)^{p}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^p,x)","F"
158,1,183,112,0.048000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^4,x)","\frac{\left(a x -1\right) c^{4} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-90 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-105 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +120 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+105 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*(a*x-1)*c^4/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-90*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-105*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+120*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+105*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
159,1,141,89,0.047000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^3,x)","\frac{\left(a x -1\right) c^{3} \left(-6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +15 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{24 a \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/24*(a*x-1)*c^3/a*(-6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+15*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
160,1,121,66,0.044000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^2,x)","\frac{\left(a x -1\right) c^{2} \left(2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/6*(a*x-1)*c^2*(2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
161,1,93,39,0.040000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c),x)","-\frac{\left(a x -1\right) c \left(x \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/2*(a*x-1)*c*(x*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","B"
162,1,249,47,0.048000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x)","\frac{-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{a \sqrt{a^{2}}\, \left(a x -1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/a*(-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/(a^2)^(1/2)/(a*x-1)/c/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
163,1,36,29,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x)","-\frac{a x +1}{3 \left(a x -1\right) c^{2} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"-1/3*(a*x+1)/(a*x-1)/c^2/((a*x-1)/(a*x+1))^(1/2)/a","A"
164,1,41,59,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x)","-\frac{\left(a x -4\right) \left(a x +1\right)}{15 \left(a x -1\right)^{2} c^{3} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"-1/15*(a*x-4)*(a*x+1)/(a*x-1)^2/c^3/((a*x-1)/(a*x+1))^(1/2)/a","A"
165,1,50,88,0.040000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x)","-\frac{\left(2 a^{2} x^{2}-10 a x +23\right) \left(a x +1\right)}{105 \left(a x -1\right)^{3} c^{4} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"-1/105*(2*a^2*x^2-10*a*x+23)*(a*x+1)/(a*x-1)^3/c^4/((a*x-1)/(a*x+1))^(1/2)/a","A"
166,1,58,117,0.036000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x)","-\frac{\left(2 x^{3} a^{3}-12 a^{2} x^{2}+33 a x -58\right) \left(a x +1\right)}{315 \left(a x -1\right)^{4} c^{5} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"-1/315*(2*a^3*x^3-12*a^2*x^2+33*a*x-58)*(a*x+1)/(a*x-1)^4/c^5/((a*x-1)/(a*x+1))^(1/2)/a","A"
167,1,29,42,0.034000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^p,x)","\frac{\left(a p x +p +2\right) \left(-a c x +c \right)^{p}}{a p \left(1+p \right)}"," ",0,"(a*p*x+p+2)*(-a*c*x+c)^p/a/p/(1+p)","A"
168,1,47,33,0.030000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^5,x)","c^{5} \left(-\frac{1}{6} x^{6} a^{5}+\frac{3}{5} a^{4} x^{5}-\frac{1}{2} x^{4} a^{3}-\frac{2}{3} x^{3} a^{2}+\frac{3}{2} a \,x^{2}-x \right)"," ",0,"c^5*(-1/6*x^6*a^5+3/5*a^4*x^5-1/2*x^4*a^3-2/3*x^3*a^2+3/2*a*x^2-x)","A"
169,1,30,33,0.033000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^4,x)","c^{4} \left(\frac{1}{5} a^{4} x^{5}-\frac{1}{2} x^{4} a^{3}+a \,x^{2}-x \right)"," ",0,"c^4*(1/5*a^4*x^5-1/2*x^4*a^3+a*x^2-x)","A"
170,1,31,33,0.032000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^3,x)","c^{3} \left(-\frac{1}{4} x^{4} a^{3}+\frac{1}{3} x^{3} a^{2}+\frac{1}{2} a \,x^{2}-x \right)"," ",0,"c^3*(-1/4*x^4*a^3+1/3*x^3*a^2+1/2*a*x^2-x)","A"
171,1,17,18,0.032000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^2,x)","c^{2} \left(\frac{1}{3} x^{3} a^{2}-x \right)"," ",0,"c^2*(1/3*x^3*a^2-x)","A"
172,1,13,12,0.030000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c),x)","c \left(-\frac{1}{2} a \,x^{2}-x \right)"," ",0,"c*(-1/2*a*x^2-x)","A"
173,1,31,32,0.039000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c),x)","-\frac{\ln \left(a x -1\right)}{c a}+\frac{2}{c a \left(a x -1\right)}"," ",0,"-1/c/a*ln(a*x-1)+2/c/a/(a*x-1)","A"
174,1,30,14,0.038000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^2,x)","\frac{-\frac{1}{a \left(a x -1\right)^{2}}-\frac{1}{a \left(a x -1\right)}}{c^{2}}"," ",0,"1/c^2*(-1/a/(a*x-1)^2-1/a/(a*x-1))","B"
175,1,30,33,0.037000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^3,x)","\frac{\frac{1}{2 a \left(a x -1\right)^{2}}+\frac{2}{3 a \left(a x -1\right)^{3}}}{c^{3}}"," ",0,"1/c^3*(1/2/a/(a*x-1)^2+2/3/a/(a*x-1)^3)","A"
176,1,30,33,0.038000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^4,x)","\frac{-\frac{1}{3 a \left(a x -1\right)^{3}}-\frac{1}{2 a \left(a x -1\right)^{4}}}{c^{4}}"," ",0,"1/c^4*(-1/3/a/(a*x-1)^3-1/2/a/(a*x-1)^4)","A"
177,0,0,188,0.334000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^p,x)","\int \frac{\left(-a c x +c \right)^{p}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^p,x)","F"
178,1,192,89,0.049000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^4,x)","\frac{\left(a x -1\right)^{2} c^{4} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+45 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -40 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*(a*x-1)^2*c^4/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+45*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-40*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-45*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","B"
179,1,124,66,0.043000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^3,x)","-\frac{\left(a x -1\right)^{2} c^{3} \left(2 x \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 x \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}+3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{8 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/8*(a*x-1)^2*c^3*(2*x*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-3*x*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)+3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
180,1,130,66,0.044000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^2,x)","\frac{\left(a x -1\right)^{2} c^{2} \left(3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{6 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/6*(a*x-1)^2*c^2*(3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
181,1,162,55,0.051000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c),x)","-\frac{\left(a x -1\right)^{2} c \left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+4 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"-1/2*(a*x-1)^2*c*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+4*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
182,1,345,70,0.052000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x)","-\frac{3 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+3 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-9 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-3 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -9 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+9 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+9 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -3 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{3 a \sqrt{a^{2}}\, \left(a x -1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/3/a*(3*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+3*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-9*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-3*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-9*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+9*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+9*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-3*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)/(a*x-1)/c/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
183,1,36,29,0.037000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x)","-\frac{a x +1}{5 \left(a x -1\right) c^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/5*(a*x+1)/(a*x-1)/c^2/((a*x-1)/(a*x+1))^(3/2)/a","A"
184,1,41,59,0.038000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x)","-\frac{\left(a x -6\right) \left(a x +1\right)}{35 \left(a x -1\right)^{2} c^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/35*(a*x-6)*(a*x+1)/(a*x-1)^2/c^3/((a*x-1)/(a*x+1))^(3/2)/a","A"
185,1,50,82,0.037000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x)","-\frac{\left(2 a^{2} x^{2}-14 a x +47\right) \left(a x +1\right)}{315 \left(a x -1\right)^{3} c^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/315*(2*a^2*x^2-14*a*x+47)*(a*x+1)/(a*x-1)^3/c^4/((a*x-1)/(a*x+1))^(3/2)/a","A"
186,1,58,109,0.038000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x)","-\frac{\left(2 x^{3} a^{3}-16 a^{2} x^{2}+61 a x -152\right) \left(a x +1\right)}{1155 \left(a x -1\right)^{4} c^{5} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/1155*(2*a^3*x^3-16*a^2*x^2+61*a*x-152)*(a*x+1)/(a*x-1)^4/c^5/((a*x-1)/(a*x+1))^(3/2)/a","A"
187,1,74,66,0.037000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^p,x)","\frac{\left(-a c x +c \right)^{p} \left(a^{2} p^{2} x^{2}-a^{2} x^{2} p +2 a \,p^{2} x +2 a p x -4 a x +p^{2}+3 p +4\right)}{\left(p^{2}-1\right) a p \left(a x -1\right)}"," ",0,"(-a*c*x+c)^p*(a^2*p^2*x^2-a^2*p*x^2+2*a*p^2*x+2*a*p*x-4*a*x+p^2+3*p+4)/(p^2-1)/a/p/(a*x-1)","A"
188,1,45,49,0.030000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^5,x)","c^{5} \left(-\frac{1}{6} x^{6} a^{5}+\frac{1}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}-\frac{2}{3} x^{3} a^{2}-\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c^5*(-1/6*x^6*a^5+1/5*a^4*x^5+1/2*x^4*a^3-2/3*x^3*a^2-1/2*a*x^2+x)","A"
189,1,23,28,0.030000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^4,x)","c^{4} \left(\frac{1}{5} a^{4} x^{5}-\frac{2}{3} x^{3} a^{2}+x \right)"," ",0,"c^4*(1/5*a^4*x^5-2/3*x^3*a^2+x)","A"
190,1,29,31,0.033000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^3,x)","c^{3} \left(-\frac{1}{4} x^{4} a^{3}-\frac{1}{3} x^{3} a^{2}+\frac{1}{2} a \,x^{2}+x \right)"," ",0,"c^3*(-1/4*x^4*a^3-1/3*x^3*a^2+1/2*a*x^2+x)","A"
191,1,16,15,0.031000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c)^2,x)","\frac{c^{2} \left(a x +1\right)^{3}}{3 a}"," ",0,"1/3*c^2*(a*x+1)^3/a","A"
192,1,25,25,0.033000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a*c*x+c),x)","-\frac{a c \,x^{2}}{2}-3 c x -\frac{4 c \ln \left(a x -1\right)}{a}"," ",0,"-1/2*a*c*x^2-3*c*x-4*c/a*ln(a*x-1)","A"
193,1,46,48,0.038000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c),x)","\frac{2}{c a \left(a x -1\right)^{2}}-\frac{\ln \left(a x -1\right)}{c a}+\frac{4}{c a \left(a x -1\right)}"," ",0,"2/c/a/(a*x-1)^2-1/c/a*ln(a*x-1)+4/c/a/(a*x-1)","A"
194,1,42,23,0.037000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^2,x)","\frac{-\frac{2}{a \left(a x -1\right)^{2}}-\frac{4}{3 a \left(a x -1\right)^{3}}-\frac{1}{a \left(a x -1\right)}}{c^{2}}"," ",0,"1/c^2*(-2/a/(a*x-1)^2-4/3/a/(a*x-1)^3-1/a/(a*x-1))","A"
195,1,41,48,0.040000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^3,x)","\frac{\frac{1}{2 a \left(a x -1\right)^{2}}+\frac{4}{3 a \left(a x -1\right)^{3}}+\frac{1}{a \left(a x -1\right)^{4}}}{c^{3}}"," ",0,"1/c^3*(1/2/a/(a*x-1)^2+4/3/a/(a*x-1)^3+1/a/(a*x-1)^4)","A"
196,1,42,49,0.039000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a*c*x+c)^4,x)","\frac{-\frac{4}{5 a \left(a x -1\right)^{5}}-\frac{1}{3 a \left(a x -1\right)^{3}}-\frac{1}{a \left(a x -1\right)^{4}}}{c^{4}}"," ",0,"1/c^4*(-4/5/a/(a*x-1)^5-1/3/a/(a*x-1)^3-1/a/(a*x-1)^4)","A"
197,0,0,88,0.378000," ","int((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(1/2),x)","\int \left(-a c x +c \right)^{p} \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(1/2),x)","F"
198,1,196,107,0.048000," ","int((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{3} \left(6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +87 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -32 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-87 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -192 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+192 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{24 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/24*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^3/a*(6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+87*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-32*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-87*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-192*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+192*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
199,1,176,84,0.049000," ","int((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{2} \left(2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^2*(2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+24*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
200,1,153,55,0.045000," ","int((-a*c*x+c)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -4 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-4*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
201,1,76,21,0.051000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, c \sqrt{a^{2}}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/c/(a^2)^(1/2)","B"
202,1,36,26,0.035000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^2,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right)}{\left(a x -1\right) a \,c^{2}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)/(a*x-1)/a/c^2","A"
203,1,41,54,0.036000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^3,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x -2\right) \left(a x +1\right)}{3 \left(a x -1\right)^{2} c^{3} a}"," ",0,"-1/3*((a*x-1)/(a*x+1))^(1/2)*(a*x-2)*(a*x+1)/(a*x-1)^2/c^3/a","A"
204,1,50,83,0.037000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^4,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(2 a^{2} x^{2}-6 a x +7\right) \left(a x +1\right)}{15 \left(a x -1\right)^{3} c^{4} a}"," ",0,"-1/15*((a*x-1)/(a*x+1))^(1/2)*(2*a^2*x^2-6*a*x+7)*(a*x+1)/(a*x-1)^3/c^4/a","A"
205,1,58,112,0.036000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^5,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(2 x^{3} a^{3}-8 a^{2} x^{2}+13 a x -12\right) \left(a x +1\right)}{35 \left(a x -1\right)^{4} c^{5} a}"," ",0,"-1/35*((a*x-1)/(a*x+1))^(1/2)*(2*a^3*x^3-8*a^2*x^2+13*a*x-12)*(a*x+1)/(a*x-1)^4/c^5/a","A"
206,0,0,40,0.506000," ","int((-a*c*x+c)^p/(a*x+1)*(a*x-1),x)","\int \frac{\left(-a c x +c \right)^{p} \left(a x -1\right)}{a x +1}\, dx"," ",0,"int((-a*c*x+c)^p/(a*x+1)*(a*x-1),x)","F"
207,1,64,85,0.036000," ","int((-a*c*x+c)^4/(a*x+1)*(a*x-1),x)","\frac{a^{4} c^{4} x^{5}}{5}-\frac{3 c^{4} x^{4} a^{3}}{2}+\frac{16 a^{2} c^{4} x^{3}}{3}-13 c^{4} x^{2} a +31 c^{4} x -\frac{32 c^{4} \ln \left(a x +1\right)}{a}"," ",0,"1/5*a^4*c^4*x^5-3/2*c^4*x^4*a^3+16/3*a^2*c^4*x^3-13*c^4*x^2*a+31*c^4*x-32*c^4*ln(a*x+1)/a","A"
208,1,53,69,0.034000," ","int((-a*c*x+c)^3/(a*x+1)*(a*x-1),x)","-\frac{c^{3} x^{4} a^{3}}{4}+\frac{5 a^{2} c^{3} x^{3}}{3}-\frac{11 c^{3} x^{2} a}{2}+15 c^{3} x -\frac{16 c^{3} \ln \left(a x +1\right)}{a}"," ",0,"-1/4*c^3*x^4*a^3+5/3*a^2*c^3*x^3-11/2*c^3*x^2*a+15*c^3*x-16*c^3*ln(a*x+1)/a","A"
209,1,42,53,0.035000," ","int((-a*c*x+c)^2/(a*x+1)*(a*x-1),x)","\frac{a^{2} c^{2} x^{3}}{3}-2 c^{2} x^{2} a +7 c^{2} x -\frac{8 c^{2} \ln \left(a x +1\right)}{a}"," ",0,"1/3*a^2*c^2*x^3-2*c^2*x^2*a+7*c^2*x-8*c^2*ln(a*x+1)/a","A"
210,1,25,24,0.034000," ","int((-a*c*x+c)/(a*x+1)*(a*x-1),x)","3 c x -\frac{a c \,x^{2}}{2}-\frac{4 c \ln \left(a x +1\right)}{a}"," ",0,"3*c*x-1/2*a*c*x^2-4*c*ln(a*x+1)/a","A"
211,1,15,14,0.039000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c),x)","-\frac{\ln \left(a x +1\right)}{a c}"," ",0,"-ln(a*x+1)/a/c","A"
212,1,30,12,0.039000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^2,x)","\frac{\ln \left(a x -1\right)}{2 c^{2} a}-\frac{\ln \left(a x +1\right)}{2 a \,c^{2}}"," ",0,"1/2/c^2/a*ln(a*x-1)-1/2*ln(a*x+1)/a/c^2","B"
213,1,45,29,0.043000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^3,x)","\frac{1}{2 c^{3} a \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{4 c^{3} a}-\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"1/2/c^3/a/(a*x-1)+1/4/c^3/a*ln(a*x-1)-1/4*ln(a*x+1)/a/c^3","A"
214,1,60,45,0.041000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^4,x)","-\frac{1}{4 c^{4} a \left(a x -1\right)^{2}}+\frac{1}{4 c^{4} a \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{4} a}-\frac{\ln \left(a x +1\right)}{8 a \,c^{4}}"," ",0,"-1/4/c^4/a/(a*x-1)^2+1/4/c^4/a/(a*x-1)+1/8/c^4/a*ln(a*x-1)-1/8*ln(a*x+1)/a/c^4","A"
215,1,75,61,0.042000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^5,x)","\frac{1}{6 c^{5} a \left(a x -1\right)^{3}}-\frac{1}{8 c^{5} a \left(a x -1\right)^{2}}+\frac{1}{8 c^{5} a \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{16 c^{5} a}-\frac{\ln \left(a x +1\right)}{16 c^{5} a}"," ",0,"1/6/c^5/a/(a*x-1)^3-1/8/c^5/a/(a*x-1)^2+1/8/c^5/a/(a*x-1)+1/16/c^5/a*ln(a*x-1)-1/16/c^5/a*ln(a*x+1)","A"
216,0,0,88,0.366000," ","int((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(3/2),x)","\int \left(-a c x +c \right)^{p} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}\, dx"," ",0,"int((-a*c*x+c)^p*((a*x-1)/(a*x+1))^(3/2),x)","F"
217,1,542,134,0.058000," ","int((-a*c*x+c)^3*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(-2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+16 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-69 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+32 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +384 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -138 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+69 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-384 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-112 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+768 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -69 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +138 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-768 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+384 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+69 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -384 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) c^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{8 a \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"1/8*(-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+16*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-69*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+32*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+384*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-138*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+69*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-384*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-112*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+768*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-69*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+138*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-768*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+384*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+69*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-384*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*c^3*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
218,1,474,111,0.056000," ","int((-a*c*x+c)^2*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+4 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +120 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-30 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+15 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-46 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+240 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +30 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+120 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+15 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -120 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) c^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 a \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"1/6*(2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+120*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-30*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+15*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-46*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+240*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+30*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+120*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+15*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-120*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*c^2*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
219,1,422,80,0.052000," ","int((-a*c*x+c)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-16 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+16 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+8 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-32 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+32 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-16 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +16 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) c \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/2*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-16*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+16*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+8*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-32*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+32*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-16*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+16*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*c*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
220,1,248,49,0.047000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c),x)","-\frac{\left(-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+\ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \sqrt{a^{2}}\, c \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-(-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/c/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)","B"
221,1,35,26,0.039000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^2,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)}{\left(a x -1\right) a \,c^{2}}"," ",0,"((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)/a/c^2","A"
222,1,33,19,0.035000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^3,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x}{\left(a x -1\right)^{2} c^{3}}"," ",0,"((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*x/(a*x-1)^2/c^3","A"
223,1,50,53,0.037000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^4,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(2 a^{2} x^{2}-2 a x -1\right) \left(a x +1\right)}{3 \left(a x -1\right)^{3} c^{4} a}"," ",0,"1/3*((a*x-1)/(a*x+1))^(3/2)*(2*a^2*x^2-2*a*x-1)*(a*x+1)/(a*x-1)^3/c^4/a","A"
224,1,57,82,0.036000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^5,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(2 x^{3} a^{3}-4 a^{2} x^{2}+a x +2\right) \left(a x +1\right)}{5 \left(a x -1\right)^{4} c^{5} a}"," ",0,"1/5*((a*x-1)/(a*x+1))^(3/2)*(2*a^3*x^3-4*a^2*x^2+a*x+2)*(a*x+1)/(a*x-1)^4/c^5/a","A"
225,1,66,109,0.039000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^6,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(8 x^{4} a^{4}-24 x^{3} a^{3}+20 a^{2} x^{2}+4 a x -13\right) \left(a x +1\right)}{35 \left(a x -1\right)^{5} c^{6} a}"," ",0,"1/35*((a*x-1)/(a*x+1))^(3/2)*(8*a^4*x^4-24*a^3*x^3+20*a^2*x^2+4*a*x-13)*(a*x+1)/(a*x-1)^5/c^6/a","A"
226,1,72,214,0.039000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(9/2),x)","\frac{2 \left(a x +1\right) \left(315 x^{4} a^{4}-1820 x^{3} a^{3}+4530 a^{2} x^{2}-6396 a x +5419\right) \left(-a c x +c \right)^{\frac{9}{2}}}{3465 a \left(a x -1\right)^{4} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/3465*(a*x+1)*(315*a^4*x^4-1820*a^3*x^3+4530*a^2*x^2-6396*a*x+5419)*(-a*c*x+c)^(9/2)/a/(a*x-1)^4/((a*x-1)/(a*x+1))^(1/2)","A"
227,1,64,165,0.038000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(7/2),x)","\frac{2 \left(a x +1\right) \left(35 x^{3} a^{3}-165 a^{2} x^{2}+321 a x -319\right) \left(-a c x +c \right)^{\frac{7}{2}}}{315 a \left(a x -1\right)^{3} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/315*(a*x+1)*(35*a^3*x^3-165*a^2*x^2+321*a*x-319)*(-a*c*x+c)^(7/2)/a/(a*x-1)^3/((a*x-1)/(a*x+1))^(1/2)","A"
228,1,56,97,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(5/2),x)","\frac{2 \left(a x +1\right) \left(15 a^{2} x^{2}-54 a x +71\right) \left(-a c x +c \right)^{\frac{5}{2}}}{105 a \left(a x -1\right)^{2} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/105*(a*x+1)*(15*a^2*x^2-54*a*x+71)*(-a*c*x+c)^(5/2)/a/(a*x-1)^2/((a*x-1)/(a*x+1))^(1/2)","A"
229,1,48,65,0.035000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(3/2),x)","\frac{2 \left(a x +1\right) \left(3 a x -7\right) \left(-a c x +c \right)^{\frac{3}{2}}}{15 a \left(a x -1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/15*(a*x+1)*(3*a*x-7)*(-a*c*x+c)^(3/2)/a/(a*x-1)/((a*x-1)/(a*x+1))^(1/2)","A"
230,1,35,34,0.033000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \sqrt{-a c x +c}}{3 \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"2/3/((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-a*c*x+c)^(1/2)/a","A"
231,1,82,94,0.056000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x)","-\frac{2 \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{-c \left(a x +1\right)}-\sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a x +1\right)}\, c a}"," ",0,"-2*(-c*(a*x-1))^(1/2)*((-c*(a*x+1))^(1/2)-c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2)))/((a*x-1)/(a*x+1))^(1/2)/(-c*(a*x+1))^(1/2)/c/a","A"
232,1,118,104,0.059000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x)","-\frac{\sqrt{-c \left(a x -1\right)}\, \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +2 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \sqrt{-c \left(a x +1\right)}\, c^{\frac{5}{2}} a}"," ",0,"-1/2/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a*x-1))^(1/2)*(2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+2*(-c*(a*x+1))^(1/2)*c^(1/2))/(-c*(a*x+1))^(1/2)/c^(5/2)/a","A"
233,1,167,157,0.065000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x)","\frac{\sqrt{-c \left(a x -1\right)}\, \left(-\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +2 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +2 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +6 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right)^{2} c^{\frac{7}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/16*(-c*(a*x-1))^(1/2)*(-2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+2*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+2*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)-2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+6*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^2/c^(7/2)/(-c*(a*x+1))^(1/2)/a","A"
234,1,219,206,0.064000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x)","\frac{\sqrt{-c \left(a x -1\right)}\, \left(-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c +9 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +6 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-9 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -20 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -50 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{192 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right)^{3} c^{\frac{9}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/192*(-c*(a*x-1))^(1/2)*(-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c+9*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+6*x^2*a^2*(-c*(a*x+1))^(1/2)*c^(1/2)-9*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-20*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-50*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^3/c^(9/2)/(-c*(a*x+1))^(1/2)/a","A"
235,1,21,32,0.035000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(7/2),x)","\frac{2 \left(-a c x +c \right)^{\frac{7}{2}} \left(7 a x +11\right)}{63 a}"," ",0,"2/63*(-a*c*x+c)^(7/2)*(7*a*x+11)/a","A"
236,1,21,32,0.042000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(5/2),x)","\frac{2 \left(-a c x +c \right)^{\frac{5}{2}} \left(5 a x +9\right)}{35 a}"," ",0,"2/35*(-a*c*x+c)^(5/2)*(5*a*x+9)/a","A"
237,1,21,32,0.033000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(3/2),x)","\frac{2 \left(-a c x +c \right)^{\frac{3}{2}} \left(3 a x +7\right)}{15 a}"," ",0,"2/15*(-a*c*x+c)^(3/2)*(3*a*x+7)/a","A"
238,1,20,32,0.034000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}\, \left(a x +5\right)}{3 a}"," ",0,"2/3*(-a*c*x+c)^(1/2)*(a*x+5)/a","A"
239,1,20,32,0.036000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^(1/2),x)","\frac{2 a x -6}{a \sqrt{-a c x +c}}"," ",0,"2*(a*x-3)/a/(-a*c*x+c)^(1/2)","A"
240,1,21,32,0.038000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^(3/2),x)","-\frac{2 \left(3 a x -1\right)}{3 a \left(-a c x +c \right)^{\frac{3}{2}}}"," ",0,"-2/3*(3*a*x-1)/a/(-a*c*x+c)^(3/2)","A"
241,1,21,32,0.035000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^(5/2),x)","-\frac{2 \left(5 a x +1\right)}{15 a \left(-a c x +c \right)^{\frac{5}{2}}}"," ",0,"-2/15*(5*a*x+1)/a/(-a*c*x+c)^(5/2)","A"
242,1,21,32,0.035000," ","int((a*x+1)/(a*x-1)/(-a*c*x+c)^(7/2),x)","-\frac{2 \left(7 a x +3\right)}{35 a \left(-a c x +c \right)^{\frac{7}{2}}}"," ",0,"-2/35*(7*a*x+3)/a/(-a*c*x+c)^(7/2)","A"
243,1,64,165,0.038000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(9/2),x)","\frac{2 \left(a x +1\right) \left(105 x^{3} a^{3}-455 a^{2} x^{2}+755 a x -533\right) \left(-a c x +c \right)^{\frac{9}{2}}}{1155 a \left(a x -1\right)^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"2/1155*(a*x+1)*(105*a^3*x^3-455*a^2*x^2+755*a*x-533)*(-a*c*x+c)^(9/2)/a/(a*x-1)^3/((a*x-1)/(a*x+1))^(3/2)","A"
244,1,56,113,0.039000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(7/2),x)","\frac{2 \left(a x +1\right) \left(35 a^{2} x^{2}-110 a x +107\right) \left(-a c x +c \right)^{\frac{7}{2}}}{315 a \left(a x -1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"2/315*(a*x+1)*(35*a^2*x^2-110*a*x+107)*(-a*c*x+c)^(7/2)/a/(a*x-1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
245,1,48,73,0.036000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(5/2),x)","\frac{2 \left(a x +1\right) \left(5 a x -9\right) \left(-a c x +c \right)^{\frac{5}{2}}}{35 a \left(a x -1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"2/35*(a*x+1)*(5*a*x-9)*(-a*c*x+c)^(5/2)/a/(a*x-1)/((a*x-1)/(a*x+1))^(3/2)","A"
246,1,35,34,0.036000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(3/2),x)","\frac{2 \left(a x +1\right) \left(-a c x +c \right)^{\frac{3}{2}}}{5 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"2/5/((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*(-a*c*x+c)^(3/2)/a","A"
247,1,107,131,0.055000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(6 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-x a \sqrt{-c \left(a x +1\right)}-7 \sqrt{-c \left(a x +1\right)}\right)}{3 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"-2/3/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(6*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-x*a*(-c*(a*x+1))^(1/2)-7*(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)/a","A"
248,1,135,147,0.067000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x)","\frac{\sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -2 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +4 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) c^{\frac{3}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)*(-c*(a*x-1))^(1/2)*(3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+4*(-c*(a*x+1))^(1/2)*c^(1/2))/c^(3/2)/(-c*(a*x+1))^(1/2)/a","A"
249,1,174,151,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x)","-\frac{\sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +10 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -2 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{8 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right) \left(a x +1\right) c^{\frac{5}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"-1/8/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)/c^(5/2)*(3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-6*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+10*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-2*(-c*(a*x+1))^(1/2)*c^(1/2))/(-c*(a*x+1))^(1/2)/a","A"
250,1,226,206,0.070000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x)","\frac{\sqrt{-c \left(a x -1\right)}\, \left(-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c +9 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +6 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-9 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +44 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c +14 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{96 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right)^{2} \left(a x +1\right) c^{\frac{7}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/96*(-c*(a*x-1))^(1/2)*(-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c+9*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+6*x^2*a^2*(-c*(a*x+1))^(1/2)*c^(1/2)-9*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+44*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c+14*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/(a*x+1)/c^(7/2)/(-c*(a*x+1))^(1/2)/a","A"
251,1,278,255,0.069000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x)","\frac{\sqrt{-c \left(a x -1\right)}\, \left(-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{4} a^{4} c +12 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c +6 x^{3} a^{3} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-18 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c -26 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+12 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -158 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -78 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{512 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right)^{3} \left(a x +1\right) c^{\frac{9}{2}} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/512*(-c*(a*x-1))^(1/2)*(-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^4*a^4*c+12*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c+6*x^3*a^3*(-c*(a*x+1))^(1/2)*c^(1/2)-18*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c-26*x^2*a^2*(-c*(a*x+1))^(1/2)*c^(1/2)+12*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-158*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-78*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3/(a*x+1)/c^(9/2)/(-c*(a*x+1))^(1/2)/a","A"
252,1,80,158,0.039000," ","int((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(63 x^{5} a^{5}-455 x^{4} a^{4}+1510 x^{3} a^{3}-3198 a^{2} x^{2}+5419 a x -11531\right) \left(-a c x +c \right)^{\frac{9}{2}} \sqrt{\frac{a x -1}{a x +1}}}{693 a \left(a x -1\right)^{5}}"," ",0,"2/693*(a*x+1)*(63*a^5*x^5-455*a^4*x^4+1510*a^3*x^3-3198*a^2*x^2+5419*a*x-11531)*(-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2)/a/(a*x-1)^5","A"
253,1,72,131,0.039000," ","int((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(35 x^{4} a^{4}-220 x^{3} a^{3}+642 a^{2} x^{2}-1276 a x +2867\right) \left(-a c x +c \right)^{\frac{7}{2}} \sqrt{\frac{a x -1}{a x +1}}}{315 a \left(a x -1\right)^{4}}"," ",0,"2/315*(a*x+1)*(35*a^4*x^4-220*a^3*x^3+642*a^2*x^2-1276*a*x+2867)*(-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2)/a/(a*x-1)^4","A"
254,1,64,104,0.039000," ","int((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(5 x^{3} a^{3}-27 a^{2} x^{2}+71 a x -177\right) \left(-a c x +c \right)^{\frac{5}{2}} \sqrt{\frac{a x -1}{a x +1}}}{35 a \left(a x -1\right)^{3}}"," ",0,"2/35*(a*x+1)*(5*a^3*x^3-27*a^2*x^2+71*a*x-177)*(-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2)/a/(a*x-1)^3","A"
255,1,56,77,0.038000," ","int((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(3 a^{2} x^{2}-14 a x +43\right) \left(-a c x +c \right)^{\frac{3}{2}} \sqrt{\frac{a x -1}{a x +1}}}{15 a \left(a x -1\right)^{2}}"," ",0,"2/15*(a*x+1)*(3*a^2*x^2-14*a*x+43)*(-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2)/a/(a*x-1)^2","A"
256,1,47,50,0.036000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(a x -5\right) \sqrt{-a c x +c}\, \sqrt{\frac{a x -1}{a x +1}}}{3 \left(a x -1\right) a}"," ",0,"2/3*(a*x+1)*(a*x-5)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)/a","A"
257,1,35,34,0.035000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}{a \sqrt{-a c x +c}}"," ",0,"2*(a*x+1)/a*((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(1/2)","A"
258,1,78,58,0.057000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(3/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)}{\left(a x -1\right) \sqrt{-c \left(a x +1\right)}\, c^{\frac{3}{2}} a}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-c*(a*x-1))^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))/(a*x-1)/(-c*(a*x+1))^(1/2)/c^(3/2)/a","A"
259,1,123,108,0.059000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(5/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c -\sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -2 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{4 c^{\frac{7}{2}} \left(a x -1\right)^{2} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"-1/4*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-c*(a*x-1))^(1/2)/c^(7/2)*(2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c-2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-2*(-c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)^2/(-c*(a*x+1))^(1/2)/a","A"
260,1,172,157,0.059000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a*c*x+c)^(7/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +6 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}-3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) c -14 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{32 c^{\frac{9}{2}} \left(a x -1\right)^{3} \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"1/32*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-c*(a*x-1))^(1/2)*(-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+6*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+6*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)-3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*c-14*(-c*(a*x+1))^(1/2)*c^(1/2))/c^(9/2)/(a*x-1)^3/(-c*(a*x+1))^(1/2)/a","A"
261,1,101,110,0.039000," ","int((-a*c*x+c)^(7/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{9}{2}}}{9}+\frac{2 \left(-a c x +c \right)^{\frac{7}{2}} c}{7}+\frac{4 \left(-a c x +c \right)^{\frac{5}{2}} c^{2}}{5}+\frac{8 c^{3} \left(-a c x +c \right)^{\frac{3}{2}}}{3}+16 \sqrt{-a c x +c}\, c^{4}-16 c^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c a}"," ",0,"-2/c/a*(1/9*(-a*c*x+c)^(9/2)+2/7*(-a*c*x+c)^(7/2)*c+4/5*(-a*c*x+c)^(5/2)*c^2+8/3*c^3*(-a*c*x+c)^(3/2)+16*(-a*c*x+c)^(1/2)*c^4-16*c^(9/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
262,1,87,93,0.037000," ","int((-a*c*x+c)^(5/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{7}{2}}}{7}+\frac{2 c \left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{4 \left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{3}+8 \sqrt{-a c x +c}\, c^{3}-8 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c a}"," ",0,"-2/c/a*(1/7*(-a*c*x+c)^(7/2)+2/5*c*(-a*c*x+c)^(5/2)+4/3*(-a*c*x+c)^(3/2)*c^2+8*(-a*c*x+c)^(1/2)*c^3-8*c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
263,1,73,76,0.040000," ","int((-a*c*x+c)^(3/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{2 c \left(-a c x +c \right)^{\frac{3}{2}}}{3}+4 \sqrt{-a c x +c}\, c^{2}-4 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c a}"," ",0,"-2/c/a*(1/5*(-a*c*x+c)^(5/2)+2/3*c*(-a*c*x+c)^(3/2)+4*(-a*c*x+c)^(1/2)*c^2-4*c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
264,1,59,61,0.041000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{3}{2}}}{3}+2 c \sqrt{-a c x +c}-2 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c a}"," ",0,"-2/c/a*(1/3*(-a*c*x+c)^(3/2)+2*c*(-a*c*x+c)^(1/2)-2*c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
265,1,45,47,0.040000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^(1/2),x)","-\frac{2 \left(\sqrt{-a c x +c}-\arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c}\right)}{c a}"," ",0,"-2/c/a*((-a*c*x+c)^(1/2)-arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^(1/2))","A"
266,1,29,28,0.040000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^(3/2),x)","\frac{\arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}}{a \,c^{\frac{3}{2}}}"," ",0,"arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)/a/c^(3/2)","A"
267,1,50,47,0.042000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^(5/2),x)","-\frac{2 \left(\frac{1}{2 c \sqrt{-a c x +c}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{4 c^{\frac{3}{2}}}\right)}{c a}"," ",0,"-2/c/a*(1/2/c/(-a*c*x+c)^(1/2)-1/4/c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
268,1,64,64,0.046000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^(7/2),x)","-\frac{2 \left(\frac{1}{4 c^{2} \sqrt{-a c x +c}}+\frac{1}{6 c \left(-a c x +c \right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{8 c^{\frac{5}{2}}}\right)}{c a}"," ",0,"-2/c/a*(1/4/c^2/(-a*c*x+c)^(1/2)+1/6/c/(-a*c*x+c)^(3/2)-1/8/c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
269,1,78,81,0.046000," ","int(1/(a*x+1)*(a*x-1)/(-a*c*x+c)^(9/2),x)","-\frac{2 \left(\frac{1}{8 c^{3} \sqrt{-a c x +c}}+\frac{1}{12 c^{2} \left(-a c x +c \right)^{\frac{3}{2}}}+\frac{1}{10 c \left(-a c x +c \right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{16 c^{\frac{7}{2}}}\right)}{c a}"," ",0,"-2/c/a*(1/8/c^3/(-a*c*x+c)^(1/2)+1/12/c^2/(-a*c*x+c)^(3/2)+1/10/c/(-a*c*x+c)^(5/2)-1/16/c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
270,1,88,312,0.039000," ","int((-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(21 x^{6} a^{6}-182 x^{5} a^{5}+755 x^{4} a^{4}-2132 x^{3} a^{3}+5419 a^{2} x^{2}-23062 a x -46355\right) \left(-a c x +c \right)^{\frac{9}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{231 a \left(a x -1\right)^{6}}"," ",0,"2/231*(a*x+1)*(21*a^6*x^6-182*a^5*x^5+755*a^4*x^4-2132*a^3*x^3+5419*a^2*x^2-23062*a*x-46355)*(-a*c*x+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^6","A"
271,1,80,263,0.038000," ","int((-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(7 x^{5} a^{5}-55 x^{4} a^{4}+214 x^{3} a^{3}-638 a^{2} x^{2}+2867 a x +5797\right) \left(-a c x +c \right)^{\frac{7}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{63 a \left(a x -1\right)^{5}}"," ",0,"2/63*(a*x+1)*(7*a^5*x^5-55*a^4*x^4+214*a^3*x^3-638*a^2*x^2+2867*a*x+5797)*(-a*c*x+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^5","A"
272,1,72,214,0.039000," ","int((-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(5 x^{4} a^{4}-36 x^{3} a^{3}+142 a^{2} x^{2}-708 a x -1451\right) \left(-a c x +c \right)^{\frac{5}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{35 a \left(a x -1\right)^{4}}"," ",0,"2/35*(a*x+1)*(5*a^4*x^4-36*a^3*x^3+142*a^2*x^2-708*a*x-1451)*(-a*c*x+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^4","A"
273,1,63,165,0.039000," ","int((-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(x^{3} a^{3}-7 a^{2} x^{2}+43 a x +91\right) \left(-a c x +c \right)^{\frac{3}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{5 a \left(a x -1\right)^{3}}"," ",0,"2/5*(a*x+1)*(a^3*x^3-7*a^2*x^2+43*a*x+91)*(-a*c*x+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^3","A"
274,1,55,113,0.036000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(a^{2} x^{2}-10 a x -23\right) \sqrt{-a c x +c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{3 a \left(a x -1\right)^{2}}"," ",0,"2/3*(a*x+1)*(a^2*x^2-10*a*x-23)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^2","A"
275,1,47,73,0.036000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \left(a x +3\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \left(a x -1\right) \sqrt{-a c x +c}}"," ",0,"2*(a*x+1)*(a*x+3)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)/(-a*c*x+c)^(1/2)","A"
276,1,35,34,0.033000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2),x)","-\frac{2 \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \left(-a c x +c \right)^{\frac{3}{2}}}"," ",0,"-2*(a*x+1)/a*((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(3/2)","A"
277,1,85,96,0.059000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(5/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(\arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{-c \left(a x +1\right)}+2 \sqrt{c}\right)}{2 \left(a x -1\right)^{2} c^{\frac{7}{2}} a}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(-c*(a*x-1))^(1/2)/c^(7/2)*(arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*(-c*(a*x+1))^(1/2)+2*c^(1/2))/a","A"
278,1,129,148,0.067000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a*c*x+c)^(7/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a \sqrt{-c \left(a x +1\right)}-3 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{-c \left(a x +1\right)}+6 x a \sqrt{c}-2 \sqrt{c}\right)}{8 \left(a x -1\right)^{3} c^{\frac{9}{2}} a}"," ",0,"-1/8*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^3*(-c*(a*x-1))^(1/2)/c^(9/2)*(3*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*(-c*(a*x+1))^(1/2)-3*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*(-c*(a*x+1))^(1/2)+6*x*a*c^(1/2)-2*c^(1/2))/a","A"
279,1,67,79,0.043000," ","int(1/((-1+x)/(1+x))^(1/2)*x*(1+x),x)","\frac{\left(-1+x \right) \left(\left(\left(1+x \right) \left(-1+x \right)\right)^{\frac{3}{2}}+3 x \sqrt{x^{2}-1}+6 \sqrt{x^{2}-1}+3 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{3 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/3*(-1+x)*(((1+x)*(-1+x))^(3/2)+3*x*(x^2-1)^(1/2)+6*(x^2-1)^(1/2)+3*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
280,1,57,61,0.041000," ","int(1/((-1+x)/(1+x))^(1/2)*(1+x),x)","\frac{\left(-1+x \right) \left(x \sqrt{x^{2}-1}+4 \sqrt{x^{2}-1}+3 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{2 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/2*(-1+x)*(x*(x^2-1)^(1/2)+4*(x^2-1)^(1/2)+3*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
281,1,22,14,0.035000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)*x,x)","-\frac{\left(1+x \right) \left(-1+x \right)^{2}}{3 \sqrt{\frac{-1+x}{1+x}}}"," ",0,"-1/3*(1+x)*(-1+x)^2/((-1+x)/(1+x))^(1/2)","A"
282,1,48,27,0.039000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x),x)","-\frac{\left(-1+x \right) \left(x \sqrt{x^{2}-1}-\ln \left(x +\sqrt{x^{2}-1}\right)\right)}{2 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"-1/2*(-1+x)*(x*(x^2-1)^(1/2)-ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
283,1,79,103,0.044000," ","int(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^2,x)","\frac{\left(-1+x \right) \left(2 x \left(x^{2}-1\right)^{\frac{3}{2}}+8 \left(\left(1+x \right) \left(-1+x \right)\right)^{\frac{3}{2}}+17 x \sqrt{x^{2}-1}+32 \sqrt{x^{2}-1}+15 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{8 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/8*(-1+x)*(2*x*(x^2-1)^(3/2)+8*((1+x)*(-1+x))^(3/2)+17*x*(x^2-1)^(1/2)+32*(x^2-1)^(1/2)+15*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
284,1,69,82,0.040000," ","int(1/((-1+x)/(1+x))^(1/2)*(1+x)^2,x)","\frac{\left(-1+x \right) \left(2 \left(\left(1+x \right) \left(-1+x \right)\right)^{\frac{3}{2}}+9 x \sqrt{x^{2}-1}+24 \sqrt{x^{2}-1}+15 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{6 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/6*(-1+x)*(2*((1+x)*(-1+x))^(3/2)+9*x*(x^2-1)^(1/2)+24*(x^2-1)^(1/2)+15*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
285,1,70,55,0.040000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)^2*x,x)","-\frac{\left(-1+x \right) \left(-6 x \left(x^{2}-1\right)^{\frac{3}{2}}+8 \left(\left(1+x \right) \left(-1+x \right)\right)^{\frac{3}{2}}-3 x \sqrt{x^{2}-1}+3 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{24 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"-1/24*(-1+x)*(-6*x*(x^2-1)^(3/2)+8*((1+x)*(-1+x))^(3/2)-3*x*(x^2-1)^(1/2)+3*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
286,1,60,41,0.040000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)^2,x)","\frac{\left(-1+x \right) \left(2 \left(\left(1+x \right) \left(-1+x \right)\right)^{\frac{3}{2}}-3 x \sqrt{x^{2}-1}+3 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{6 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/6*(-1+x)*(2*((1+x)*(-1+x))^(3/2)-3*x*(x^2-1)^(1/2)+3*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)","A"
287,1,16,18,0.035000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1+x),x)","\frac{-1+x}{\sqrt{\frac{-1+x}{1+x}}}"," ",0,"(-1+x)/((-1+x)/(1+x))^(1/2)","A"
288,1,35,18,0.048000," ","int(1/((-1+x)/(1+x))^(1/2)/(1+x),x)","\frac{\left(-1+x \right) \ln \left(x +\sqrt{x^{2}-1}\right)}{\sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}}"," ",0,"1/((-1+x)/(1+x))^(1/2)*(-1+x)/((1+x)*(-1+x))^(1/2)*ln(x+(x^2-1)^(1/2))","A"
289,1,106,41,0.049000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1-x),x)","\frac{\left(x^{2}-1\right)^{\frac{3}{2}}-2 x^{2} \sqrt{x^{2}-1}-2 \ln \left(x +\sqrt{x^{2}-1}\right) x^{2}+4 x \sqrt{x^{2}-1}+4 \ln \left(x +\sqrt{x^{2}-1}\right) x -2 \sqrt{x^{2}-1}-2 \ln \left(x +\sqrt{x^{2}-1}\right)}{\left(-1+x \right) \sqrt{\left(1+x \right) \left(-1+x \right)}\, \sqrt{\frac{-1+x}{1+x}}}"," ",0,"((x^2-1)^(3/2)-2*x^2*(x^2-1)^(1/2)-2*ln(x+(x^2-1)^(1/2))*x^2+4*x*(x^2-1)^(1/2)+4*ln(x+(x^2-1)^(1/2))*x-2*(x^2-1)^(1/2)-2*ln(x+(x^2-1)^(1/2)))/(-1+x)/((1+x)*(-1+x))^(1/2)/((-1+x)/(1+x))^(1/2)","B"
290,1,106,29,0.045000," ","int(1/((-1+x)/(1+x))^(1/2)/(1-x),x)","\frac{\left(x^{2}-1\right)^{\frac{3}{2}}-x^{2} \sqrt{x^{2}-1}-\ln \left(x +\sqrt{x^{2}-1}\right) x^{2}+2 x \sqrt{x^{2}-1}+2 \ln \left(x +\sqrt{x^{2}-1}\right) x -\sqrt{x^{2}-1}-\ln \left(x +\sqrt{x^{2}-1}\right)}{\left(-1+x \right) \sqrt{\left(1+x \right) \left(-1+x \right)}\, \sqrt{\frac{-1+x}{1+x}}}"," ",0,"((x^2-1)^(3/2)-x^2*(x^2-1)^(1/2)-ln(x+(x^2-1)^(1/2))*x^2+2*x*(x^2-1)^(1/2)+2*ln(x+(x^2-1)^(1/2))*x-(x^2-1)^(1/2)-ln(x+(x^2-1)^(1/2)))/(-1+x)/((1+x)*(-1+x))^(1/2)/((-1+x)/(1+x))^(1/2)","B"
291,1,110,37,0.050000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^2,x)","\frac{\left(-1+x \right) \left(\left(x^{2}-1\right)^{\frac{3}{2}}-x^{2} \sqrt{x^{2}-1}+2 \ln \left(x +\sqrt{x^{2}-1}\right) x^{2}-2 x \sqrt{x^{2}-1}+4 \ln \left(x +\sqrt{x^{2}-1}\right) x -\sqrt{x^{2}-1}+2 \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{2 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{\left(1+x \right) \left(-1+x \right)}\, \left(1+x \right)^{2}}"," ",0,"1/2*(-1+x)*((x^2-1)^(3/2)-x^2*(x^2-1)^(1/2)+2*ln(x+(x^2-1)^(1/2))*x^2-2*x*(x^2-1)^(1/2)+4*ln(x+(x^2-1)^(1/2))*x-(x^2-1)^(1/2)+2*ln(x+(x^2-1)^(1/2)))/((-1+x)/(1+x))^(1/2)/((1+x)*(-1+x))^(1/2)/(1+x)^2","B"
292,1,21,17,0.037000," ","int(1/((-1+x)/(1+x))^(1/2)/(1+x)^2,x)","\frac{-1+x}{\left(1+x \right) \sqrt{\frac{-1+x}{1+x}}}"," ",0,"1/(1+x)*(-1+x)/((-1+x)/(1+x))^(1/2)","A"
293,1,146,45,0.051000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^2,x)","-\frac{3 x \left(x^{2}-1\right)^{\frac{3}{2}}-3 x^{3} \sqrt{x^{2}-1}-3 \ln \left(x +\sqrt{x^{2}-1}\right) x^{3}-2 \left(x^{2}-1\right)^{\frac{3}{2}}+9 x^{2} \sqrt{x^{2}-1}+9 \ln \left(x +\sqrt{x^{2}-1}\right) x^{2}-9 x \sqrt{x^{2}-1}-9 \ln \left(x +\sqrt{x^{2}-1}\right) x +3 \sqrt{x^{2}-1}+3 \ln \left(x +\sqrt{x^{2}-1}\right)}{3 \left(-1+x \right)^{2} \sqrt{\left(1+x \right) \left(-1+x \right)}\, \sqrt{\frac{-1+x}{1+x}}}"," ",0,"-1/3*(3*x*(x^2-1)^(3/2)-3*x^3*(x^2-1)^(1/2)-3*ln(x+(x^2-1)^(1/2))*x^3-2*(x^2-1)^(3/2)+9*x^2*(x^2-1)^(1/2)+9*ln(x+(x^2-1)^(1/2))*x^2-9*x*(x^2-1)^(1/2)-9*ln(x+(x^2-1)^(1/2))*x+3*(x^2-1)^(1/2)+3*ln(x+(x^2-1)^(1/2)))/(-1+x)^2/((1+x)*(-1+x))^(1/2)/((-1+x)/(1+x))^(1/2)","B"
294,1,22,20,0.034000," ","int(1/((-1+x)/(1+x))^(1/2)/(1-x)^2,x)","-\frac{1+x}{3 \left(-1+x \right) \sqrt{\frac{-1+x}{1+x}}}"," ",0,"-1/3*(1+x)/(-1+x)/((-1+x)/(1+x))^(1/2)","A"
295,0,0,57,0.361000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a*c*x+c)^(1/2),x)","\int \frac{x^{m} \sqrt{-a c x +c}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a*c*x+c)^(1/2),x)","F"
296,1,49,116,0.038000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \left(15 a^{2} x^{2}-12 a x +8\right) \sqrt{-a c x +c}}{105 a^{3} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/105*(a*x+1)*(15*a^2*x^2-12*a*x+8)*(-a*c*x+c)^(1/2)/a^3/((a*x-1)/(a*x+1))^(1/2)","A"
297,1,41,76,0.036000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \left(3 a x -2\right) \sqrt{-a c x +c}}{15 a^{2} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/15*(a*x+1)*(3*a*x-2)*(-a*c*x+c)^(1/2)/a^2/((a*x-1)/(a*x+1))^(1/2)","A"
298,1,35,34,0.033000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2),x)","\frac{2 \left(a x +1\right) \sqrt{-a c x +c}}{3 \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"2/3/((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-a*c*x+c)^(1/2)/a","A"
299,1,70,76,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x,x)","-\frac{2 \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{c}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right)-\sqrt{-c \left(a x +1\right)}\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a x +1\right)}}"," ",0,"-2/((a*x-1)/(a*x+1))^(1/2)*(-c*(a*x-1))^(1/2)*(c^(1/2)*arctan((-c*(a*x+1))^(1/2)/c^(1/2))-(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)","A"
300,1,78,79,0.059000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a*c*x+c)^(1/2)/x^2,x)","-\frac{\left(\arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x a c +\sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right) \sqrt{-c \left(a x -1\right)}}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a x +1\right)}\, x \sqrt{c}}"," ",0,"-(arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+(-c*(a*x+1))^(1/2)*c^(1/2))*(-c*(a*x-1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)/(-c*(a*x+1))^(1/2)/x/c^(1/2)","A"
301,1,45,83,0.039000," ","int((a*x+1)/(a*x-1)*x^3*(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}\, \left(35 x^{4} a^{4}+85 x^{3} a^{3}+102 a^{2} x^{2}+136 a x +272\right)}{315 a^{4}}"," ",0,"2/315*(-a*c*x+c)^(1/2)*(35*a^4*x^4+85*a^3*x^3+102*a^2*x^2+136*a*x+272)/a^4","A"
302,1,37,66,0.037000," ","int((a*x+1)/(a*x-1)*x^2*(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}\, \left(15 x^{3} a^{3}+39 a^{2} x^{2}+52 a x +104\right)}{105 a^{3}}"," ",0,"2/105*(-a*c*x+c)^(1/2)*(15*a^3*x^3+39*a^2*x^2+52*a*x+104)/a^3","A"
303,1,28,49,0.033000," ","int((a*x+1)/(a*x-1)*x*(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}\, \left(a^{2} x^{2}+3 a x +6\right)}{5 a^{2}}"," ",0,"2/5*(-a*c*x+c)^(1/2)*(a^2*x^2+3*a*x+6)/a^2","A"
304,1,20,32,0.033000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2),x)","\frac{2 \sqrt{-a c x +c}\, \left(a x +5\right)}{3 a}"," ",0,"2/3*(-a*c*x+c)^(1/2)*(a*x+5)/a","A"
305,1,32,31,0.039000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2)/x,x)","2 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right) \sqrt{c}+2 \sqrt{-a c x +c}"," ",0,"2*arctanh((-a*c*x+c)^(1/2)/c^(1/2))*c^(1/2)+2*(-a*c*x+c)^(1/2)","A"
306,1,45,34,0.045000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2)/x^2,x)","-2 a c \left(-\frac{\sqrt{-a c x +c}}{2 x a c}-\frac{3 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}\right)"," ",0,"-2*a*c*(-1/2*(-a*c*x+c)^(1/2)/x/a/c-3/2/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
307,1,65,52,0.046000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2)/x^3,x)","2 a^{2} c^{2} \left(\frac{-\frac{7 \left(-a c x +c \right)^{\frac{3}{2}}}{8 c}+\frac{9 \sqrt{-a c x +c}}{8}}{x^{2} a^{2} c^{2}}+\frac{7 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{8 c^{\frac{3}{2}}}\right)"," ",0,"2*a^2*c^2*((-7/8/c*(-a*c*x+c)^(3/2)+9/8*(-a*c*x+c)^(1/2))/x^2/a^2/c^2+7/8/c^(3/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
308,1,80,69,0.047000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2)/x^4,x)","-2 c^{3} a^{3} \left(-\frac{\frac{11 \left(-a c x +c \right)^{\frac{5}{2}}}{16 c^{2}}-\frac{11 \left(-a c x +c \right)^{\frac{3}{2}}}{6 c}+\frac{21 \sqrt{-a c x +c}}{16}}{x^{3} a^{3} c^{3}}-\frac{11 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{16 c^{\frac{5}{2}}}\right)"," ",0,"-2*c^3*a^3*(-(11/16/c^2*(-a*c*x+c)^(5/2)-11/6/c*(-a*c*x+c)^(3/2)+21/16*(-a*c*x+c)^(1/2))/x^3/a^3/c^3-11/16/c^(5/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
309,1,93,86,0.046000," ","int((a*x+1)/(a*x-1)*(-a*c*x+c)^(1/2)/x^5,x)","2 c^{4} a^{4} \left(\frac{-\frac{75 \left(-a c x +c \right)^{\frac{7}{2}}}{128 c^{3}}+\frac{275 \left(-a c x +c \right)^{\frac{5}{2}}}{128 c^{2}}-\frac{365 \left(-a c x +c \right)^{\frac{3}{2}}}{128 c}+\frac{181 \sqrt{-a c x +c}}{128}}{x^{4} a^{4} c^{4}}+\frac{75 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{128 c^{\frac{7}{2}}}\right)"," ",0,"2*c^4*a^4*((-75/128/c^3*(-a*c*x+c)^(7/2)+275/128/c^2*(-a*c*x+c)^(5/2)-365/128/c*(-a*c*x+c)^(3/2)+181/128*(-a*c*x+c)^(1/2))/x^4/a^4/c^4+75/128/c^(7/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
310,1,161,251,0.059000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-35 x^{4} a^{4} \sqrt{-c \left(a x +1\right)}-95 x^{3} a^{3} \sqrt{-c \left(a x +1\right)}-138 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}+630 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-236 x a \sqrt{-c \left(a x +1\right)}-788 \sqrt{-c \left(a x +1\right)}\right)}{315 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}\, a^{4}}"," ",0,"-2/315/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(-35*x^4*a^4*(-c*(a*x+1))^(1/2)-95*x^3*a^3*(-c*(a*x+1))^(1/2)-138*x^2*a^2*(-c*(a*x+1))^(1/2)+630*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-236*x*a*(-c*(a*x+1))^(1/2)-788*(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)/a^4","A"
311,1,143,211,0.060000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-3 x^{3} a^{3} \sqrt{-c \left(a x +1\right)}-9 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}+42 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-16 x a \sqrt{-c \left(a x +1\right)}-52 \sqrt{-c \left(a x +1\right)}\right)}{21 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}\, a^{3}}"," ",0,"-2/21/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(-3*x^3*a^3*(-c*(a*x+1))^(1/2)-9*x^2*a^2*(-c*(a*x+1))^(1/2)+42*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-16*x*a*(-c*(a*x+1))^(1/2)-52*(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)/a^3","A"
312,1,125,171,0.057000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-3 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}+30 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-11 x a \sqrt{-c \left(a x +1\right)}-38 \sqrt{-c \left(a x +1\right)}\right)}{15 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}\, a^{2}}"," ",0,"-2/15/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(-3*x^2*a^2*(-c*(a*x+1))^(1/2)+30*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-11*x*a*(-c*(a*x+1))^(1/2)-38*(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)/a^2","A"
313,1,107,131,0.053000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2),x)","-\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(6 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)-x a \sqrt{-c \left(a x +1\right)}-7 \sqrt{-c \left(a x +1\right)}\right)}{3 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}\, a}"," ",0,"-2/3/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(6*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))-x*a*(-c*(a*x+1))^(1/2)-7*(-c*(a*x+1))^(1/2))/(-c*(a*x+1))^(1/2)/a","A"
314,1,107,134,0.061000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x,x)","\frac{2 \left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-2 \sqrt{c}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right)+\sqrt{c}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right)+\sqrt{-c \left(a x +1\right)}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x +1\right)}}"," ",0,"2*(a*x-1)*(-c*(a*x-1))^(1/2)*(-2*c^(1/2)*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))+c^(1/2)*arctan((-c*(a*x+1))^(1/2)/c^(1/2))+(-c*(a*x+1))^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/(-c*(a*x+1))^(1/2)","A"
315,1,117,136,0.066000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^2,x)","\frac{\left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-4 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x a c +5 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x a c +\sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x \sqrt{c}\, \sqrt{-c \left(a x +1\right)}}"," ",0,"1/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(-c*(a*x-1))^(1/2)*(-4*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x*a*c+5*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+(-c*(a*x+1))^(1/2)*c^(1/2))/x/c^(1/2)/(-c*(a*x+1))^(1/2)","A"
316,1,144,176,0.066000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^3,x)","\frac{\left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-16 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{2} a^{2} c +23 c \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x^{2} a^{2}+9 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+2 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{4 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{c}\, \sqrt{-c \left(a x +1\right)}\, x^{2}}"," ",0,"1/4*(a*x-1)*(-c*(a*x-1))^(1/2)*(-16*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^2*a^2*c+23*c*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x^2*a^2+9*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+2*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/c^(1/2)/(-c*(a*x+1))^(1/2)/x^2","A"
317,1,165,218,0.072000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^4,x)","\frac{\left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-96 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{3} a^{3} c +135 c \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x^{3} a^{3}+57 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+26 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+8 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{24 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{c}\, \sqrt{-c \left(a x +1\right)}\, x^{3}}"," ",0,"1/24*(a*x-1)*(-c*(a*x-1))^(1/2)*(-96*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^3*a^3*c+135*c*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x^3*a^3+57*x^2*a^2*(-c*(a*x+1))^(1/2)*c^(1/2)+26*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+8*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/c^(1/2)/(-c*(a*x+1))^(1/2)/x^3","A"
318,1,186,258,0.072000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a*c*x+c)^(1/2)/x^5,x)","\frac{\left(a x -1\right) \sqrt{-c \left(a x -1\right)}\, \left(-768 \sqrt{2}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}\, \sqrt{2}}{2 \sqrt{c}}\right) x^{4} a^{4} c +1089 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) c \,x^{4} a^{4}+447 x^{3} a^{3} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+214 x^{2} a^{2} \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+136 x a \sqrt{-c \left(a x +1\right)}\, \sqrt{c}+48 \sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{192 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{c}\, \sqrt{-c \left(a x +1\right)}\, x^{4}}"," ",0,"1/192*(a*x-1)*(-c*(a*x-1))^(1/2)*(-768*2^(1/2)*arctan(1/2*(-c*(a*x+1))^(1/2)*2^(1/2)/c^(1/2))*x^4*a^4*c+1089*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*c*x^4*a^4+447*x^3*a^3*(-c*(a*x+1))^(1/2)*c^(1/2)+214*x^2*a^2*(-c*(a*x+1))^(1/2)*c^(1/2)+136*x*a*(-c*(a*x+1))^(1/2)*c^(1/2)+48*(-c*(a*x+1))^(1/2)*c^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/c^(1/2)/(-c*(a*x+1))^(1/2)/x^4","A"
319,1,37,100,0.037000," ","int(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(3/2),x)","\frac{2 \left(-1+x \right) \left(3 x^{3}+12 x^{2}+23 x +46\right)}{21 \sqrt{1+x}\, \sqrt{\frac{-1+x}{1+x}}}"," ",0,"2/21*(-1+x)*(3*x^3+12*x^2+23*x+46)/(1+x)^(1/2)/((-1+x)/(1+x))^(1/2)","A"
320,1,32,74,0.037000," ","int(1/((-1+x)/(1+x))^(1/2)*(1+x)^(3/2),x)","\frac{2 \left(-1+x \right) \left(3 x^{2}+14 x +43\right)}{15 \sqrt{1+x}\, \sqrt{\frac{-1+x}{1+x}}}"," ",0,"2/15*(-1+x)*(3*x^2+14*x+43)/(1+x)^(1/2)/((-1+x)/(1+x))^(1/2)","A"
321,1,34,80,0.036000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2)*x,x)","-\frac{2 \left(1+x \right) \left(15 x^{2}-33 x +22\right) \sqrt{1-x}}{105 \sqrt{\frac{-1+x}{1+x}}}"," ",0,"-2/105*(1+x)*(15*x^2-33*x+22)*(1-x)^(1/2)/((-1+x)/(1+x))^(1/2)","A"
322,1,29,52,0.037000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)^(3/2),x)","-\frac{2 \left(1+x \right) \left(3 x -7\right) \sqrt{1-x}}{15 \sqrt{\frac{-1+x}{1+x}}}"," ",0,"-2/15*(1+x)*(3*x-7)*(1-x)^(1/2)/((-1+x)/(1+x))^(1/2)","A"
323,1,30,74,0.036000," ","int(1/((-1+x)/(1+x))^(1/2)*x*(1+x)^(1/2),x)","\frac{2 \left(-1+x \right) \left(x^{2}+3 x +6\right)}{5 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"2/5*(-1+x)*(x^2+3*x+6)/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2)","A"
324,1,25,48,0.036000," ","int(1/((-1+x)/(1+x))^(1/2)*(1+x)^(1/2),x)","\frac{2 \left(-1+x \right) \left(x +5\right)}{3 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"2/3*(-1+x)*(x+5)/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2)","A"
325,1,29,55,0.033000," ","int(1/((-1+x)/(1+x))^(1/2)*x*(1-x)^(1/2),x)","\frac{2 \left(1+x \right) \left(3 x -2\right) \sqrt{1-x}}{15 \sqrt{\frac{-1+x}{1+x}}}"," ",0,"2/15*(1+x)*(3*x-2)*(1-x)^(1/2)/((-1+x)/(1+x))^(1/2)","A"
326,1,24,23,0.034000," ","int(1/((-1+x)/(1+x))^(1/2)*(1-x)^(1/2),x)","\frac{2 \left(1+x \right) \sqrt{1-x}}{3 \sqrt{\frac{-1+x}{1+x}}}"," ",0,"2/3/((-1+x)/(1+x))^(1/2)*(1+x)*(1-x)^(1/2)","A"
327,1,25,51,0.035000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(1/2),x)","\frac{2 \left(-1+x \right) \left(x +2\right)}{3 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"2/3*(-1+x)*(x+2)/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2)","A"
328,1,22,24,0.034000," ","int(1/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2),x)","\frac{-2+2 x}{\sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"2*(-1+x)/((-1+x)/(1+x))^(1/2)/(1+x)^(1/2)","A"
329,1,65,98,0.047000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(1/2),x)","-\frac{2 \sqrt{1-x}\, \left(\sqrt{-1-x}\, x -3 \sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right)+4 \sqrt{-1-x}\right)}{3 \sqrt{\frac{-1+x}{1+x}}\, \sqrt{-1-x}}"," ",0,"-2/3*(1-x)^(1/2)*((-1-x)^(1/2)*x-3*2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))+4*(-1-x)^(1/2))/((-1+x)/(1+x))^(1/2)/(-1-x)^(1/2)","A"
330,1,54,70,0.045000," ","int(1/((-1+x)/(1+x))^(1/2)/(1-x)^(1/2),x)","-\frac{2 \sqrt{1-x}\, \left(-\sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right)+\sqrt{-1-x}\right)}{\sqrt{\frac{-1+x}{1+x}}\, \sqrt{-1-x}}"," ",0,"-2*(1-x)^(1/2)*(-2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))+(-1-x)^(1/2))/((-1+x)/(1+x))^(1/2)/(-1-x)^(1/2)","A"
331,1,47,67,0.047000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1+x)^(3/2),x)","\frac{\sqrt{-1+x}\, \left(2 \sqrt{-1+x}-\sqrt{2}\, \arctan \left(\frac{\sqrt{-1+x}\, \sqrt{2}}{2}\right)\right)}{\sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"1/((-1+x)/(1+x))^(1/2)*(-1+x)^(1/2)/(1+x)^(1/2)*(2*(-1+x)^(1/2)-2^(1/2)*arctan(1/2*(-1+x)^(1/2)*2^(1/2)))","A"
332,1,37,41,0.046000," ","int(1/((-1+x)/(1+x))^(1/2)/(1+x)^(3/2),x)","\frac{\sqrt{-1+x}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-1+x}\, \sqrt{2}}{2}\right)}{\sqrt{\frac{-1+x}{1+x}}\, \sqrt{1+x}}"," ",0,"1/((-1+x)/(1+x))^(1/2)*(-1+x)^(1/2)/(1+x)^(1/2)*2^(1/2)*arctan(1/2*(-1+x)^(1/2)*2^(1/2))","A"
333,1,90,100,0.056000," ","int(1/((-1+x)/(1+x))^(1/2)*x/(1-x)^(3/2),x)","-\frac{\sqrt{1-x}\, \left(5 \sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right) x -5 \sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right)-4 \sqrt{-1-x}\, x +6 \sqrt{-1-x}\right)}{2 \sqrt{\frac{-1+x}{1+x}}\, \left(-1+x \right) \sqrt{-1-x}}"," ",0,"-1/2/((-1+x)/(1+x))^(1/2)/(-1+x)*(1-x)^(1/2)*(5*2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))*x-5*2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))-4*(-1-x)^(1/2)*x+6*(-1-x)^(1/2))/(-1-x)^(1/2)","A"
334,1,79,70,0.053000," ","int(1/((-1+x)/(1+x))^(1/2)/(1-x)^(3/2),x)","-\frac{\sqrt{1-x}\, \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right) x -\sqrt{2}\, \arctan \left(\frac{\sqrt{-1-x}\, \sqrt{2}}{2}\right)+2 \sqrt{-1-x}\right)}{2 \sqrt{\frac{-1+x}{1+x}}\, \left(-1+x \right) \sqrt{-1-x}}"," ",0,"-1/2/((-1+x)/(1+x))^(1/2)/(-1+x)*(1-x)^(1/2)*(2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))*x-2^(1/2)*arctan(1/2*(-1-x)^(1/2)*2^(1/2))+2*(-1-x)^(1/2))/(-1-x)^(1/2)","A"
335,0,0,115,0.358000," ","int(x^m*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\int x^{m} \sqrt{-a c x +c}\, \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int(x^m*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","F"
336,1,64,118,0.038000," ","int(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(15 x^{3} a^{3}-39 a^{2} x^{2}+52 a x -104\right) \sqrt{-a c x +c}\, \sqrt{\frac{a x -1}{a x +1}}}{105 a^{3} \left(a x -1\right)}"," ",0,"2/105*(a*x+1)*(15*a^3*x^3-39*a^2*x^2+52*a*x-104)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/a^3/(a*x-1)","A"
337,1,55,86,0.036000," ","int(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(a^{2} x^{2}-3 a x +6\right) \sqrt{-a c x +c}\, \sqrt{\frac{a x -1}{a x +1}}}{5 a^{2} \left(a x -1\right)}"," ",0,"2/5*(a*x+1)*(a^2*x^2-3*a*x+6)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/a^2/(a*x-1)","A"
338,1,47,50,0.033000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{2 \left(a x +1\right) \left(a x -5\right) \sqrt{-a c x +c}\, \sqrt{\frac{a x -1}{a x +1}}}{3 \left(a x -1\right) a}"," ",0,"2/3*(a*x+1)*(a*x-5)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)/a","A"
339,1,80,76,0.055000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x)","\frac{2 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{c}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right)+\sqrt{-c \left(a x +1\right)}\right)}{\left(a x -1\right) \sqrt{-c \left(a x +1\right)}}"," ",0,"2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-c*(a*x-1))^(1/2)*(c^(1/2)*arctan((-c*(a*x+1))^(1/2)/c^(1/2))+(-c*(a*x+1))^(1/2))/(a*x-1)/(-c*(a*x+1))^(1/2)","A"
340,1,92,78,0.063000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(3 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x a c -\sqrt{-c \left(a x +1\right)}\, \sqrt{c}\right)}{\left(a x -1\right) \sqrt{-c \left(a x +1\right)}\, x \sqrt{c}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-c*(a*x-1))^(1/2)*(3*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x*a*c-(-c*(a*x+1))^(1/2)*c^(1/2))/(a*x-1)/(-c*(a*x+1))^(1/2)/x/c^(1/2)","A"
341,1,101,112,0.043000," ","int(x^3*(-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{9}{2}}}{9}-\frac{2 \left(-a c x +c \right)^{\frac{7}{2}} c}{7}+\frac{2 \left(-a c x +c \right)^{\frac{5}{2}} c^{2}}{5}+\frac{2 c^{3} \left(-a c x +c \right)^{\frac{3}{2}}}{3}+4 \sqrt{-a c x +c}\, c^{4}-4 c^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{4} a^{4}}"," ",0,"2/c^4/a^4*(1/9*(-a*c*x+c)^(9/2)-1/7*(-a*c*x+c)^(7/2)*c+1/5*(-a*c*x+c)^(5/2)*c^2+1/3*c^3*(-a*c*x+c)^(3/2)+2*(-a*c*x+c)^(1/2)*c^4-2*c^(9/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
342,1,75,78,0.040000," ","int(x^2*(-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{7}{2}}}{7}+\frac{\left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{3}+2 \sqrt{-a c x +c}\, c^{3}-2 c^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c^{3} a^{3}}"," ",0,"-2/c^3/a^3*(1/7*(-a*c*x+c)^(7/2)+1/3*(-a*c*x+c)^(3/2)*c^2+2*(-a*c*x+c)^(1/2)*c^3-2*c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
343,1,73,78,0.042000," ","int(x*(-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\frac{2 \left(-a c x +c \right)^{\frac{5}{2}}}{5}+\frac{2 c \left(-a c x +c \right)^{\frac{3}{2}}}{3}+4 \sqrt{-a c x +c}\, c^{2}-4 c^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{a^{2} c^{2}}"," ",0,"2/c^2/a^2*(1/5*(-a*c*x+c)^(5/2)+1/3*c*(-a*c*x+c)^(3/2)+2*(-a*c*x+c)^(1/2)*c^2-2*c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
344,1,59,61,0.038000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{2 \left(\frac{\left(-a c x +c \right)^{\frac{3}{2}}}{3}+2 c \sqrt{-a c x +c}-2 c^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)\right)}{c a}"," ",0,"-2/c/a*(1/3*(-a*c*x+c)^(3/2)+2*c*(-a*c*x+c)^(1/2)-2*c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2)))","A"
345,1,58,57,0.046000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1)/x,x)","2 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right) \sqrt{c}-4 \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right) \sqrt{2}\, \sqrt{c}+2 \sqrt{-a c x +c}"," ",0,"2*arctanh((-a*c*x+c)^(1/2)/c^(1/2))*c^(1/2)-4*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))*2^(1/2)*c^(1/2)+2*(-a*c*x+c)^(1/2)","A"
346,1,71,61,0.047000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1)/x^2,x)","-2 a c \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{\sqrt{c}}-\frac{\sqrt{-a c x +c}}{2 x a c}+\frac{5 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}\right)"," ",0,"-2*a*c*(-2*2^(1/2)/c^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/2*(-a*c*x+c)^(1/2)/x/a/c+5/2/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2)))","A"
347,1,95,81,0.050000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1)/x^3,x)","2 a^{2} c^{2} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{3}{2}}}-\frac{\frac{-\frac{9 \left(-a c x +c \right)^{\frac{3}{2}}}{8}+\frac{7 c \sqrt{-a c x +c}}{8}}{x^{2} a^{2} c^{2}}-\frac{23 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{8 \sqrt{c}}}{c}\right)"," ",0,"2*a^2*c^2*(-2/c^(3/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c*((-9/8*(-a*c*x+c)^(3/2)+7/8*c*(-a*c*x+c)^(1/2))/x^2/a^2/c^2-23/8/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
348,1,110,98,0.047000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1)/x^4,x)","-2 c^{3} a^{3} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{5}{2}}}-\frac{-\frac{-\frac{19 \left(-a c x +c \right)^{\frac{5}{2}}}{16}+\frac{11 c \left(-a c x +c \right)^{\frac{3}{2}}}{6}-\frac{13 \sqrt{-a c x +c}\, c^{2}}{16}}{x^{3} a^{3} c^{3}}-\frac{45 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{16 \sqrt{c}}}{c^{2}}\right)"," ",0,"-2*c^3*a^3*(-2/c^(5/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c^2*(-(-19/16*(-a*c*x+c)^(5/2)+11/6*c*(-a*c*x+c)^(3/2)-13/16*(-a*c*x+c)^(1/2)*c^2)/x^3/a^3/c^3-45/16/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
349,1,123,115,0.049000," ","int((-a*c*x+c)^(1/2)/(a*x+1)*(a*x-1)/x^5,x)","2 c^{4} a^{4} \left(-\frac{2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a c x +c}\, \sqrt{2}}{2 \sqrt{c}}\right)}{c^{\frac{7}{2}}}-\frac{\frac{-\frac{149 \left(-a c x +c \right)^{\frac{7}{2}}}{128}+\frac{1127 c \left(-a c x +c \right)^{\frac{5}{2}}}{384}-\frac{1049 \left(-a c x +c \right)^{\frac{3}{2}} c^{2}}{384}+\frac{107 \sqrt{-a c x +c}\, c^{3}}{128}}{x^{4} a^{4} c^{4}}-\frac{363 \arctanh \left(\frac{\sqrt{-a c x +c}}{\sqrt{c}}\right)}{128 \sqrt{c}}}{c^{3}}\right)"," ",0,"2*c^4*a^4*(-2/c^(7/2)*2^(1/2)*arctanh(1/2*(-a*c*x+c)^(1/2)*2^(1/2)/c^(1/2))-1/c^3*((-149/128*(-a*c*x+c)^(7/2)+1127/384*c*(-a*c*x+c)^(5/2)-1049/384*(-a*c*x+c)^(3/2)*c^2+107/128*(-a*c*x+c)^(1/2)*c^3)/x^4/a^4/c^4-363/128/c^(1/2)*arctanh((-a*c*x+c)^(1/2)/c^(1/2))))","A"
350,1,80,233,0.039000," ","int(x^3*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(5 x^{5} a^{5}-20 x^{4} a^{4}+41 x^{3} a^{3}-82 a^{2} x^{2}+328 a x +656\right) \sqrt{-a c x +c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{45 a^{4} \left(a x -1\right)^{2}}"," ",0,"2/45*(a*x+1)*(5*a^5*x^5-20*a^4*x^4+41*a^3*x^3-82*a^2*x^2+328*a*x+656)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/a^4/(a*x-1)^2","A"
351,1,72,191,0.037000," ","int(x^2*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(15 x^{4} a^{4}-66 x^{3} a^{3}+167 a^{2} x^{2}-668 a x -1336\right) \sqrt{-a c x +c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{105 a^{3} \left(a x -1\right)^{2}}"," ",0,"2/105*(a*x+1)*(15*a^4*x^4-66*a^3*x^3+167*a^2*x^2-668*a*x-1336)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/a^3/(a*x-1)^2","A"
352,1,64,150,0.036000," ","int(x*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(3 x^{3} a^{3}-16 a^{2} x^{2}+79 a x +158\right) \sqrt{-a c x +c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{15 a^{2} \left(a x -1\right)^{2}}"," ",0,"2/15*(a*x+1)*(3*a^3*x^3-16*a^2*x^2+79*a*x+158)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/a^2/(a*x-1)^2","A"
353,1,55,113,0.037000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{2 \left(a x +1\right) \left(a^{2} x^{2}-10 a x -23\right) \sqrt{-a c x +c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{3 a \left(a x -1\right)^{2}}"," ",0,"2/3*(a*x+1)*(a^2*x^2-10*a*x-23)*(-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^2","A"
354,1,80,116,0.060000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x)","\frac{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(\sqrt{c}\, \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) \sqrt{-c \left(a x +1\right)}+a c x +5 c \right)}{\left(a x -1\right)^{2} c}"," ",0,"2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(-c*(a*x-1))^(1/2)*(c^(1/2)*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*(-c*(a*x+1))^(1/2)+a*c*x+5*c)/c","A"
355,1,86,116,0.067000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \left(7 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x a \sqrt{-c \left(a x +1\right)}+9 x a \sqrt{c}+\sqrt{c}\right) \sqrt{-c \left(a x -1\right)}}{\left(a x -1\right)^{2} \sqrt{c}\, x}"," ",0,"-((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*(7*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x*a*(-c*(a*x+1))^(1/2)+9*x*a*c^(1/2)+c^(1/2))*(-c*(a*x-1))^(1/2)/(a*x-1)^2/c^(1/2)/x","A"
356,1,103,154,0.068000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(47 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x^{2} a^{2} \sqrt{-c \left(a x +1\right)}+47 x^{2} a^{2} \sqrt{c}+13 x a \sqrt{c}-2 \sqrt{c}\right)}{4 \left(a x -1\right)^{2} \sqrt{c}\, x^{2}}"," ",0,"1/4*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(-c*(a*x-1))^(1/2)*(47*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x^2*a^2*(-c*(a*x+1))^(1/2)+47*x^2*a^2*c^(1/2)+13*x*a*c^(1/2)-2*c^(1/2))/c^(1/2)/x^2","A"
357,1,114,194,0.067000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(357 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x^{3} a^{3} \sqrt{-c \left(a x +1\right)}+357 x^{3} a^{3} \sqrt{c}+119 x^{2} a^{2} \sqrt{c}-38 x a \sqrt{c}+8 \sqrt{c}\right)}{24 \left(a x -1\right)^{2} \sqrt{c}\, x^{3}}"," ",0,"-1/24*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(-c*(a*x-1))^(1/2)*(357*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x^3*a^3*(-c*(a*x+1))^(1/2)+357*x^3*a^3*c^(1/2)+119*x^2*a^2*c^(1/2)-38*x*a*c^(1/2)+8*c^(1/2))/c^(1/2)/x^3","A"
358,1,125,234,0.069000," ","int((-a*c*x+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{-c \left(a x -1\right)}\, \left(3345 \arctan \left(\frac{\sqrt{-c \left(a x +1\right)}}{\sqrt{c}}\right) x^{4} a^{4} \sqrt{-c \left(a x +1\right)}+3345 x^{4} a^{4} \sqrt{c}+1115 x^{3} a^{3} \sqrt{c}-446 x^{2} a^{2} \sqrt{c}+200 x a \sqrt{c}-48 \sqrt{c}\right)}{192 \left(a x -1\right)^{2} \sqrt{c}\, x^{4}}"," ",0,"1/192*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(-c*(a*x-1))^(1/2)*(3345*arctan((-c*(a*x+1))^(1/2)/c^(1/2))*x^4*a^4*(-c*(a*x+1))^(1/2)+3345*x^4*a^4*c^(1/2)+1115*x^3*a^3*c^(1/2)-446*x^2*a^2*c^(1/2)+200*x*a*c^(1/2)-48*c^(1/2))/c^(1/2)/x^4","A"
359,1,104,254,0.043000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(2+1/2*n),x)","\frac{2 \left(a x +1\right) \left(a^{2} n^{2} x^{2}+6 a^{2} n \,x^{2}+8 a^{2} x^{2}-2 a \,n^{2} x -20 a n x -32 a x +n^{2}+14 n +56\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{2+\frac{n}{2}}}{\left(a x -1\right)^{2} a \left(n^{3}+12 n^{2}+44 n +48\right)}"," ",0,"2*(a*x+1)*(a^2*n^2*x^2+6*a^2*n*x^2+8*a^2*x^2-2*a*n^2*x-20*a*n*x-32*a*x+n^2+14*n+56)*exp(n*arccoth(a*x))*(-a*c*x+c)^(2+1/2*n)/(a*x-1)^2/a/(n^3+12*n^2+44*n+48)","A"
360,1,61,115,0.036000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(1+1/2*n),x)","\frac{2 \left(-a c x +c \right)^{1+\frac{n}{2}} {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(a n x +2 a x -n -6\right) \left(a x +1\right)}{\left(a x -1\right) a \left(n^{2}+6 n +8\right)}"," ",0,"2*(-a*c*x+c)^(1+1/2*n)*exp(n*arccoth(a*x))*(a*n*x+2*a*x-n-6)*(a*x+1)/(a*x-1)/a/(n^2+6*n+8)","A"
361,1,34,33,0.036000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2*n),x)","\frac{2 \,{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(a x +1\right) \left(-a c x +c \right)^{\frac{n}{2}}}{a \left(2+n \right)}"," ",0,"2*exp(n*arccoth(a*x))*(a*x+1)*(-a*c*x+c)^(1/2*n)/a/(2+n)","A"
362,0,0,72,0.368000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(-1+1/2*n),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{-1+\frac{n}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^(-1+1/2*n),x)","F"
363,0,0,80,0.367000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(-2+1/2*n),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{-2+\frac{n}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^(-2+1/2*n),x)","F"
364,0,0,100,0.367000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^p,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{p}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^p,x)","F"
365,0,0,75,0.357000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^3,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{3}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^3,x)","F"
366,0,0,75,0.356000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^2,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{2}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^2,x)","F"
367,0,0,73,0.058000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c),x)","F"
368,0,0,67,0.359000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{-a c x +c}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a*c*x+c),x)","F"
369,1,33,44,0.038000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^2,x)","-\frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(a x +1\right)}{\left(a x -1\right) c^{2} \left(2+n \right) a}"," ",0,"-exp(n*arccoth(a*x))*(a*x+1)/(a*x-1)/c^2/(2+n)/a","A"
370,1,46,96,0.038000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^3,x)","-\frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(a x -n -3\right) \left(a x +1\right)}{\left(a x -1\right)^{2} c^{3} \left(n^{2}+6 n +8\right) a}"," ",0,"-exp(n*arccoth(a*x))*(a*x-n-3)*(a*x+1)/(a*x-1)^2/c^3/(n^2+6*n+8)/a","A"
371,1,68,208,0.039000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^4,x)","-\frac{\left(a x +1\right) \left(2 a^{2} x^{2}-2 a n x -8 a x +n^{2}+8 n +14\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(a x -1\right)^{3} c^{4} a \left(n^{2}+8 n +12\right) \left(4+n \right)}"," ",0,"-(a*x+1)*(2*a^2*x^2-2*a*n*x-8*a*x+n^2+8*n+14)*exp(n*arccoth(a*x))/(a*x-1)^3/c^4/a/(n^2+8*n+12)/(4+n)","A"
372,0,0,86,0.369000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(5/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{\frac{5}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^(5/2),x)","F"
373,0,0,86,0.385000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(3/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a c x +c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^(3/2),x)","F"
374,0,0,86,0.388000," ","int(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \sqrt{-a c x +c}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a*c*x+c)^(1/2),x)","F"
375,0,0,86,0.358000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\sqrt{-a c x +c}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a*c*x+c)^(1/2),x)","F"
376,0,0,86,0.354000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(-a c x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a*c*x+c)^(3/2),x)","F"
377,0,0,145,0.347000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(-a c x +c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a*c*x+c)^(5/2),x)","F"
378,0,0,211,0.350000," ","int(exp(n*arccoth(a*x))/(-a*c*x+c)^(7/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(-a c x +c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a*c*x+c)^(7/2),x)","F"
379,1,224,100,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^4,x)","-\frac{\left(a x -1\right) c^{4} \left(-18 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+18 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+18 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-9 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"-1/6*(a*x-1)*c^4*(-18*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+18*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+18*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-9*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","B"
380,1,200,78,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^3,x)","-\frac{\left(a x -1\right) c^{3} \left(-4 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+4 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+4 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{3} x^{2} \sqrt{a^{2}}}"," ",0,"-1/2*(a*x-1)*c^3*(-4*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+4*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+4*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^3/x^2/(a^2)^(1/2)","B"
381,1,168,58,0.047000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^2,x)","-\frac{\left(a x -1\right) c^{2} \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"-(a*x-1)*c^2*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","B"
382,1,63,25,0.044000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x),x)","\frac{\left(a x -1\right) c \left(\sqrt{a^{2} x^{2}-1}+\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a}"," ",0,"1/((a*x-1)/(a*x+1))^(1/2)*(a*x-1)/((a*x-1)*(a*x+1))^(1/2)*c/a*((a^2*x^2-1)^(1/2)+arctan(1/(a^2*x^2-1)^(1/2)))","B"
383,1,250,64,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x)","\frac{2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{a \sqrt{a^{2}}\, \left(a x -1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a^2)^(1/2)/(a*x-1)/c/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
384,1,339,93,0.057000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x)","\frac{9 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+9 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-6 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+5 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -9 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-9 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{3 a \left(a x -1\right)^{2} \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/3*(9*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+9*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+5*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-9*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-9*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a*x-1)^2/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
385,1,431,122,0.057000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x)","\frac{60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+60 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-45 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-240 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+76 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +360 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-34 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-240 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +60 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+60 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{15 a \left(a x -1\right)^{3} \sqrt{a^{2}}\, c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/15*(60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+60*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-240*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+76*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+360*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-34*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-240*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+60*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+60*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a*x-1)^3/(a^2)^(1/2)/c^3/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
386,1,523,151,0.062000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x)","-\frac{-525 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-525 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+420 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+2625 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+2625 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-1076 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-5250 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-5250 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+970 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +5250 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+5250 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-299 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-2625 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -2625 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+525 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{105 a \left(a x -1\right)^{4} \sqrt{a^{2}}\, c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-1/105*(-525*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-525*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+420*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+2625*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+2625*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-1076*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-5250*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-5250*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+970*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+5250*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+5250*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-299*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-2625*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-2625*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+525*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a*x-1)^4/(a^2)^(1/2)/c^4/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
387,1,60,59,0.039000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^5,x)","-\frac{c^{5}}{4 a^{5} x^{4}}+\frac{c^{5}}{a^{4} x^{3}}-\frac{c^{5}}{x^{2} a^{3}}-\frac{2 c^{5}}{a^{2} x}+c^{5} x -\frac{3 c^{5} \ln \left(x \right)}{a}"," ",0,"-1/4*c^5/a^5/x^4+c^5/a^4/x^3-c^5/x^2/a^3-2*c^5/a^2/x+c^5*x-3*c^5*ln(x)/a","A"
388,1,39,38,0.040000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^4,x)","\frac{c^{4}}{3 a^{4} x^{3}}-\frac{c^{4}}{x^{2} a^{3}}+c^{4} x -\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"1/3*c^4/a^4/x^3-c^4/x^2/a^3+c^4*x-2*c^4*ln(x)/a","A"
389,1,38,37,0.039000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^3,x)","-\frac{c^{3}}{2 x^{2} a^{3}}+\frac{c^{3}}{a^{2} x}+c^{3} x -\frac{c^{3} \ln \left(x \right)}{a}"," ",0,"-1/2*c^3/x^2/a^3+c^3/a^2/x+c^3*x-c^3*ln(x)/a","A"
390,1,17,16,0.037000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^2,x)","\frac{c^{2} \left(a^{2} x +\frac{1}{x}\right)}{a^{2}}"," ",0,"c^2/a^2*(a^2*x+1/x)","A"
391,1,12,11,0.034000," ","int((a*x+1)/(a*x-1)*(c-c/a/x),x)","c x +\frac{c \ln \left(x \right)}{a}"," ",0,"c*x+c*ln(x)/a","A"
392,1,36,37,0.041000," ","int((a*x+1)/(a*x-1)/(c-c/a/x),x)","\frac{x}{c}+\frac{3 \ln \left(a x -1\right)}{c a}-\frac{2}{c a \left(a x -1\right)}"," ",0,"x/c+3/c/a*ln(a*x-1)-2/c/a/(a*x-1)","A"
393,1,51,53,0.040000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^2,x)","\frac{x}{c^{2}}+\frac{4 \ln \left(a x -1\right)}{a \,c^{2}}-\frac{5}{a \,c^{2} \left(a x -1\right)}-\frac{1}{a \,c^{2} \left(a x -1\right)^{2}}"," ",0,"x/c^2+4/a/c^2*ln(a*x-1)-5/a/c^2/(a*x-1)-1/a/c^2/(a*x-1)^2","A"
394,1,66,69,0.043000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^3,x)","\frac{x}{c^{3}}+\frac{5 \ln \left(a x -1\right)}{a \,c^{3}}-\frac{9}{a \,c^{3} \left(a x -1\right)}-\frac{2}{3 a \,c^{3} \left(a x -1\right)^{3}}-\frac{7}{2 a \,c^{3} \left(a x -1\right)^{2}}"," ",0,"x/c^3+5/a/c^3*ln(a*x-1)-9/a/c^3/(a*x-1)-2/3/a/c^3/(a*x-1)^3-7/2/a/c^3/(a*x-1)^2","A"
395,1,81,85,0.041000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^4,x)","\frac{x}{c^{4}}+\frac{6 \ln \left(a x -1\right)}{a \,c^{4}}-\frac{14}{a \,c^{4} \left(a x -1\right)}-\frac{1}{2 a \,c^{4} \left(a x -1\right)^{4}}-\frac{3}{a \,c^{4} \left(a x -1\right)^{3}}-\frac{8}{a \,c^{4} \left(a x -1\right)^{2}}"," ",0,"x/c^4+6/a/c^4*ln(a*x-1)-14/a/c^4/(a*x-1)-1/2/a/c^4/(a*x-1)^4-3/a/c^4/(a*x-1)^3-8/a/c^4/(a*x-1)^2","A"
396,1,233,91,0.053000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^4,x)","-\frac{\left(a x -1\right)^{2} c^{4} \left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-9 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+3 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"-1/6*(a*x-1)^2*c^4*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-9*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+3*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","B"
397,1,105,53,0.048000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^3,x)","-\frac{\left(a x -1\right)^{2} c^{3} \left(-3 a^{2} x^{2} \sqrt{a^{2} x^{2}-1}-3 a^{2} x^{2} \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}}\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{3} x^{2}}"," ",0,"-1/2*(a*x-1)^2*c^3*(-3*a^2*x^2*(a^2*x^2-1)^(1/2)-3*a^2*x^2*arctan(1/(a^2*x^2-1)^(1/2))+(a^2*x^2-1)^(3/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^3/x^2","A"
398,1,174,59,0.050000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^2,x)","\frac{\left(a x -1\right)^{2} c^{2} \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"(a*x-1)^2*c^2*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","B"
399,1,145,45,0.051000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x),x)","-\frac{\left(a x -1\right)^{2} c \left(\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}+\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}-2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"-(a*x-1)^2*c*((a^2*x^2-1)^(1/2)*(a^2)^(1/2)+arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)-2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
400,1,346,93,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x)","\frac{12 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+12 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-36 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-9 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -36 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+36 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+7 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+36 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -12 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-12 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{3 a \left(a x -1\right) \sqrt{a^{2}}\, c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/3*(12*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+12*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-36*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-9*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-36*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+36*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+7*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+36*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-12*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-12*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a*x-1)/(a^2)^(1/2)/c/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
401,1,438,122,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x)","\frac{75 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+75 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-300 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-60 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-300 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+450 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+97 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +450 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-300 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-43 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +75 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+75 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{15 a \left(a x -1\right)^{2} \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/15*(75*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+75*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-300*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-60*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-300*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+450*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+97*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+450*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-300*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-43*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+75*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+75*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a*x-1)^2/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
402,1,530,145,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x)","-\frac{-42 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-42 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+35 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+210 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+210 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-87 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-420 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-420 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+78 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +420 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+420 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-24 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-210 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -210 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+42 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+42 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{7 a \left(a x -1\right)^{3} \sqrt{a^{2}}\, c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/7*(-42*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-42*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+35*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+210*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+210*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-87*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-420*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-420*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+78*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+420*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+420*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-24*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-210*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-210*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+42*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+42*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a*x-1)^3/(a^2)^(1/2)/c^3/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
403,1,622,180,0.068000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x)","-\frac{-2205 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}-2205 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+1890 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+13230 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+13230 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-6376 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-33075 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-33075 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+8646 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+44100 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+44100 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-5349 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-33075 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+1259 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+13230 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +13230 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-2205 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-2205 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{315 a \left(a x -1\right)^{4} \sqrt{a^{2}}\, c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/315*(-2205*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6-2205*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+1890*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+13230*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+13230*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-6376*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-33075*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-33075*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+8646*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+44100*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+44100*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-5349*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-33075*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+1259*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+13230*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+13230*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-2205*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-2205*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a*x-1)^4/(a^2)^(1/2)/c^4/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
404,1,61,60,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^5,x)","\frac{c^{5}}{4 a^{5} x^{4}}-\frac{c^{5}}{3 a^{4} x^{3}}-\frac{c^{5}}{x^{2} a^{3}}+\frac{2 c^{5}}{a^{2} x}+c^{5} x -\frac{c^{5} \ln \left(x \right)}{a}"," ",0,"1/4*c^5/a^5/x^4-1/3*c^5/a^4/x^3-c^5/x^2/a^3+2*c^5/a^2/x+c^5*x-c^5*ln(x)/a","A"
405,1,27,28,0.038000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^4,x)","\frac{c^{4} \left(x \,a^{4}+\frac{2 a^{2}}{x}-\frac{1}{3 x^{3}}\right)}{a^{4}}"," ",0,"c^4/a^4*(x*a^4+2*a^2/x-1/3/x^3)","A"
406,1,37,36,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^3,x)","\frac{c^{3}}{2 x^{2} a^{3}}+\frac{c^{3}}{a^{2} x}+c^{3} x +\frac{c^{3} \ln \left(x \right)}{a}"," ",0,"1/2*c^3/x^2/a^3+c^3/a^2/x+c^3*x+c^3*ln(x)/a","A"
407,1,28,27,0.040000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x)^2,x)","-\frac{c^{2}}{a^{2} x}+c^{2} x +\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"-c^2/a^2/x+c^2*x+2*c^2*ln(x)/a","A"
408,1,25,25,0.039000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a/x),x)","c x +\frac{4 c \ln \left(a x -1\right)}{a}-\frac{c \ln \left(x \right)}{a}"," ",0,"c*x+4*c/a*ln(a*x-1)-c*ln(x)/a","A"
409,1,51,53,0.039000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x),x)","\frac{x}{c}+\frac{5 \ln \left(a x -1\right)}{c a}-\frac{8}{c a \left(a x -1\right)}-\frac{2}{c a \left(a x -1\right)^{2}}"," ",0,"x/c+5/c/a*ln(a*x-1)-8/c/a/(a*x-1)-2/c/a/(a*x-1)^2","A"
410,1,66,69,0.042000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^2,x)","\frac{x}{c^{2}}+\frac{6 \ln \left(a x -1\right)}{a \,c^{2}}-\frac{13}{a \,c^{2} \left(a x -1\right)}-\frac{4}{3 a \,c^{2} \left(a x -1\right)^{3}}-\frac{6}{a \,c^{2} \left(a x -1\right)^{2}}"," ",0,"x/c^2+6/a/c^2*ln(a*x-1)-13/a/c^2/(a*x-1)-4/3/a/c^2/(a*x-1)^3-6/a/c^2/(a*x-1)^2","A"
411,1,81,85,0.040000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^3,x)","\frac{x}{c^{3}}+\frac{7 \ln \left(a x -1\right)}{a \,c^{3}}-\frac{19}{a \,c^{3} \left(a x -1\right)}-\frac{1}{a \,c^{3} \left(a x -1\right)^{4}}-\frac{16}{3 a \,c^{3} \left(a x -1\right)^{3}}-\frac{25}{2 a \,c^{3} \left(a x -1\right)^{2}}"," ",0,"x/c^3+7/a/c^3*ln(a*x-1)-19/a/c^3/(a*x-1)-1/a/c^3/(a*x-1)^4-16/3/a/c^3/(a*x-1)^3-25/2/a/c^3/(a*x-1)^2","A"
412,1,96,101,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a/x)^4,x)","\frac{x}{c^{4}}+\frac{8 \ln \left(a x -1\right)}{a \,c^{4}}-\frac{26}{a \,c^{4} \left(a x -1\right)}-\frac{5}{a \,c^{4} \left(a x -1\right)^{4}}-\frac{4}{5 a \,c^{4} \left(a x -1\right)^{5}}-\frac{41}{3 a \,c^{4} \left(a x -1\right)^{3}}-\frac{22}{a \,c^{4} \left(a x -1\right)^{2}}"," ",0,"x/c^4+8/a/c^4*ln(a*x-1)-26/a/c^4/(a*x-1)-5/a/c^4/(a*x-1)^4-4/5/a/c^4/(a*x-1)^5-41/3/a/c^4/(a*x-1)^3-22/a/c^4/(a*x-1)^2","A"
413,1,290,117,0.055000," ","int((c-c/a/x)^4*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{4} \left(-66 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+96 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+66 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-75 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-75 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+66 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-96 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-15 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^4*(-66*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+96*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+66*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-75*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-75*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+66*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-96*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-15*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","B"
414,1,266,94,0.056000," ","int((c-c/a/x)^3*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{3} \left(-8 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+16 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+8 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -13 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-13 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+8 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-16 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{3} x^{2} \sqrt{a^{2}}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^3*(-8*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+16*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+8*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-13*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-13*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+8*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-16*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^3/x^2/(a^2)^(1/2)","B"
415,1,227,71,0.054000," ","int((c-c/a/x)^2*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{2} \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -3 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^2*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-3*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","B"
416,1,137,45,0.052000," ","int((c-c/a/x)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c \left(2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}-2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c*(2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)-2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","B"
417,1,28,17,0.036000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right)}{a c}"," ",0,"1/a*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)/c","A"
418,1,256,67,0.056000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^2,x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right)}{2 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, c^{2} \left(a x -1\right)^{2} \sqrt{a^{2}}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)/a*(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/c^2/(a*x-1)^2/(a^2)^(1/2)","B"
419,1,344,93,0.057000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^3,x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+27 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-72 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-15 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -81 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+72 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+13 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+81 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right)}{12 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, c^{3} \sqrt{a^{2}}\, \left(a x -1\right)^{3}}"," ",0,"1/12*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)/a*(24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+27*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-72*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-15*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-81*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+72*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+13*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+81*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/c^3/(a^2)^(1/2)/(a*x-1)^3","B"
420,1,436,122,0.061000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^4,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-125 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+85 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+500 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-148 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -750 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+67 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+500 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-125 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-120 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{40 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, c^{4} \sqrt{a^{2}}\, \left(a x -1\right)^{4}}"," ",0,"-1/40*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)/a*(-125*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+85*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+500*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-148*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-750*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+67*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+500*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-125*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-120*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)*(a*x+1))^(1/2)/c^4/(a^2)^(1/2)/(a*x-1)^4","B"
421,1,64,63,0.042000," ","int((c-c/a/x)^4/(a*x+1)*(a*x-1),x)","\frac{c^{4}}{3 a^{4} x^{3}}-\frac{3 c^{4}}{x^{2} a^{3}}+\frac{16 c^{4}}{a^{2} x}+c^{4} x +\frac{26 c^{4} \ln \left(x \right)}{a}-\frac{32 c^{4} \ln \left(a x +1\right)}{a}"," ",0,"1/3*c^4/a^4/x^3-3*c^4/x^2/a^3+16*c^4/a^2/x+c^4*x+26*c^4*ln(x)/a-32*c^4*ln(a*x+1)/a","A"
422,1,53,52,0.040000," ","int((c-c/a/x)^3/(a*x+1)*(a*x-1),x)","-\frac{c^{3}}{2 x^{2} a^{3}}+\frac{5 c^{3}}{a^{2} x}+c^{3} x +\frac{11 c^{3} \ln \left(x \right)}{a}-\frac{16 c^{3} \ln \left(a x +1\right)}{a}"," ",0,"-1/2*c^3/x^2/a^3+5*c^3/a^2/x+c^3*x+11*c^3*ln(x)/a-16*c^3*ln(a*x+1)/a","A"
423,1,41,40,0.041000," ","int((c-c/a/x)^2/(a*x+1)*(a*x-1),x)","\frac{c^{2}}{a^{2} x}+c^{2} x +\frac{4 c^{2} \ln \left(x \right)}{a}-\frac{8 c^{2} \ln \left(a x +1\right)}{a}"," ",0,"c^2/a^2/x+c^2*x+4*c^2*ln(x)/a-8*c^2*ln(a*x+1)/a","A"
424,1,24,23,0.041000," ","int((c-c/a/x)/(a*x+1)*(a*x-1),x)","c x +\frac{c \ln \left(x \right)}{a}-\frac{4 c \ln \left(a x +1\right)}{a}"," ",0,"c*x+c*ln(x)/a-4*c*ln(a*x+1)/a","A"
425,1,21,20,0.033000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x),x)","\frac{x}{c}-\frac{\ln \left(a x +1\right)}{a c}"," ",0,"x/c-ln(a*x+1)/a/c","A"
426,1,35,18,0.038000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^2,x)","\frac{x}{c^{2}}+\frac{\ln \left(a x -1\right)}{2 a \,c^{2}}-\frac{\ln \left(a x +1\right)}{2 a \,c^{2}}"," ",0,"x/c^2+1/2/a/c^2*ln(a*x-1)-1/2*ln(a*x+1)/a/c^2","A"
427,1,50,51,0.043000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^3,x)","\frac{x}{c^{3}}-\frac{1}{2 a \,c^{3} \left(a x -1\right)}+\frac{5 \ln \left(a x -1\right)}{4 a \,c^{3}}-\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"x/c^3-1/2/a/c^3/(a*x-1)+5/4/a/c^3*ln(a*x-1)-1/4*ln(a*x+1)/a/c^3","A"
428,1,65,67,0.043000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^4,x)","\frac{x}{c^{4}}-\frac{1}{4 a \,c^{4} \left(a x -1\right)^{2}}-\frac{7}{4 a \,c^{4} \left(a x -1\right)}+\frac{17 \ln \left(a x -1\right)}{8 a \,c^{4}}-\frac{\ln \left(a x +1\right)}{8 a \,c^{4}}"," ",0,"x/c^4-1/4/a/c^4/(a*x-1)^2-7/4/a/c^4/(a*x-1)+17/8/a/c^4*ln(a*x-1)-1/8*ln(a*x+1)/a/c^4","A"
429,1,672,144,0.061000," ","int((c-c/a/x)^4*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-138 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+138 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-549 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}-273 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+138 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+96 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-96 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+255 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-684 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-546 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+276 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+192 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+192 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-192 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+98 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-273 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-273 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+138 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+96 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-96 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-17 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right) c^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 a^{4} \sqrt{a^{2}}\, x^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/6*(-138*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+138*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-549*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5-273*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+138*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+96*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-96*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+255*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-684*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-546*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+276*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+192*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+192*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-192*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+98*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-273*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-273*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+138*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+96*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-96*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-17*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/a^4*c^4*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x^3/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
430,1,450,121,0.058000," ","int((c-c/a/x)^3*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-12 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+12 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-57 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-33 a^{4} x^{4} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+12 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+32 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+23 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-78 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-66 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+24 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+10 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -33 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-33 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+12 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right) c^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a^{3} \sqrt{a^{2}}\, x^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/2*(-12*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+12*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-57*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-33*a^4*x^4*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+12*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+32*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+23*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-78*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-66*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+24*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+10*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-33*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-33*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+12*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/a^3*c^3*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x^2/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
431,1,600,97,0.054000," ","int((c-c/a/x)^2*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}-4 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-7 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-5 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+8 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -8 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -11 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-10 a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+2 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+8 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-5 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -5 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right) c^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a^{2} \sqrt{a^{2}}\, x \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4-4*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-7*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-5*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+8*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-8*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-11*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-10*a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+2*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+8*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-5*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-5*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/a^2*c^2*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/x/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
432,1,376,69,0.053000," ","int((c-c/a/x)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}-a^{2} x^{2} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+4 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-8 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -2 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+8 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}-\arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}+4 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) c \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-(-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2-a^2*x^2*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+4*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-8*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+8*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)-arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)+4*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*c*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
433,1,250,66,0.053000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x),x)","-\frac{\left(2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-2 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a \sqrt{a^{2}}\, c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-2*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/c/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
434,1,250,68,0.057000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^2,x)","-\frac{\left(2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/2*(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
435,1,44,41,0.036000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^3,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a^{2} x^{2}-2\right) \left(a x +1\right)}{a \left(a x -1\right)^{2} c^{3}}"," ",0,"1/a*((a*x-1)/(a*x+1))^(3/2)*(a^2*x^2-2)*(a*x+1)/(a*x-1)^2/c^3","A"
436,1,523,97,0.065000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^4,x)","-\frac{\left(-45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+21 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+11 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+90 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-5 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -90 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-19 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{24 a \sqrt{a^{2}}\, c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)^{4}}"," ",0,"-1/24*(-45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+21*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+11*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+90*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-5*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-90*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-19*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/c^4/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)^4","B"
437,1,615,122,0.068000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^5,x)","-\frac{\left(-75 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}-60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+45 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+150 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+2 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+75 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-64 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-300 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-14 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +75 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+60 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+37 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+150 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-75 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-60 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{30 a \sqrt{a^{2}}\, c^{5} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)^{5}}"," ",0,"-1/30*(-75*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6-60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+45*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+150*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+2*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+75*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-64*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-300*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-14*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+75*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+60*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+37*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+150*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-75*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-60*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/c^5/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)^5","B"
438,1,166,199,0.067000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(9/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(210 a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, x^{4}+584 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-735 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{4} a^{4}-712 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+324 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-60 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{210 \sqrt{\frac{a x -1}{a x +1}}\, x^{3} a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/210/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*c^4*(210*a^(9/2)*((a*x+1)*x)^(1/2)*x^4+584*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-735*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^4*a^4-712*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+324*a^(3/2)*x*((a*x+1)*x)^(1/2)-60*((a*x+1)*x)^(1/2)*a^(1/2))/x^3/a^(9/2)/((a*x+1)*x)^(1/2)","A"
439,1,149,166,0.069000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(30 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}+112 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-75 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{3} a^{3}-56 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+12 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{30 \sqrt{\frac{a x -1}{a x +1}}\, x^{2} a^{\frac{7}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/30/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*c^3*(30*a^(7/2)*x^3*((a*x+1)*x)^(1/2)+112*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-75*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^3*a^3-56*a^(3/2)*x*((a*x+1)*x)^(1/2)+12*((a*x+1)*x)^(1/2)*a^(1/2))/x^2/a^(7/2)/((a*x+1)*x)^(1/2)","A"
440,1,132,135,0.068000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(6 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+20 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-9 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}-4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, x \,a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/6/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*c^2*(6*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+20*a^(3/2)*x*((a*x+1)*x)^(1/2)-9*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2-4*((a*x+1)*x)^(1/2)*a^(1/2))/x/a^(5/2)/((a*x+1)*x)^(1/2)","A"
441,1,105,101,0.062000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(-2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, a^{\frac{3}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"-1/2/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(-2*a^(3/2)*x*((a*x+1)*x)^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-4*((a*x+1)*x)^(1/2)*a^(1/2))/((a*x+1)*x)^(1/2)","A"
442,1,87,66,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)/a^(1/2)","A"
443,1,151,131,0.081000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-2 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, a^{\frac{3}{2}} c \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-2*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
444,1,259,188,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x -7 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +10 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x -8 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-10 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+7 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) a^{\frac{3}{2}} c^{2} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(c*(a*x-1)/a/x)^(1/2)*x*(4*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x-7*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+10*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x-8*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-10*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)+7*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^2/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
445,1,366,238,0.072000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(32 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}-79 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}-140 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +112 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{3} \sqrt{\frac{1}{a}}\, x^{2}+158 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +92 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-224 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x +112 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-79 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{32 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right)^{2} a^{\frac{3}{2}} c^{3} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/32/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(32*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2-79*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2-140*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+112*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^3*(1/a)^(1/2)*x^2+158*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+92*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-224*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x+112*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-79*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^3/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
446,1,163,123,0.052000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(9/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(210 a^{\frac{9}{2}} \sqrt{a \,x^{2}-x}\, x^{5}-168 a^{\frac{7}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{3}+16 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2}-105 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{5} a^{4}+24 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x -12 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{42 x^{4} \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}}}"," ",0,"1/42*(c*(a*x-1)/a/x)^(1/2)*c^4*(210*a^(9/2)*(a*x^2-x)^(1/2)*x^5-168*a^(7/2)*(a*x^2-x)^(3/2)*x^3+16*a^(5/2)*(a*x^2-x)^(3/2)*x^2-105*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^5*a^4+24*a^(3/2)*(a*x^2-x)^(3/2)*x-12*(a*x^2-x)^(3/2)*a^(1/2))/x^4/((a*x-1)*x)^(1/2)/a^(9/2)","A"
447,1,144,102,0.053000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(-30 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} x^{4}+20 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2}+15 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{3}+4 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x -4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{10 x^{3} \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}}}"," ",0,"-1/10*(c*(a*x-1)/a/x)^(1/2)/x^3*c^3*(-30*(a*x^2-x)^(1/2)*a^(7/2)*x^4+20*a^(5/2)*(a*x^2-x)^(3/2)*x^2+15*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^3+4*a^(3/2)*(a*x^2-x)^(3/2)*x-4*(a*x^2-x)^(3/2)*a^(1/2))/((a*x-1)*x)^(1/2)/a^(7/2)","A"
448,1,108,81,0.052000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(5/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(-6 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x^{3}+3 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\right)}{6 x^{2} \sqrt{\left(a x -1\right) x}\, a^{\frac{5}{2}}}"," ",0,"-1/6*(c*(a*x-1)/a/x)^(1/2)/x^2*c^2*(-6*(a*x^2-x)^(1/2)*a^(5/2)*x^3+3*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^2+4*(a*x^2-x)^(3/2)*a^(1/2))/((a*x-1)*x)^(1/2)/a^(5/2)","A"
449,1,103,60,0.048000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(-2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} x^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}+\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a \right)}{2 x \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)/x*c*(-2*(a*x^2-x)^(1/2)*a^(3/2)*x^2+4*(a*x^2-x)^(3/2)*a^(1/2)+ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a)/((a*x-1)*x)^(1/2)/a^(3/2)","A"
450,1,120,42,0.051000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, \sqrt{a}-4 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(1/2)-4*((a*x-1)*x)^(1/2)*a^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/a^(1/2)","B"
451,1,194,60,0.052000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(10 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+5 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}-8 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-20 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x -10 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a +10 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+5 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, c \left(a x -1\right)^{2} \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(10*a^(5/2)*((a*x-1)*x)^(1/2)*x^2+5*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2-8*a^(3/2)*((a*x-1)*x)^(3/2)-20*a^(3/2)*((a*x-1)*x)^(1/2)*x-10*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a+10*((a*x-1)*x)^(1/2)*a^(1/2)+5*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c/(a*x-1)^2/a^(1/2)","B"
452,1,260,81,0.056000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(42 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}+21 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}-36 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -126 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}-63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}+28 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+126 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x +63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a -42 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-21 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{6 \sqrt{\left(a x -1\right) x}\, c^{2} \sqrt{a}\, \left(a x -1\right)^{3}}"," ",0,"1/6*(c*(a*x-1)/a/x)^(1/2)*x*(42*a^(7/2)*((a*x-1)*x)^(1/2)*x^3+21*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3-36*a^(5/2)*((a*x-1)*x)^(3/2)*x-126*a^(5/2)*((a*x-1)*x)^(1/2)*x^2-63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2+28*a^(3/2)*((a*x-1)*x)^(3/2)+126*a^(3/2)*((a*x-1)*x)^(1/2)*x+63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a-42*((a*x-1)*x)^(1/2)*a^(1/2)-21*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^2/a^(1/2)/(a*x-1)^3","B"
453,1,328,102,0.056000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(90 a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{4}+45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{4}-80 a^{\frac{7}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{2}-360 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}-180 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}+132 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x +540 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+270 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}-60 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-360 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x -180 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a +90 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{10 \sqrt{\left(a x -1\right) x}\, c^{3} \sqrt{a}\, \left(a x -1\right)^{4}}"," ",0,"1/10*(c*(a*x-1)/a/x)^(1/2)*x*(90*a^(9/2)*((a*x-1)*x)^(1/2)*x^4+45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^4-80*a^(7/2)*((a*x-1)*x)^(3/2)*x^2-360*a^(7/2)*((a*x-1)*x)^(1/2)*x^3-180*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3+132*a^(5/2)*((a*x-1)*x)^(3/2)*x+540*a^(5/2)*((a*x-1)*x)^(1/2)*x^2+270*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2-60*a^(3/2)*((a*x-1)*x)^(3/2)-360*a^(3/2)*((a*x-1)*x)^(1/2)*x-180*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a+90*((a*x-1)*x)^(1/2)*a^(1/2)+45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^3/a^(1/2)/(a*x-1)^4","B"
454,1,396,123,0.060000," ","int((a*x+1)/(a*x-1)/(c-c/a/x)^(7/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2310 \sqrt{\left(a x -1\right) x}\, a^{\frac{11}{2}} x^{5}+2100 \left(\left(a x -1\right) x \right)^{\frac{3}{2}} a^{\frac{9}{2}} x^{3}-1155 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{5} a^{5}+11550 a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{4}-5368 a^{\frac{7}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x^{2}+5775 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{4} a^{4}-23100 a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{3}+4928 a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -11550 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{3} a^{3}+23100 a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}-1540 a^{\frac{3}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+11550 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{2}-11550 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x -5775 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x a +2310 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+1155 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{210 \sqrt{\left(a x -1\right) x}\, c^{4} \sqrt{a}\, \left(a x -1\right)^{5}}"," ",0,"-1/210*(c*(a*x-1)/a/x)^(1/2)*x*(-2310*((a*x-1)*x)^(1/2)*a^(11/2)*x^5+2100*((a*x-1)*x)^(3/2)*a^(9/2)*x^3-1155*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^5*a^5+11550*a^(9/2)*((a*x-1)*x)^(1/2)*x^4-5368*a^(7/2)*((a*x-1)*x)^(3/2)*x^2+5775*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^4*a^4-23100*a^(7/2)*((a*x-1)*x)^(1/2)*x^3+4928*a^(5/2)*((a*x-1)*x)^(3/2)*x-11550*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^3*a^3+23100*a^(5/2)*((a*x-1)*x)^(1/2)*x^2-1540*a^(3/2)*((a*x-1)*x)^(3/2)+11550*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^2-11550*a^(3/2)*((a*x-1)*x)^(1/2)*x-5775*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a+2310*((a*x-1)*x)^(1/2)*a^(1/2)+1155*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/c^4/a^(1/2)/(a*x-1)^5","B"
455,1,178,234,0.069000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(9/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(70 a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, x^{4}+328 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-105 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{4} a^{4}-24 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-52 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+20 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{70 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x^{3} a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/70/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c^4*(70*a^(9/2)*((a*x+1)*x)^(1/2)*x^4+328*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-105*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^4*a^4-24*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-52*a^(3/2)*x*((a*x+1)*x)^(1/2)+20*((a*x+1)*x)^(1/2)*a^(1/2))/x^3/a^(9/2)/((a*x+1)*x)^(1/2)","A"
456,1,161,203,0.069000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(7/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(30 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}+88 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-15 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{3} a^{3}+16 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-12 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{30 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x^{2} a^{\frac{7}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/30/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c^3*(30*a^(7/2)*x^3*((a*x+1)*x)^(1/2)+88*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-15*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^3*a^3+16*a^(3/2)*x*((a*x+1)*x)^(1/2)-12*((a*x+1)*x)^(1/2)*a^(1/2))/x^2/a^(7/2)/((a*x+1)*x)^(1/2)","A"
457,1,144,134,0.067000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(5/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(6 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}+4 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{6 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x \,a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/6/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)/x*c^2/a^(5/2)*(6*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2+4*a^(3/2)*x*((a*x+1)*x)^(1/2)+4*((a*x+1)*x)^(1/2)*a^(1/2))/((a*x+1)*x)^(1/2)","A"
458,1,118,102,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(3/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) a^{\frac{3}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c/a^(3/2)*(2*a^(3/2)*x*((a*x+1)*x)^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-4*((a*x+1)*x)^(1/2)*a^(1/2))/((a*x+1)*x)^(1/2)","A"
459,1,160,131,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}+5 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2)+5*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2))/((a*x+1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","A"
460,1,259,188,0.068000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x -5 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x -6 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+5 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) a^{\frac{3}{2}} c \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x-5*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x-6*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)+5*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
461,1,373,238,0.071000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}-51 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}-92 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +72 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{3} \sqrt{\frac{1}{a}}\, x^{2}+102 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +60 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-144 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x +72 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-51 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{16 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right) \left(a x +1\right) a^{\frac{3}{2}} c^{2} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/16/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2-51*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2-92*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+72*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^3*(1/a)^(1/2)*x^2+102*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+60*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-144*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x+72*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-51*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^2/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
462,1,480,288,0.075000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(192 \sqrt{\left(a x +1\right) x}\, a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, x^{3}-747 a^{\frac{7}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{3}-1660 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}+1056 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{4} \sqrt{\frac{1}{a}}\, x^{3}+2241 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}+2216 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x -3168 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{3} \sqrt{\frac{1}{a}}\, x^{2}-2241 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x -876 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+3168 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x -1056 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+747 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{192 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right)^{2} \left(a x +1\right) a^{\frac{3}{2}} c^{3} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/192/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(192*((a*x+1)*x)^(1/2)*a^(9/2)*(1/a)^(1/2)*x^3-747*a^(7/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^3-1660*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2+1056*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^4*(1/a)^(1/2)*x^3+2241*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2+2216*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x-3168*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^3*(1/a)^(1/2)*x^2-2241*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x-876*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+3168*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x-1056*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)+747*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^3/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
463,1,161,193,0.070000," ","int((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(10 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-184 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-45 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{3} a^{3}+32 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{10 x^{2} a^{\frac{7}{2}} \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/10*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c^3*(10*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-184*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-45*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^3*a^3+32*a^(3/2)*x*((a*x+1)*x)^(1/2)-4*((a*x+1)*x)^(1/2)*a^(1/2))/x^2/a^(7/2)/(a*x-1)/((a*x+1)*x)^(1/2)","A"
464,1,144,141,0.070000," ","int((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(6 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-44 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-21 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}+4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{6 x \,a^{\frac{5}{2}} \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c^2*(6*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-44*a^(3/2)*x*((a*x+1)*x)^(1/2)-21*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2+4*((a*x+1)*x)^(1/2)*a^(1/2))/x/a^(5/2)/(a*x-1)/((a*x+1)*x)^(1/2)","A"
465,1,118,122,0.066000," ","int((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-5 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{2 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*c*(2*a^(3/2)*x*((a*x+1)*x)^(1/2)-5*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-4*((a*x+1)*x)^(1/2)*a^(1/2))/a^(3/2)/(a*x-1)/((a*x+1)*x)^(1/2)","A"
466,1,101,67,0.060000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(1/2)-3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/(a*x-1)/((a*x+1)*x)^(1/2)/a^(1/2)","A"
467,1,104,66,0.051000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{a}\, c \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(1/2)-ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(1/2)/c/(a*x-1)/((a*x+1)*x)^(1/2)","A"
468,1,162,130,0.068000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(3/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{2 a^{\frac{3}{2}} c^{2} \left(a x -1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^2/(a*x-1)/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
469,1,264,188,0.074000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(8 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x -9 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x -12 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+12 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x -12 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+9 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{8 a^{\frac{3}{2}} c^{3} \left(a x -1\right)^{2} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/8*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(8*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x-9*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x-12*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+12*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x-12*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)+9*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^3/(a*x-1)^2/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
470,1,371,238,0.076000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(64 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}-115 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}-220 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +160 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{3} \sqrt{\frac{1}{a}}\, x^{2}+230 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +140 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-320 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x +160 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-115 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{64 a^{\frac{3}{2}} c^{4} \left(a x -1\right)^{3} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/64*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(64*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2-115*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2-220*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+160*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^3*(1/a)^(1/2)*x^2+230*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+140*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-320*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x+160*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-115*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^4/(a*x-1)^3/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
471,1,281,136,0.076000," ","int((c-c/a/x)^(7/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(-1110 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x^{4}+480 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{4}+660 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+555 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-720 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-480 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{5}{2}} \sqrt{2}\, x^{4}-92 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+12 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{30 x^{3} a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/30*(c*(a*x-1)/a/x)^(1/2)/x^3*c^3/a^(7/2)*(-1110*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x^4+480*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^4+660*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+555*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-720*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-480*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(5/2)*2^(1/2)*x^4-92*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+12*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
472,1,257,115,0.051000," ","int((c-c/a/x)^(5/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(-90 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, x^{3}+48 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+48 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+45 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-48 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-72 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{6 x^{2} a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/6*(c*(a*x-1)/a/x)^(1/2)/x^2*c^2/a^(5/2)*(-90*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)*x^3+48*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+48*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+45*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-48*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-72*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-4*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
473,1,229,94,0.055000," ","int((c-c/a/x)^(3/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(-10 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, x^{2}+8 a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}+4 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}+5 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a -8 \sqrt{a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-12 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a \right)}{2 x \,a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)/x*c/a^(3/2)*(-10*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)*x^2+8*a^(3/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2+4*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2)+5*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a-8*a^(1/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-12*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a)/((a*x-1)*x)^(1/2)/(1/a)^(1/2)","B"
474,1,190,75,0.050000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}+6 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2)+6*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","B"
475,1,136,78,0.043000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+3 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+2 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{2 \sqrt{\left(a x -1\right) x}\, c \,a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(-2*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+3*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+2*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c/a^(3/2)/(1/a)^(1/2)","A"
476,1,134,77,0.048000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^(3/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+\ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{2 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{2} \sqrt{\frac{1}{a}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(-2*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^2/(1/a)^(1/2)","A"
477,1,370,98,0.057000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^(5/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(8 \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+2 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{3}-4 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-\ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{5}{2}} \sqrt{2}\, x^{2}-16 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x -4 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x \,a^{2}+2 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}} \sqrt{2}\, x +8 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{4 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{3} \left(a x -1\right)^{2} \sqrt{\frac{1}{a}}}"," ",0,"1/4*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(8*(1/a)^(1/2)*a^(7/2)*((a*x-1)*x)^(1/2)*x^2+2*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^3-4*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(3/2)-ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(5/2)*2^(1/2)*x^2-16*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)*x-4*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a^2+2*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)*2^(1/2)*x+8*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)-2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^3/(a*x-1)^2/(1/a)^(1/2)","B"
478,1,497,120,0.056000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^(7/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(84 a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+36 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{4}-3 a^{\frac{7}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-60 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x -252 \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}-108 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{3}+9 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{5}{2}} \sqrt{2}\, x^{2}+52 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}+252 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x +108 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x \,a^{2}-9 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}} \sqrt{2}\, x -84 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-36 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+3 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{24 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{4} \left(a x -1\right)^{3} \sqrt{\frac{1}{a}}}"," ",0,"1/24*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(84*a^(9/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+36*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^4-3*a^(7/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-60*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)*x-252*(1/a)^(1/2)*a^(7/2)*((a*x-1)*x)^(1/2)*x^2-108*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^3+9*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(5/2)*2^(1/2)*x^2+52*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(3/2)+252*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)*x+108*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a^2-9*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)*2^(1/2)*x-84*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-36*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+3*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^4/(a*x-1)^3/(1/a)^(1/2)","B"
479,1,626,141,0.061000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a/x)^(9/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-1260 \sqrt{\left(a x -1\right) x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, x^{4}+1020 \left(\left(a x -1\right) x \right)^{\frac{3}{2}} a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, x^{2}-600 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{5}+15 a^{\frac{9}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{4}+5040 a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}-1792 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \left(\left(a x -1\right) x \right)^{\frac{3}{2}} x +2400 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{4}-60 a^{\frac{7}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-7560 \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+820 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \left(\left(a x -1\right) x \right)^{\frac{3}{2}}-3600 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a^{3}+90 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{5}{2}} \sqrt{2}\, x^{2}+5040 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}\, x +2400 \sqrt{\frac{1}{a}}\, \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x \,a^{2}-60 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}} \sqrt{2}\, x -1260 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-600 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+15 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}\right)}{240 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, c^{5} \left(a x -1\right)^{4} \sqrt{\frac{1}{a}}}"," ",0,"-1/240*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(-1260*((a*x-1)*x)^(1/2)*a^(11/2)*(1/a)^(1/2)*x^4+1020*((a*x-1)*x)^(3/2)*a^(9/2)*(1/a)^(1/2)*x^2-600*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^5+15*a^(9/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^4+5040*a^(9/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3-1792*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(3/2)*x+2400*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^4-60*a^(7/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-7560*(1/a)^(1/2)*a^(7/2)*((a*x-1)*x)^(1/2)*x^2+820*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(3/2)-3600*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a^3+90*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(5/2)*2^(1/2)*x^2+5040*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)*x+2400*(1/a)^(1/2)*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x*a^2-60*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)*2^(1/2)*x-1260*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-600*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+15*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2))/((a*x-1)*x)^(1/2)/c^5/(a*x-1)^4/(1/a)^(1/2)","B"
480,1,229,293,0.076000," ","int((c-c/a/x)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{4} \left(14 \sqrt{\left(a x +1\right) x}\, a^{\frac{11}{2}} x^{5}+3510 a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, x^{4}+1440 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-105 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{5} a^{5}-105 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{4} a^{4}-220 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+40 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{14 \left(a x -1\right)^{2} x^{3} a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/14*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*c^4*(14*((a*x+1)*x)^(1/2)*a^(11/2)*x^5+3510*a^(9/2)*((a*x+1)*x)^(1/2)*x^4+1440*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-105*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^5*a^5-105*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^4*a^4-220*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+40*a^(3/2)*x*((a*x+1)*x)^(1/2)-4*((a*x+1)*x)^(1/2)*a^(1/2))/x^3/a^(9/2)/((a*x+1)*x)^(1/2)","A"
481,1,212,243,0.075000," ","int((c-c/a/x)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{3} \left(30 a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, x^{4}+3182 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-195 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{4} a^{4}+1096 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-195 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{3} a^{3}-124 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+12 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{30 \left(a x -1\right)^{2} x^{2} a^{\frac{7}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/30*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*c^3*(30*a^(9/2)*((a*x+1)*x)^(1/2)*x^4+3182*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-195*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^4*a^4+1096*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-195*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^3*a^3-124*a^(3/2)*x*((a*x+1)*x)^(1/2)+12*((a*x+1)*x)^(1/2)*a^(1/2))/x^2/a^(7/2)/((a*x+1)*x)^(1/2)","A"
482,1,195,193,0.075000," ","int((c-c/a/x)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c^{2} \left(6 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}+266 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-33 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{3} a^{3}+64 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-33 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}-4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{6 \left(a x -1\right)^{2} x \,a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*c^2*(6*a^(7/2)*x^3*((a*x+1)*x)^(1/2)+266*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-33*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^3*a^3+64*a^(3/2)*x*((a*x+1)*x)^(1/2)-33*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2-4*((a*x+1)*x)^(1/2)*a^(1/2))/x/a^(5/2)/((a*x+1)*x)^(1/2)","A"
483,1,169,140,0.080000," ","int((c-c/a/x)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, c \left(2 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+38 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-9 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}-9 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +4 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{2 \left(a x -1\right)^{2} a^{\frac{3}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*c*(2*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+38*a^(3/2)*x*((a*x+1)*x)^(1/2)-9*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2-9*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+4*((a*x+1)*x)^(1/2)*a^(1/2))/a^(3/2)/((a*x+1)*x)^(1/2)","A"
484,1,146,122,0.068000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +18 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right)^{2} \sqrt{a}\, \sqrt{\left(a x +1\right) x}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(2*a^(3/2)*x*((a*x+1)*x)^(1/2)-7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+18*((a*x+1)*x)^(1/2)*a^(1/2)-7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(1/2)/((a*x+1)*x)^(1/2)","A"
485,1,149,102,0.060000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(1/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+5 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -10 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+5 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right)^{2} \sqrt{a}\, c \sqrt{\left(a x +1\right) x}}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x/a^(1/2)/c*(-2*a^(3/2)*x*((a*x+1)*x)^(1/2)+5*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-10*((a*x+1)*x)^(1/2)*a^(1/2)+5*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)","A"
486,1,149,101,0.060000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -6 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right)^{2} \sqrt{a}\, c^{2} \sqrt{\left(a x +1\right) x}}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x/a^(1/2)/c^2*(-2*a^(3/2)*x*((a*x+1)*x)^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-6*((a*x+1)*x)^(1/2)*a^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)","A"
487,1,262,172,0.071000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(5/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-4 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x +2 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{2} \sqrt{\frac{1}{a}}\, x -8 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+\sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}+2 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{4 \left(a x -1\right)^{2} a^{\frac{3}{2}} c^{3} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}}"," ",0,"-1/4*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)/c^3*(-4*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x+2*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^2*(1/a)^(1/2)*x-8*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2)+2*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2))/(1/a)^(1/2)/((a*x+1)*x)^(1/2)","A"
488,1,290,228,0.074000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a/x)^(7/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}-11 a^{\frac{5}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}+4 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +8 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a^{3} \sqrt{\frac{1}{a}}\, x^{2}-28 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-8 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+11 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{16 \left(a x -1\right)^{3} a^{\frac{3}{2}} c^{4} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}}"," ",0,"1/16*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^3*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2-11*a^(5/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2+4*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+8*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a^3*(1/a)^(1/2)*x^2-28*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-8*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)+11*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(3/2)/c^4/(1/a)^(1/2)/((a*x+1)*x)^(1/2)","A"
489,0,0,56,0.049000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a/x)^(1/2),x)","\int \frac{x^{m} \sqrt{c -\frac{c}{a x}}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a/x)^(1/2),x)","F"
490,1,121,136,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+4 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-6 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{48 \sqrt{\frac{a x -1}{a x +1}}\, a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/48/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*x/a^(5/2)*(16*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+4*a^(3/2)*x*((a*x+1)*x)^(1/2)-6*((a*x+1)*x)^(1/2)*a^(1/2)+3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)","A"
491,1,102,102,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a/x)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-4 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{8 \sqrt{\frac{a x -1}{a x +1}}\, a^{\frac{3}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"-1/8/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(-4*a^(3/2)*x*((a*x+1)*x)^(1/2)-2*((a*x+1)*x)^(1/2)*a^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)","A"
492,1,87,66,0.053000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/((a*x+1)*x)^(1/2)/a^(1/2)","A"
493,1,88,64,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)*(ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-2*((a*x+1)*x)^(1/2)*a^(1/2))/((a*x+1)*x)^(1/2)/a^(1/2)","A"
494,1,41,31,0.036000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^2,x)","-\frac{2 \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{3 x \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-2/3*(a*x+1)/x/((a*x-1)/(a*x+1))^(1/2)*(c*(a*x-1)/a/x)^(1/2)","A"
495,1,47,65,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^3,x)","\frac{2 \left(a x +1\right) \left(2 a x -3\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{15 x^{2} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/15*(a*x+1)*(2*a*x-3)*(c*(a*x-1)/a/x)^(1/2)/x^2/((a*x-1)/(a*x+1))^(1/2)","A"
496,1,55,99,0.038000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^4,x)","-\frac{2 \left(a x +1\right) \left(8 a^{2} x^{2}-12 a x +15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{105 x^{3} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-2/105*(a*x+1)*(8*a^2*x^2-12*a*x+15)*(c*(a*x-1)/a/x)^(1/2)/x^3/((a*x-1)/(a*x+1))^(1/2)","A"
497,1,63,135,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^(1/2)/x^5,x)","\frac{2 \left(a x +1\right) \left(16 x^{3} a^{3}-24 a^{2} x^{2}+30 a x -35\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{315 x^{4} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"2/315*(a*x+1)*(16*a^3*x^3-24*a^2*x^2+30*a*x-35)*(c*(a*x-1)/a/x)^(1/2)/x^4/((a*x-1)/(a*x+1))^(1/2)","A"
498,1,172,106,0.047000," ","int((a*x+1)/(a*x-1)*x^3*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(32 x \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}}+112 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{5}{2}}+212 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x -106 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}+256 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}+128 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-53 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{128 \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}}}"," ",0,"1/128*(c*(a*x-1)/a/x)^(1/2)*x*(32*x*(a*x^2-x)^(3/2)*a^(7/2)+112*(a*x^2-x)^(3/2)*a^(5/2)+212*(a*x^2-x)^(1/2)*a^(5/2)*x-106*(a*x^2-x)^(1/2)*a^(3/2)+256*a^(3/2)*((a*x-1)*x)^(1/2)+128*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-53*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(9/2)","A"
499,1,155,85,0.046000," ","int((a*x+1)/(a*x-1)*x^2*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{5}{2}}+60 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x -30 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}+96 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}+48 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-15 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{48 \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}}}"," ",0,"1/48*(c*(a*x-1)/a/x)^(1/2)*x*(16*(a*x^2-x)^(3/2)*a^(5/2)+60*(a*x^2-x)^(1/2)*a^(5/2)*x-30*(a*x^2-x)^(1/2)*a^(3/2)+96*a^(3/2)*((a*x-1)*x)^(1/2)+48*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-15*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(7/2)","A"
500,1,139,64,0.042000," ","int((a*x+1)/(a*x-1)*x*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} x -2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}}+16 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}+8 a \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \right)}{8 \sqrt{\left(a x -1\right) x}\, a^{\frac{5}{2}}}"," ",0,"1/8*(c*(a*x-1)/a/x)^(1/2)*x*(4*(a*x^2-x)^(1/2)*a^(5/2)*x-2*(a*x^2-x)^(1/2)*a^(3/2)+16*a^(3/2)*((a*x-1)*x)^(1/2)+8*a*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a)/((a*x-1)*x)^(1/2)/a^(5/2)","B"
501,1,118,42,0.048000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 \sqrt{\left(a x -1\right) x}\, \sqrt{a}-2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)+2 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right)\right)}{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"1/2*(c*(a*x-1)/a/x)^(1/2)*x*(4*((a*x-1)*x)^(1/2)*a^(1/2)-2*(a*x^2-x)^(1/2)*a^(1/2)+ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))+2*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2)))/((a*x-1)*x)^(1/2)/a^(1/2)","B"
502,1,99,39,0.053000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2)/x,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-2 a^{\frac{3}{2}} \sqrt{\left(a x -1\right) x}\, x^{2}+2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}-\ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) x^{2} a \right)}{x \sqrt{\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"-(c*(a*x-1)/a/x)^(1/2)/x*(-2*a^(3/2)*((a*x-1)*x)^(1/2)*x^2+2*(a*x^2-x)^(3/2)*a^(1/2)-ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*x^2*a)/((a*x-1)*x)^(1/2)/a^(1/2)","B"
503,1,27,36,0.036000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2)/x^2,x)","\frac{2 \left(5 a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{3 x}"," ",0,"2/3*(5*a*x+1)*(c*(a*x-1)/a/x)^(1/2)/x","A"
504,1,35,61,0.038000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2)/x^3,x)","\frac{2 \left(6 a^{2} x^{2}+3 a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{5 x^{2}}"," ",0,"2/5*(6*a^2*x^2+3*a*x+1)*(c*(a*x-1)/a/x)^(1/2)/x^2","A"
505,1,43,82,0.038000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2)/x^4,x)","\frac{2 \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(104 x^{3} a^{3}+52 a^{2} x^{2}+39 a x +15\right)}{105 x^{3}}"," ",0,"2/105*(c*(a*x-1)/a/x)^(1/2)*(104*a^3*x^3+52*a^2*x^2+39*a*x+15)/x^3","A"
506,1,51,103,0.037000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^(1/2)/x^5,x)","\frac{2 \left(272 x^{4} a^{4}+136 x^{3} a^{3}+102 a^{2} x^{2}+85 a x +35\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}}{315 x^{4}}"," ",0,"2/315*(272*a^4*x^4+136*a^3*x^3+102*a^2*x^2+85*a*x+35)*(c*(a*x-1)/a/x)^(1/2)/x^4","A"
507,1,224,264,0.063000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a/x)^(1/2),x)","-\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-96 \sqrt{\left(a x +1\right) x}\, a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, x^{3}-272 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}-428 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x -894 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+768 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}-1089 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{384 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/384/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x/a^(9/2)*(-96*((a*x+1)*x)^(1/2)*a^(9/2)*(1/a)^(1/2)*x^3-272*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2-428*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x-894*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+768*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2)-1089*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2))/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
508,1,202,220,0.061000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a/x)^(1/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x^{2}+52 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +114 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-96 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}+135 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{48 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) a^{\frac{7}{2}} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/48/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(7/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x^2+52*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+114*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-96*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2)+135*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2))/a^(7/2)/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
509,1,180,176,0.062000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a/x)^(1/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, x +18 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}+23 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}-16 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}\right)}{8 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"1/8/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(4*a^(5/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*x+18*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)+23*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2)-16*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2))/a^(5/2)/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
510,1,160,131,0.066000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2),x)","\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) \sqrt{a}+5 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x +1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*a^(1/2)+5*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*a*(1/a)^(1/2))/((a*x+1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","A"
511,1,161,125,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x,x)","-\frac{\left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(2 \sqrt{a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x -\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x a -2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(2*a^(1/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x-ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*(1/a)^(1/2)*x*a-2*((a*x+1)*x)^(1/2)*a^(1/2)*(1/a)^(1/2))/((a*x+1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","A"
512,1,141,104,0.083000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^2,x)","-\frac{2 \left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(3 a \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{2}-7 a \sqrt{\frac{1}{a}}\, x \sqrt{\left(a x +1\right) x}-\sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\right)}{3 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"-2/3/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)/x*(3*a*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^2-7*a*(1/a)^(1/2)*x*((a*x+1)*x)^(1/2)-(1/a)^(1/2)*((a*x+1)*x)^(1/2))/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
513,1,165,143,0.069000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^3,x)","\frac{2 \left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-15 a^{2} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{3}+38 x^{2} \sqrt{\left(a x +1\right) x}\, a^{2} \sqrt{\frac{1}{a}}+11 a \sqrt{\frac{1}{a}}\, x \sqrt{\left(a x +1\right) x}+3 \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\right)}{15 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x^{2} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"2/15/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(-15*a^2*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^3+38*x^2*((a*x+1)*x)^(1/2)*a^2*(1/a)^(1/2)+11*a*(1/a)^(1/2)*x*((a*x+1)*x)^(1/2)+3*(1/a)^(1/2)*((a*x+1)*x)^(1/2))/x^2/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
514,1,187,176,0.072000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^4,x)","\frac{2 \left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-21 a^{3} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{4}+52 x^{3} \sqrt{\left(a x +1\right) x}\, a^{3} \sqrt{\frac{1}{a}}+16 x^{2} \sqrt{\left(a x +1\right) x}\, a^{2} \sqrt{\frac{1}{a}}+9 a \sqrt{\frac{1}{a}}\, x \sqrt{\left(a x +1\right) x}+3 \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\right)}{21 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x^{3} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"2/21/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(-21*a^3*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^4+52*x^3*((a*x+1)*x)^(1/2)*a^3*(1/a)^(1/2)+16*x^2*((a*x+1)*x)^(1/2)*a^2*(1/a)^(1/2)+9*a*(1/a)^(1/2)*x*((a*x+1)*x)^(1/2)+3*(1/a)^(1/2)*((a*x+1)*x)^(1/2))/x^3/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
515,1,209,256,0.073000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a/x)^(1/2)/x^5,x)","\frac{2 \left(a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-315 a^{4} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\, a +3 a x +1}{a x -1}\right) x^{5}+788 x^{4} \sqrt{\left(a x +1\right) x}\, a^{4} \sqrt{\frac{1}{a}}+236 x^{3} \sqrt{\left(a x +1\right) x}\, a^{3} \sqrt{\frac{1}{a}}+138 x^{2} \sqrt{\left(a x +1\right) x}\, a^{2} \sqrt{\frac{1}{a}}+95 a \sqrt{\frac{1}{a}}\, x \sqrt{\left(a x +1\right) x}+35 \sqrt{\frac{1}{a}}\, \sqrt{\left(a x +1\right) x}\right)}{315 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) x^{4} \sqrt{\left(a x +1\right) x}\, \sqrt{\frac{1}{a}}}"," ",0,"2/315/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(-315*a^4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x+1)*x)^(1/2)*a+3*a*x+1)/(a*x-1))*x^5+788*x^4*((a*x+1)*x)^(1/2)*a^4*(1/a)^(1/2)+236*x^3*((a*x+1)*x)^(1/2)*a^3*(1/a)^(1/2)+138*x^2*((a*x+1)*x)^(1/2)*a^2*(1/a)^(1/2)+95*a*(1/a)^(1/2)*x*((a*x+1)*x)^(1/2)+35*(1/a)^(1/2)*((a*x+1)*x)^(1/2))/x^4/((a*x+1)*x)^(1/2)/(1/a)^(1/2)","A"
516,0,0,114,0.049000," ","int(x^m*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\int x^{m} \sqrt{c -\frac{c}{a x}}\, \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int(x^m*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","F"
517,1,133,136,0.060000," ","int(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-44 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+66 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-33 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{48 a^{\frac{5}{2}} \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/48*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-44*a^(3/2)*x*((a*x+1)*x)^(1/2)+66*((a*x+1)*x)^(1/2)*a^(1/2)-33*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(5/2)/(a*x-1)/((a*x+1)*x)^(1/2)","A"
518,1,116,102,0.056000," ","int(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-14 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{8 a^{\frac{3}{2}} \left(a x -1\right) \sqrt{\left(a x +1\right) x}}"," ",0,"1/8*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x/a^(3/2)*(4*a^(3/2)*x*((a*x+1)*x)^(1/2)-14*((a*x+1)*x)^(1/2)*a^(1/2)+7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/(a*x-1)/((a*x+1)*x)^(1/2)","A"
519,1,101,67,0.061000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-3 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*x*(2*((a*x+1)*x)^(1/2)*a^(1/2)-3*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/(a*x-1)/((a*x+1)*x)^(1/2)/a^(1/2)","A"
520,1,100,64,0.065000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{\left(a x -1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(c*(a*x-1)/a/x)^(1/2)*(ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+2*((a*x+1)*x)^(1/2)*a^(1/2))/(a*x-1)/((a*x+1)*x)^(1/2)/a^(1/2)","A"
521,1,54,58,0.035000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x)","-\frac{2 \left(a x +1\right) \left(5 a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{\frac{a x -1}{a x +1}}}{3 \left(a x -1\right) x}"," ",0,"-2/3*(a*x+1)*(5*a*x-1)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)/x","A"
522,1,62,95,0.037000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^3,x)","\frac{2 \left(a x +1\right) \left(6 a^{2} x^{2}-3 a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{\frac{a x -1}{a x +1}}}{5 x^{2} \left(a x -1\right)}"," ",0,"2/5*(a*x+1)*(6*a^2*x^2-3*a*x+1)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2/(a*x-1)","A"
523,1,70,125,0.037000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^4,x)","-\frac{2 \left(a x +1\right) \left(104 x^{3} a^{3}-52 a^{2} x^{2}+39 a x -15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \sqrt{\frac{a x -1}{a x +1}}}{105 x^{3} \left(a x -1\right)}"," ",0,"-2/105*(a*x+1)*(104*a^3*x^3-52*a^2*x^2+39*a*x-15)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^3/(a*x-1)","A"
524,1,259,139,0.050000," ","int(x^3*(c-c/a/x)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(-96 x \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{9}{2}} \sqrt{\frac{1}{a}}+176 \sqrt{\frac{1}{a}}\, \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}}-252 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} x +126 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}}+768 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}-1152 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}-768 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}}+63 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{384 \sqrt{\left(a x -1\right) x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/384*(c*(a*x-1)/a/x)^(1/2)*x*(-96*x*(a*x^2-x)^(3/2)*a^(9/2)*(1/a)^(1/2)+176*(1/a)^(1/2)*(a*x^2-x)^(3/2)*a^(7/2)-252*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(7/2)*x+126*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(5/2)+768*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)-1152*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2-768*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)+63*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(11/2)/(1/a)^(1/2)","A"
525,1,237,118,0.046000," ","int(x^2*(c-c/a/x)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 \sqrt{\frac{1}{a}}\, \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{7}{2}}-36 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} x +18 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}}+96 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}-96 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}}-144 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}+9 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{48 \sqrt{\left(a x -1\right) x}\, a^{\frac{9}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/48*(c*(a*x-1)/a/x)^(1/2)*x*(16*(1/a)^(1/2)*(a*x^2-x)^(3/2)*a^(7/2)-36*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(7/2)*x+18*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(5/2)+96*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)-96*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)-144*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2+9*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(9/2)/(1/a)^(1/2)","A"
526,1,216,97,0.042000," ","int(x*(c-c/a/x)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} x -2 \sqrt{\frac{1}{a}}\, \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}}-16 \sqrt{\frac{1}{a}}\, a^{\frac{5}{2}} \sqrt{\left(a x -1\right) x}+16 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{3}{2}}+24 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, a^{2}\right)}{8 \sqrt{\left(a x -1\right) x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}}"," ",0,"1/8*(c*(a*x-1)/a/x)^(1/2)*x*(4*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(7/2)*x-2*(1/a)^(1/2)*(a*x^2-x)^(1/2)*a^(5/2)-16*(1/a)^(1/2)*a^(5/2)*((a*x-1)*x)^(1/2)+16*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(3/2)+24*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*a^2)/((a*x-1)*x)^(1/2)/a^(7/2)/(1/a)^(1/2)","B"
527,1,190,75,0.050000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-4 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}-\ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}+4 \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{a}+6 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) a \sqrt{\frac{1}{a}}\right)}{2 \sqrt{\left(a x -1\right) x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}}"," ",0,"-1/2*(c*(a*x-1)/a/x)^(1/2)*x*(2*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)-4*((a*x-1)*x)^(1/2)*a^(3/2)*(1/a)^(1/2)-ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2)+4*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(1/2)+6*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*a*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(3/2)/(1/a)^(1/2)","B"
528,1,228,69,0.055000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1)/x,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-4 \sqrt{a \,x^{2}-x}\, a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, x^{2}+2 a^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{2}+2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}+2 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a -2 \sqrt{a}\, \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{2}-3 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{2} a \right)}{x \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-(c*(a*x-1)/a/x)^(1/2)/x*(-4*(a*x^2-x)^(1/2)*a^(3/2)*(1/a)^(1/2)*x^2+2*a^(3/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^2+2*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2)+2*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a-2*a^(1/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^2-3*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^2*a)/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
529,1,254,67,0.052000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1)/x^2,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-18 \sqrt{a \,x^{2}-x}\, a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, x^{3}+6 a^{\frac{5}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{3}+12 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+9 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-6 a^{\frac{3}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{3}-9 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{3} a^{2}-2 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{3 x^{2} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"1/3*(c*(a*x-1)/a/x)^(1/2)/x^2*(-18*(a*x^2-x)^(1/2)*a^(5/2)*(1/a)^(1/2)*x^3+6*a^(5/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^3+12*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+9*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-6*a^(3/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^3-9*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^3*a^2-2*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
530,1,278,94,0.053000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1)/x^3,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-90 \sqrt{a \,x^{2}-x}\, a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, x^{4}+30 a^{\frac{7}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{4}+60 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+45 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-30 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) a^{\frac{5}{2}} \sqrt{2}\, x^{4}-45 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{4} a^{3}-16 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+6 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{15 x^{3} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/15*(c*(a*x-1)/a/x)^(1/2)/x^3*(-90*(a*x^2-x)^(1/2)*a^(7/2)*(1/a)^(1/2)*x^4+30*a^(7/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^4+60*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+45*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-30*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*a^(5/2)*2^(1/2)*x^4-45*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^4*a^3-16*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+6*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
531,1,302,94,0.059000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1)/x^4,x)","\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-126 \sqrt{a \,x^{2}-x}\, \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} x^{5}+42 \sqrt{\frac{1}{a}}\, a^{\frac{9}{2}} \sqrt{\left(a x -1\right) x}\, x^{5}+84 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} x^{3}+63 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-42 \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) \sqrt{2}\, a^{\frac{7}{2}} x^{5}-63 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{5} a^{4}-20 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}+12 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}-6 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{21 x^{4} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"1/21*(c*(a*x-1)/a/x)^(1/2)/x^4*(-126*(a*x^2-x)^(1/2)*(1/a)^(1/2)*a^(9/2)*x^5+42*(1/a)^(1/2)*a^(9/2)*((a*x-1)*x)^(1/2)*x^5+84*(a*x^2-x)^(3/2)*(1/a)^(1/2)*a^(7/2)*x^3+63*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-42*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*2^(1/2)*a^(7/2)*x^5-63*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^5*a^4-20*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)+12*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)-6*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
532,1,326,136,0.058000," ","int((c-c/a/x)^(1/2)/(a*x+1)*(a*x-1)/x^5,x)","-\frac{\sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(-1890 \sqrt{a \,x^{2}-x}\, a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, x^{6}+630 a^{\frac{11}{2}} \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, x^{6}+1260 \left(a \,x^{2}-x \right)^{\frac{3}{2}} a^{\frac{9}{2}} \sqrt{\frac{1}{a}}\, x^{4}+945 \ln \left(\frac{2 \sqrt{a \,x^{2}-x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{6} a^{5}-630 a^{\frac{9}{2}} \sqrt{2}\, \ln \left(\frac{2 \sqrt{2}\, \sqrt{\frac{1}{a}}\, \sqrt{\left(a x -1\right) x}\, a -3 a x +1}{a x +1}\right) x^{6}-945 \ln \left(\frac{2 \sqrt{\left(a x -1\right) x}\, \sqrt{a}+2 a x -1}{2 \sqrt{a}}\right) \sqrt{\frac{1}{a}}\, x^{6} a^{5}-316 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{\frac{1}{a}}\, a^{\frac{7}{2}} x^{3}+156 a^{\frac{5}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x^{2} \sqrt{\frac{1}{a}}-120 a^{\frac{3}{2}} \left(a \,x^{2}-x \right)^{\frac{3}{2}} x \sqrt{\frac{1}{a}}+70 \left(a \,x^{2}-x \right)^{\frac{3}{2}} \sqrt{a}\, \sqrt{\frac{1}{a}}\right)}{315 x^{5} \sqrt{\left(a x -1\right) x}\, \sqrt{a}\, \sqrt{\frac{1}{a}}}"," ",0,"-1/315*(c*(a*x-1)/a/x)^(1/2)/x^5*(-1890*(a*x^2-x)^(1/2)*a^(11/2)*(1/a)^(1/2)*x^6+630*a^(11/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*x^6+1260*(a*x^2-x)^(3/2)*a^(9/2)*(1/a)^(1/2)*x^4+945*ln(1/2*(2*(a*x^2-x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^6*a^5-630*a^(9/2)*2^(1/2)*ln((2*2^(1/2)*(1/a)^(1/2)*((a*x-1)*x)^(1/2)*a-3*a*x+1)/(a*x+1))*x^6-945*ln(1/2*(2*((a*x-1)*x)^(1/2)*a^(1/2)+2*a*x-1)/a^(1/2))*(1/a)^(1/2)*x^6*a^5-316*(a*x^2-x)^(3/2)*(1/a)^(1/2)*a^(7/2)*x^3+156*a^(5/2)*(a*x^2-x)^(3/2)*x^2*(1/a)^(1/2)-120*a^(3/2)*(a*x^2-x)^(3/2)*x*(1/a)^(1/2)+70*(a*x^2-x)^(3/2)*a^(1/2)*(1/a)^(1/2))/((a*x-1)*x)^(1/2)/a^(1/2)/(1/a)^(1/2)","B"
533,1,197,255,0.069000," ","int(x^3*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(96 a^{\frac{9}{2}} \sqrt{\left(a x +1\right) x}\, x^{4}-400 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}+892 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-2230 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+3345 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -6690 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+3345 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{384 \left(a x -1\right)^{2} a^{\frac{7}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/384*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(96*a^(9/2)*((a*x+1)*x)^(1/2)*x^4-400*a^(7/2)*x^3*((a*x+1)*x)^(1/2)+892*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-2230*a^(3/2)*x*((a*x+1)*x)^(1/2)+3345*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-6690*((a*x+1)*x)^(1/2)*a^(1/2)+3345*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(7/2)/((a*x+1)*x)^(1/2)","A"
534,1,180,211,0.070000," ","int(x^2*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(16 a^{\frac{7}{2}} x^{3} \sqrt{\left(a x +1\right) x}-76 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}+238 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-357 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +714 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-357 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{48 \left(a x -1\right)^{2} a^{\frac{5}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/48*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(16*a^(7/2)*x^3*((a*x+1)*x)^(1/2)-76*a^(5/2)*x^2*((a*x+1)*x)^(1/2)+238*a^(3/2)*x*((a*x+1)*x)^(1/2)-357*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+714*((a*x+1)*x)^(1/2)*a^(1/2)-357*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(5/2)/((a*x+1)*x)^(1/2)","A"
535,1,163,167,0.066000," ","int(x*(c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(4 a^{\frac{5}{2}} x^{2} \sqrt{\left(a x +1\right) x}-26 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}+47 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a -94 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+47 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{8 \left(a x -1\right)^{2} a^{\frac{3}{2}} \sqrt{\left(a x +1\right) x}}"," ",0,"1/8*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(4*a^(5/2)*x^2*((a*x+1)*x)^(1/2)-26*a^(3/2)*x*((a*x+1)*x)^(1/2)+47*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a-94*((a*x+1)*x)^(1/2)*a^(1/2)+47*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(3/2)/((a*x+1)*x)^(1/2)","A"
536,1,146,122,0.070000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, x \left(2 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +18 \sqrt{\left(a x +1\right) x}\, \sqrt{a}-7 \ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right)\right)}{2 \left(a x -1\right)^{2} \sqrt{a}\, \sqrt{\left(a x +1\right) x}}"," ",0,"1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*x*(2*a^(3/2)*x*((a*x+1)*x)^(1/2)-7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+18*((a*x+1)*x)^(1/2)*a^(1/2)-7*ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/a^(1/2)/((a*x+1)*x)^(1/2)","A"
537,1,151,116,0.069000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(10 a^{\frac{3}{2}} x \sqrt{\left(a x +1\right) x}-\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x^{2} a^{2}-\ln \left(\frac{2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+2 a x +1}{2 \sqrt{a}}\right) x a +2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right)}{\left(a x -1\right)^{2} \sqrt{a}\, \sqrt{\left(a x +1\right) x}}"," ",0,"-((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)^2*(c*(a*x-1)/a/x)^(1/2)*(10*a^(3/2)*x*((a*x+1)*x)^(1/2)-ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x^2*a^2-ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2))*x*a+2*((a*x+1)*x)^(1/2)*a^(1/2))/a^(1/2)/((a*x+1)*x)^(1/2)","A"
538,1,62,91,0.040000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x)","\frac{2 \left(a x +1\right) \left(23 a^{2} x^{2}+10 a x -1\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{3 x \left(a x -1\right)^{2}}"," ",0,"2/3*(a*x+1)*(23*a^2*x^2+10*a*x-1)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x/(a*x-1)^2","A"
539,1,70,128,0.039000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x)","-\frac{2 \left(a x +1\right) \left(158 x^{3} a^{3}+79 a^{2} x^{2}-16 a x +3\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{15 x^{2} \left(a x -1\right)^{2}}"," ",0,"-2/15*(a*x+1)*(158*a^3*x^3+79*a^2*x^2-16*a*x+3)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2/(a*x-1)^2","A"
540,1,78,160,0.041000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x)","\frac{2 \left(a x +1\right) \left(1336 x^{4} a^{4}+668 x^{3} a^{3}-167 a^{2} x^{2}+66 a x -15\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{105 x^{3} \left(a x -1\right)^{2}}"," ",0,"2/105*(a*x+1)*(1336*a^4*x^4+668*a^3*x^3-167*a^2*x^2+66*a*x-15)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3/(a*x-1)^2","A"
541,1,86,247,0.041000," ","int((c-c/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x)","-\frac{2 \left(a x +1\right) \left(656 x^{5} a^{5}+328 x^{4} a^{4}-82 x^{3} a^{3}+41 a^{2} x^{2}-20 a x +5\right) \sqrt{\frac{c \left(a x -1\right)}{a x}}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{45 x^{4} \left(a x -1\right)^{2}}"," ",0,"-2/45*(a*x+1)*(656*a^5*x^5+328*a^4*x^4-82*a^3*x^3+41*a^2*x^2-20*a*x+5)*(c*(a*x-1)/a/x)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4/(a*x-1)^2","A"
542,0,0,167,0.055000," ","int(exp(n*arccoth(a*x))*(c-c/a/x),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a x}\right)\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a/x),x)","F"
543,0,0,107,0.055000," ","int(exp(n*arccoth(a*x))/(c-c/a/x),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{c -\frac{c}{a x}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a/x),x)","F"
544,0,0,154,0.056000," ","int(exp(n*arccoth(a*x))/(c-c/a/x)^2,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(c -\frac{c}{a x}\right)^{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a/x)^2,x)","F"
545,0,0,93,0.050000," ","int(exp(n*arccoth(a*x))*(c-c/a/x)^(3/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a x}\right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a/x)^(3/2),x)","F"
546,0,0,93,0.050000," ","int(exp(n*arccoth(a*x))*(c-c/a/x)^(1/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \sqrt{c -\frac{c}{a x}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a/x)^(1/2),x)","F"
547,0,0,93,0.051000," ","int(exp(n*arccoth(a*x))/(c-c/a/x)^(1/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\sqrt{c -\frac{c}{a x}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a/x)^(1/2),x)","F"
548,0,0,93,0.050000," ","int(exp(n*arccoth(a*x))/(c-c/a/x)^(3/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(c -\frac{c}{a x}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a/x)^(3/2),x)","F"
549,0,0,98,0.097000," ","int(exp(n*arccoth(a*x))*(c-c/a/x)^p,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a x}\right)^{p}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a/x)^p,x)","F"
550,0,0,69,0.087000," ","int(exp(2*p*arccoth(a*x))*(c-c/a/x)^p,x)","\int {\mathrm e}^{2 p \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a x}\right)^{p}\, dx"," ",0,"int(exp(2*p*arccoth(a*x))*(c-c/a/x)^p,x)","F"
551,0,0,91,0.093000," ","int((c-c/a/x)^p/exp(2*p*arccoth(a*x)),x)","\int \left(c -\frac{c}{a x}\right)^{p} {\mathrm e}^{-2 p \,\mathrm{arccoth}\left(a x \right)}\, dx"," ",0,"int((c-c/a/x)^p/exp(2*p*arccoth(a*x)),x)","F"
552,0,0,59,0.365000," ","int((a*x+1)/(a*x-1)*(c-c/a/x)^p,x)","\int \frac{\left(a x +1\right) \left(c -\frac{c}{a x}\right)^{p}}{a x -1}\, dx"," ",0,"int((a*x+1)/(a*x-1)*(c-c/a/x)^p,x)","F"
553,0,0,76,0.046000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^p,x)","\int \frac{\left(c -\frac{c}{a x}\right)^{p}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a/x)^p,x)","F"
554,0,0,76,0.048000," ","int((c-c/a/x)^p*((a*x-1)/(a*x+1))^(1/2),x)","\int \left(c -\frac{c}{a x}\right)^{p} \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int((c-c/a/x)^p*((a*x-1)/(a*x+1))^(1/2),x)","F"
555,0,0,114,0.354000," ","int((c-c/a/x)^p/(a*x+1)*(a*x-1),x)","\int \frac{\left(c -\frac{c}{a x}\right)^{p} \left(a x -1\right)}{a x +1}\, dx"," ",0,"int((c-c/a/x)^p/(a*x+1)*(a*x-1),x)","F"
556,1,279,333,0.064000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^4,x)","-\frac{\left(a x -1\right) c^{4} \left(-128 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-144 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+384 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+456 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-384 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-522 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +384 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-256 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+315 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -315 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{1152 a \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/1152*(a*x-1)*c^4/a*(-128*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6-144*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5+384*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+456*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-384*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-522*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+384*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-256*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+315*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-315*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
557,1,231,265,0.052000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^3,x)","-\frac{\left(a x -1\right) c^{3} \left(48 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+56 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-96 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-126 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -64 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+105 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +112 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-105 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{336 a \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/336*(a*x-1)*c^3/a*(48*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+56*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-96*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-126*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-64*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+105*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+112*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-105*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
558,1,183,197,0.046000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^2,x)","\frac{\left(a x -1\right) c^{2} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -40 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+45 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*(a*x-1)*c^2/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-45*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-40*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+45*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
559,1,119,121,0.042000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c),x)","-\frac{\left(a x -1\right) c \left(3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"-1/6*(a*x-1)*c*(3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
560,1,23,22,0.035000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x)","\frac{1}{\sqrt{\frac{a x -1}{a x +1}}\, a c}"," ",0,"1/((a*x-1)/(a*x+1))^(1/2)/a/c","A"
561,1,49,65,0.038000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x)","\frac{2 a^{2} x^{2}-2 a x -1}{3 \left(a^{2} x^{2}-1\right) c^{2} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"1/3*(2*a^2*x^2-2*a*x-1)/(a^2*x^2-1)/c^2/((a*x-1)/(a*x+1))^(1/2)/a","A"
562,1,65,106,0.039000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x)","\frac{8 x^{4} a^{4}-8 x^{3} a^{3}-12 a^{2} x^{2}+12 a x +3}{15 \left(a^{2} x^{2}-1\right)^{2} c^{3} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"1/15*(8*a^4*x^4-8*a^3*x^3-12*a^2*x^2+12*a*x+3)/(a^2*x^2-1)^2/c^3/((a*x-1)/(a*x+1))^(1/2)/a","A"
563,1,81,147,0.041000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x)","\frac{16 x^{6} a^{6}-16 x^{5} a^{5}-40 x^{4} a^{4}+40 x^{3} a^{3}+30 a^{2} x^{2}-30 a x -5}{35 \left(a^{2} x^{2}-1\right)^{3} c^{4} \sqrt{\frac{a x -1}{a x +1}}\, a}"," ",0,"1/35*(16*a^6*x^6-16*a^5*x^5-40*a^4*x^4+40*a^3*x^3+30*a^2*x^2-30*a*x-5)/(a^2*x^2-1)^3/c^4/((a*x-1)/(a*x+1))^(1/2)/a","A"
564,1,85,76,0.033000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^5,x)","c^{5} \left(-\frac{1}{11} a^{10} x^{11}-\frac{1}{5} a^{9} x^{10}+\frac{1}{3} x^{9} a^{8}+a^{7} x^{8}-\frac{2}{7} a^{6} x^{7}-2 x^{6} a^{5}-\frac{2}{5} a^{4} x^{5}+2 x^{4} a^{3}+x^{3} a^{2}-a \,x^{2}-x \right)"," ",0,"c^5*(-1/11*a^10*x^11-1/5*a^9*x^10+1/3*x^9*a^8+a^7*x^8-2/7*a^6*x^7-2*x^6*a^5-2/5*a^4*x^5+2*x^4*a^3+x^3*a^2-a*x^2-x)","A"
565,1,63,61,0.036000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^4,x)","c^{4} \left(\frac{1}{9} x^{9} a^{8}+\frac{1}{4} a^{7} x^{8}-\frac{2}{7} a^{6} x^{7}-x^{6} a^{5}+\frac{3}{2} x^{4} a^{3}+\frac{2}{3} x^{3} a^{2}-a \,x^{2}-x \right)"," ",0,"c^4*(1/9*x^9*a^8+1/4*a^7*x^8-2/7*a^6*x^7-x^6*a^5+3/2*x^4*a^3+2/3*x^3*a^2-a*x^2-x)","A"
566,1,54,46,0.033000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^3,x)","c^{3} \left(-\frac{1}{7} a^{6} x^{7}-\frac{1}{3} x^{6} a^{5}+\frac{1}{5} a^{4} x^{5}+x^{4} a^{3}+\frac{1}{3} x^{3} a^{2}-a \,x^{2}-x \right)"," ",0,"c^3*(-1/7*a^6*x^7-1/3*x^6*a^5+1/5*a^4*x^5+x^4*a^3+1/3*x^3*a^2-a*x^2-x)","A"
567,1,31,31,0.030000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^2,x)","c^{2} \left(\frac{1}{5} a^{4} x^{5}+\frac{1}{2} x^{4} a^{3}-a \,x^{2}-x \right)"," ",0,"c^2*(1/5*a^4*x^5+1/2*x^4*a^3-a*x^2-x)","A"
568,1,14,13,0.032000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c),x)","-\frac{c \left(a x +1\right)^{3}}{3 a}"," ",0,"-1/3*c*(a*x+1)^3/a","A"
569,1,15,16,0.032000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c),x)","\frac{1}{c a \left(a x -1\right)}"," ",0,"1/c/a/(a*x-1)","A"
570,1,60,45,0.041000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^2,x)","-\frac{1}{4 c^{2} a \left(a x -1\right)^{2}}+\frac{1}{4 a \,c^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{2} a}-\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"-1/4/c^2/a/(a*x-1)^2+1/4/a/c^2/(a*x-1)+1/8/c^2/a*ln(a*x-1)-1/8*ln(a*x+1)/a/c^2","A"
571,1,90,76,0.044000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^3,x)","\frac{1}{12 c^{3} a \left(a x -1\right)^{3}}-\frac{1}{8 c^{3} a \left(a x -1\right)^{2}}+\frac{3}{16 a \,c^{3} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{3} a}+\frac{1}{16 a \,c^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 a \,c^{3}}"," ",0,"1/12/c^3/a/(a*x-1)^3-1/8/c^3/a/(a*x-1)^2+3/16/a/c^3/(a*x-1)+1/8/c^3/a*ln(a*x-1)+1/16/a/c^3/(a*x+1)-1/8*ln(a*x+1)/a/c^3","A"
572,1,120,107,0.043000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^4,x)","-\frac{1}{32 c^{4} a \left(a x -1\right)^{4}}+\frac{1}{16 c^{4} a \left(a x -1\right)^{3}}-\frac{3}{32 c^{4} a \left(a x -1\right)^{2}}+\frac{5}{32 a \,c^{4} \left(a x -1\right)}+\frac{15 \ln \left(a x -1\right)}{128 c^{4} a}+\frac{1}{64 a \,c^{4} \left(a x +1\right)^{2}}+\frac{5}{64 a \,c^{4} \left(a x +1\right)}-\frac{15 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"-1/32/c^4/a/(a*x-1)^4+1/16/c^4/a/(a*x-1)^3-3/32/c^4/a/(a*x-1)^2+5/32/a/c^4/(a*x-1)+15/128/c^4/a*ln(a*x-1)+1/64/a/c^4/(a*x+1)^2+5/64/a/c^4/(a*x+1)-15/128*ln(a*x+1)/a/c^4","A"
573,1,288,333,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^4,x)","\frac{\left(a x -1\right)^{2} c^{4} \left(896 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}+3024 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+1920 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-4200 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-6528 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-1134 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +8064 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-4352 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+3465 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -3465 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{8064 a \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/8064*(a*x-1)^2*c^4/a*(896*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6+3024*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5+1920*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-4200*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-6528*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-1134*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+8064*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-4352*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+3465*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-3465*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
574,1,240,265,0.053000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^3,x)","-\frac{\left(a x -1\right)^{2} c^{3} \left(80 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+288 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-70 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +192 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-315 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -560 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+315 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{560 a \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/560*(a*x-1)^2*c^3/a*(80*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+288*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-70*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+192*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-315*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-560*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+315*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
575,1,192,197,0.049000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^2,x)","\frac{\left(a x -1\right)^{2} c^{2} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+90 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+105 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +120 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-105 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*(a*x-1)^2*c^2/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+90*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+105*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+120*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-105*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
576,1,183,121,0.048000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c),x)","-\frac{\left(a x -1\right)^{2} c \left(9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a +24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{6 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"-1/6*(a*x-1)^2*c*(9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a+24*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
577,1,24,23,0.038000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x)","\frac{1}{3 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a c}"," ",0,"1/3/((a*x-1)/(a*x+1))^(3/2)/a/c","A"
578,1,49,65,0.040000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x)","-\frac{2 a^{2} x^{2}-6 a x +7}{15 \left(a^{2} x^{2}-1\right) c^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/15*(2*a^2*x^2-6*a*x+7)/(a^2*x^2-1)/c^2/((a*x-1)/(a*x+1))^(3/2)/a","A"
579,1,65,106,0.040000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x)","-\frac{8 x^{4} a^{4}-24 x^{3} a^{3}+20 a^{2} x^{2}+4 a x -13}{35 \left(a^{2} x^{2}-1\right)^{2} c^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/35*(8*a^4*x^4-24*a^3*x^3+20*a^2*x^2+4*a*x-13)/(a^2*x^2-1)^2/c^3/((a*x-1)/(a*x+1))^(3/2)/a","A"
580,1,81,147,0.042000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x)","-\frac{16 x^{6} a^{6}-48 x^{5} a^{5}+24 x^{4} a^{4}+56 x^{3} a^{3}-66 a^{2} x^{2}+6 a x +19}{63 \left(a^{2} x^{2}-1\right)^{3} c^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a}"," ",0,"-1/63*(16*a^6*x^6-48*a^5*x^5+24*a^4*x^4+56*a^3*x^3-66*a^2*x^2+6*a*x+19)/(a^2*x^2-1)^3/c^4/((a*x-1)/(a*x+1))^(3/2)/a","A"
581,1,75,60,0.032000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^5,x)","c^{5} \left(-\frac{1}{11} a^{10} x^{11}-\frac{2}{5} a^{9} x^{10}-\frac{1}{3} x^{9} a^{8}+a^{7} x^{8}+2 a^{6} x^{7}-\frac{14}{5} a^{4} x^{5}-2 x^{4} a^{3}+x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^5*(-1/11*a^10*x^11-2/5*a^9*x^10-1/3*x^9*a^8+a^7*x^8+2*a^6*x^7-14/5*a^4*x^5-2*x^4*a^3+x^3*a^2+2*a*x^2+x)","A"
582,1,69,46,0.033000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^4,x)","c^{4} \left(\frac{1}{9} x^{9} a^{8}+\frac{1}{2} a^{7} x^{8}+\frac{4}{7} a^{6} x^{7}-\frac{2}{3} x^{6} a^{5}-2 a^{4} x^{5}-x^{4} a^{3}+\frac{4}{3} x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^4*(1/9*x^9*a^8+1/2*a^7*x^8+4/7*a^6*x^7-2/3*x^6*a^5-2*a^4*x^5-x^4*a^3+4/3*x^3*a^2+2*a*x^2+x)","A"
583,1,45,31,0.031000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^3,x)","c^{3} \left(-\frac{1}{7} a^{6} x^{7}-\frac{2}{3} x^{6} a^{5}-a^{4} x^{5}+\frac{5}{3} x^{3} a^{2}+2 a \,x^{2}+x \right)"," ",0,"c^3*(-1/7*a^6*x^7-2/3*x^6*a^5-a^4*x^5+5/3*x^3*a^2+2*a*x^2+x)","A"
584,1,16,15,0.033000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^2,x)","\frac{c^{2} \left(a x +1\right)^{5}}{5 a}"," ",0,"1/5*c^2*(a*x+1)^5/a","A"
585,1,34,44,0.038000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c),x)","-\frac{a^{2} c \,x^{3}}{3}-2 a c \,x^{2}-7 c x -\frac{8 c \ln \left(a x -1\right)}{a}"," ",0,"-1/3*a^2*c*x^3-2*a*c*x^2-7*c*x-8*c/a*ln(a*x-1)","A"
586,1,28,13,0.037000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c),x)","\frac{\frac{1}{a \left(a x -1\right)^{2}}+\frac{1}{a \left(a x -1\right)}}{c}"," ",0,"1/c*(1/a/(a*x-1)^2+1/a/(a*x-1))","B"
587,1,16,16,0.031000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^2,x)","-\frac{1}{3 c^{2} a \left(a x -1\right)^{3}}"," ",0,"-1/3/c^2/a/(a*x-1)^3","A"
588,1,90,77,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^3,x)","\frac{1}{8 c^{3} a \left(a x -1\right)^{4}}-\frac{1}{12 c^{3} a \left(a x -1\right)^{3}}+\frac{1}{16 c^{3} a \left(a x -1\right)^{2}}-\frac{1}{16 a \,c^{3} \left(a x -1\right)}-\frac{\ln \left(a x -1\right)}{32 c^{3} a}+\frac{\ln \left(a x +1\right)}{32 a \,c^{3}}"," ",0,"1/8/c^3/a/(a*x-1)^4-1/12/c^3/a/(a*x-1)^3+1/16/c^3/a/(a*x-1)^2-1/16/a/c^3/(a*x-1)-1/32/c^3/a*ln(a*x-1)+1/32*ln(a*x+1)/a/c^3","A"
589,1,120,108,0.045000," ","int(1/(a*x-1)^2*(a*x+1)^2/(-a^2*c*x^2+c)^4,x)","-\frac{1}{20 c^{4} a \left(a x -1\right)^{5}}+\frac{1}{16 c^{4} a \left(a x -1\right)^{4}}-\frac{1}{16 c^{4} a \left(a x -1\right)^{3}}+\frac{1}{16 c^{4} a \left(a x -1\right)^{2}}-\frac{5}{64 a \,c^{4} \left(a x -1\right)}-\frac{3 \ln \left(a x -1\right)}{64 c^{4} a}-\frac{1}{64 a \,c^{4} \left(a x +1\right)}+\frac{3 \ln \left(a x +1\right)}{64 a \,c^{4}}"," ",0,"-1/20/c^4/a/(a*x-1)^5+1/16/c^4/a/(a*x-1)^4-1/16/c^4/a/(a*x-1)^3+1/16/c^4/a/(a*x-1)^2-5/64/a/c^4/(a*x-1)-3/64/c^4/a*ln(a*x-1)-1/64/a/c^4/(a*x+1)+3/64*ln(a*x+1)/a/c^4","A"
590,1,279,333,0.066000," ","int((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{4} \left(-128 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}+144 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+384 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-456 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-384 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+522 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +384 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-256 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-315 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +315 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{1152 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/1152*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^4/a*(-128*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6+144*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5+384*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-456*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-384*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+522*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+384*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-256*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-315*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+315*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
591,1,231,265,0.053000," ","int((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{3} \left(48 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-56 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-96 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+126 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -64 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-105 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +112 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+105 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{336 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/336*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^3/a*(48*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-56*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-96*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+126*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-64*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-105*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+112*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+105*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
592,1,183,197,0.050000," ","int((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{2} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+45 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -40 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^2/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+45*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-40*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-45*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
593,1,119,121,0.046000," ","int((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c \left(3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c*(3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-3*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
594,1,24,23,0.036000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}}{a c}"," ",0,"-1/a/c*((a*x-1)/(a*x+1))^(1/2)","A"
595,1,49,65,0.040000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^2,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(2 a^{2} x^{2}+2 a x -1\right)}{3 \left(a^{2} x^{2}-1\right) a \,c^{2}}"," ",0,"-1/3*((a*x-1)/(a*x+1))^(1/2)*(2*a^2*x^2+2*a*x-1)/(a^2*x^2-1)/a/c^2","A"
596,1,65,106,0.038000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^3,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(8 x^{4} a^{4}+8 x^{3} a^{3}-12 a^{2} x^{2}-12 a x +3\right)}{15 \left(a^{2} x^{2}-1\right)^{2} c^{3} a}"," ",0,"-1/15*((a*x-1)/(a*x+1))^(1/2)*(8*a^4*x^4+8*a^3*x^3-12*a^2*x^2-12*a*x+3)/(a^2*x^2-1)^2/c^3/a","A"
597,1,81,147,0.042000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^4,x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(16 x^{6} a^{6}+16 x^{5} a^{5}-40 x^{4} a^{4}-40 x^{3} a^{3}+30 a^{2} x^{2}+30 a x -5\right)}{35 \left(a^{2} x^{2}-1\right)^{3} c^{4} a}"," ",0,"-1/35*((a*x-1)/(a*x+1))^(1/2)*(16*a^6*x^6+16*a^5*x^5-40*a^4*x^4-40*a^3*x^3+30*a^2*x^2+30*a*x-5)/(a^2*x^2-1)^3/c^4/a","A"
598,1,61,65,0.033000," ","int((-a^2*c*x^2+c)^4/(a*x+1)*(a*x-1),x)","c^{4} \left(\frac{1}{9} x^{9} a^{8}-\frac{1}{4} a^{7} x^{8}-\frac{2}{7} a^{6} x^{7}+x^{6} a^{5}-\frac{3}{2} x^{4} a^{3}+\frac{2}{3} x^{3} a^{2}+a \,x^{2}-x \right)"," ",0,"c^4*(1/9*x^9*a^8-1/4*a^7*x^8-2/7*a^6*x^7+x^6*a^5-3/2*x^4*a^3+2/3*x^3*a^2+a*x^2-x)","A"
599,1,54,49,0.033000," ","int((-a^2*c*x^2+c)^3/(a*x+1)*(a*x-1),x)","c^{3} \left(-\frac{1}{7} a^{6} x^{7}+\frac{1}{3} x^{6} a^{5}+\frac{1}{5} a^{4} x^{5}-x^{4} a^{3}+\frac{1}{3} x^{3} a^{2}+a \,x^{2}-x \right)"," ",0,"c^3*(-1/7*a^6*x^7+1/3*x^6*a^5+1/5*a^4*x^5-x^4*a^3+1/3*x^3*a^2+a*x^2-x)","A"
600,1,30,33,0.035000," ","int((-a^2*c*x^2+c)^2/(a*x+1)*(a*x-1),x)","c^{2} \left(\frac{1}{5} a^{4} x^{5}-\frac{1}{2} x^{4} a^{3}+a \,x^{2}-x \right)"," ",0,"c^2*(1/5*a^4*x^5-1/2*x^4*a^3+a*x^2-x)","A"
601,1,14,14,0.034000," ","int((-a^2*c*x^2+c)/(a*x+1)*(a*x-1),x)","-\frac{c \left(a x -1\right)^{3}}{3 a}"," ",0,"-1/3*c*(a*x-1)^3/a","A"
602,1,15,14,0.033000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c),x)","\frac{1}{a c \left(a x +1\right)}"," ",0,"1/a/c/(a*x+1)","A"
603,1,60,43,0.041000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^2,x)","\frac{\ln \left(a x -1\right)}{8 c^{2} a}+\frac{1}{4 a \,c^{2} \left(a x +1\right)^{2}}+\frac{1}{4 a \,c^{2} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"1/8/c^2/a*ln(a*x-1)+1/4/a/c^2/(a*x+1)^2+1/4/a/c^2/(a*x+1)-1/8*ln(a*x+1)/a/c^2","A"
604,1,90,74,0.044000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^3,x)","\frac{1}{16 a \,c^{3} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 c^{3} a}+\frac{1}{12 a \,c^{3} \left(a x +1\right)^{3}}+\frac{1}{8 a \,c^{3} \left(a x +1\right)^{2}}+\frac{3}{16 a \,c^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 a \,c^{3}}"," ",0,"1/16/a/c^3/(a*x-1)+1/8/c^3/a*ln(a*x-1)+1/12/a/c^3/(a*x+1)^3+1/8/a/c^3/(a*x+1)^2+3/16/a/c^3/(a*x+1)-1/8*ln(a*x+1)/a/c^3","A"
605,1,120,105,0.047000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^4,x)","-\frac{1}{64 c^{4} a \left(a x -1\right)^{2}}+\frac{5}{64 a \,c^{4} \left(a x -1\right)}+\frac{15 \ln \left(a x -1\right)}{128 c^{4} a}+\frac{1}{32 a \,c^{4} \left(a x +1\right)^{4}}+\frac{1}{16 a \,c^{4} \left(a x +1\right)^{3}}+\frac{3}{32 a \,c^{4} \left(a x +1\right)^{2}}+\frac{5}{32 a \,c^{4} \left(a x +1\right)}-\frac{15 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"-1/64/c^4/a/(a*x-1)^2+5/64/a/c^4/(a*x-1)+15/128/c^4/a*ln(a*x-1)+1/32/a/c^4/(a*x+1)^4+1/16/a/c^4/(a*x+1)^3+3/32/a/c^4/(a*x+1)^2+5/32/a/c^4/(a*x+1)-15/128*ln(a*x+1)/a/c^4","A"
606,1,288,333,0.066000," ","int((-a^2*c*x^2+c)^4*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{4} \left(896 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-3024 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+1920 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+4200 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-6528 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+1134 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +8064 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-4352 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-3465 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +3465 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{8064 a \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/8064*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^4/a*(896*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6-3024*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5+1920*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+4200*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-6528*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+1134*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+8064*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-4352*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-3465*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+3465*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
607,1,240,265,0.052000," ","int((-a^2*c*x^2+c)^3*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{3} \left(80 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+288 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+70 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +192 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+315 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -560 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-315 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{560 a \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"-1/560*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^3/a*(80*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+288*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+70*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+192*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+315*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-560*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-315*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
608,1,192,197,0.048000," ","int((-a^2*c*x^2+c)^2*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{2} \left(24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-90 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +16 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-105 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +120 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+105 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a \right)}{120 a \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}"," ",0,"1/120*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^2/a*(24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-90*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+16*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-105*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+120*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+105*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/(a^2)^(1/2)","A"
609,1,183,121,0.046000," ","int((-a^2*c*x^2+c)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c \left(9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -2 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-9 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) a -24 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right)}{6 \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a \sqrt{a^{2}}}"," ",0,"1/6*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c*(9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-2*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-9*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*a-24*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/a/(a^2)^(1/2)","A"
610,1,24,23,0.040000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{3 a c}"," ",0,"-1/3/a/c*((a*x-1)/(a*x+1))^(3/2)","A"
611,1,49,65,0.040000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^2,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(2 a^{2} x^{2}+6 a x +7\right)}{15 \left(a^{2} x^{2}-1\right) a \,c^{2}}"," ",0,"1/15*((a*x-1)/(a*x+1))^(3/2)*(2*a^2*x^2+6*a*x+7)/(a^2*x^2-1)/a/c^2","A"
612,1,65,106,0.038000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^3,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(8 x^{4} a^{4}+24 x^{3} a^{3}+20 a^{2} x^{2}-4 a x -13\right)}{35 \left(a^{2} x^{2}-1\right)^{2} c^{3} a}"," ",0,"1/35*((a*x-1)/(a*x+1))^(3/2)*(8*a^4*x^4+24*a^3*x^3+20*a^2*x^2-4*a*x-13)/(a^2*x^2-1)^2/c^3/a","A"
613,1,81,147,0.040000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^4,x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(16 x^{6} a^{6}+48 x^{5} a^{5}+24 x^{4} a^{4}-56 x^{3} a^{3}-66 a^{2} x^{2}-6 a x +19\right)}{63 \left(a^{2} x^{2}-1\right)^{3} c^{4} a}"," ",0,"1/63*((a*x-1)/(a*x+1))^(3/2)*(16*a^6*x^6+48*a^5*x^5+24*a^4*x^4-56*a^3*x^3-66*a^2*x^2-6*a*x+19)/(a^2*x^2-1)^3/c^4/a","A"
614,1,116,201,0.036000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(9/2),x)","\frac{x \left(63 a^{9} x^{9}+70 x^{8} a^{8}-315 a^{7} x^{7}-360 x^{6} a^{6}+630 x^{5} a^{5}+756 x^{4} a^{4}-630 x^{3} a^{3}-840 a^{2} x^{2}+315 a x +630\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}{630 \left(a x -1\right)^{4} \left(a x +1\right)^{5} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/630*x*(63*a^9*x^9+70*a^8*x^8-315*a^7*x^7-360*a^6*x^6+630*a^5*x^5+756*a^4*x^4-630*a^3*x^3-840*a^2*x^2+315*a*x+630)*(-a^2*c*x^2+c)^(9/2)/(a*x-1)^4/(a*x+1)^5/((a*x-1)/(a*x+1))^(1/2)","A"
615,1,100,161,0.040000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(7/2),x)","\frac{x \left(35 a^{7} x^{7}+40 x^{6} a^{6}-140 x^{5} a^{5}-168 x^{4} a^{4}+210 x^{3} a^{3}+280 a^{2} x^{2}-140 a x -280\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{280 \left(a x -1\right)^{3} \left(a x +1\right)^{4} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/280*x*(35*a^7*x^7+40*a^6*x^6-140*a^5*x^5-168*a^4*x^4+210*a^3*x^3+280*a^2*x^2-140*a*x-280)*(-a^2*c*x^2+c)^(7/2)/(a*x-1)^3/(a*x+1)^4/((a*x-1)/(a*x+1))^(1/2)","A"
616,1,84,120,0.039000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(5 x^{5} a^{5}+6 x^{4} a^{4}-15 x^{3} a^{3}-20 a^{2} x^{2}+15 a x +30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{30 \left(a x -1\right)^{2} \left(a x +1\right)^{3} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/30*x*(5*a^5*x^5+6*a^4*x^4-15*a^3*x^3-20*a^2*x^2+15*a*x+30)*(-a^2*c*x^2+c)^(5/2)/(a*x-1)^2/(a*x+1)^3/((a*x-1)/(a*x+1))^(1/2)","A"
617,1,68,81,0.040000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(3 x^{3} a^{3}+4 a^{2} x^{2}-6 a x -12\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{12 \left(a x -1\right) \left(a x +1\right)^{2} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/12*x*(3*a^3*x^3+4*a^2*x^2-6*a*x-12)*(-a^2*c*x^2+c)^(3/2)/(a*x-1)/(a*x+1)^2/((a*x-1)/(a*x+1))^(1/2)","A"
618,1,44,58,0.035000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \left(a x +2\right) \sqrt{-a^{2} c \,x^{2}+c}}{2 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/2*x*(a*x+2)*(-a^2*c*x^2+c)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
619,1,51,34,0.065000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\ln \left(a x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}}{a c \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-ln(a*x-1)*(-c*(a^2*x^2-1))^(1/2)/a/c/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
620,1,84,79,0.058000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-\ln \left(a x -1\right)+\ln \left(a x +1\right)+2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a}"," ",0,"-1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)-ln(a*x-1)+ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a","A"
621,1,169,160,0.062000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-3 \ln \left(a x -1\right) x^{2} a^{2}+3 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)-6 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)-4\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a \left(a x +1\right)}"," ",0,"-1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-3*ln(a*x-1)*x^2*a^2+3*ln(a*x+1)*x^2*a^2+6*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)-6*a*x+3*ln(a*x-1)-3*ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a/(a*x+1)","A"
622,1,241,241,0.064000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}-15 \ln \left(a x -1\right) x^{4} a^{4}+15 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}-30 \ln \left(a x -1\right) x^{3} a^{3}+30 a^{3} x^{3} \ln \left(a x +1\right)-30 x^{3} a^{3}+30 \ln \left(a x -1\right) x^{2} a^{2}-30 \ln \left(a x +1\right) x^{2} a^{2}-50 a^{2} x^{2}+15 \ln \left(a x -1\right) x a -15 a x \ln \left(a x +1\right)+50 a x -15 \ln \left(a x -1\right)+15 \ln \left(a x +1\right)+16\right)}{96 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right)^{2} \left(a^{2} x^{2}-1\right) c^{4} a \left(a x +1\right)^{2}}"," ",0,"-1/96/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^2*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5-15*ln(a*x-1)*x^4*a^4+15*ln(a*x+1)*x^4*a^4+30*x^4*a^4-30*ln(a*x-1)*x^3*a^3+30*a^3*x^3*ln(a*x+1)-30*x^3*a^3+30*ln(a*x-1)*x^2*a^2-30*ln(a*x+1)*x^2*a^2-50*a^2*x^2+15*ln(a*x-1)*x*a-15*a*x*ln(a*x+1)+50*a*x-15*ln(a*x-1)+15*ln(a*x+1)+16)/(a^2*x^2-1)/c^4/a/(a*x+1)^2","A"
623,1,350,144,0.045000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(9/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}{10}+\frac{9 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{80}+\frac{21 c^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{160}+\frac{21 c^{3} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{128}+\frac{63 c^{4} x \sqrt{-a^{2} c \,x^{2}+c}}{256}+\frac{63 c^{5} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{256 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{9}{2}}}{9 a}-\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{7}{2}} x}{4}-\frac{7 c^{2} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}} x}{24}-\frac{35 c^{3} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{96}-\frac{35 c^{4} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{64}-\frac{35 c^{5} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{64 \sqrt{a^{2} c}}"," ",0,"1/10*x*(-a^2*c*x^2+c)^(9/2)+9/80*c*x*(-a^2*c*x^2+c)^(7/2)+21/160*c^2*x*(-a^2*c*x^2+c)^(5/2)+21/128*c^3*x*(-a^2*c*x^2+c)^(3/2)+63/256*c^4*x*(-a^2*c*x^2+c)^(1/2)+63/256*c^5/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/9/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(9/2)-1/4*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(7/2)*x-7/24*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)*x-35/96*c^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x-35/64*c^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x-35/64*c^5/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
624,1,296,125,0.044000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(7/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{8}+\frac{7 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{48}+\frac{35 c^{2} x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{192}+\frac{35 c^{3} x \sqrt{-a^{2} c \,x^{2}+c}}{128}+\frac{35 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{128 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{7}{2}}}{7 a}-\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}} x}{3}-\frac{5 c^{2} \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{12}-\frac{5 c^{3} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{8}-\frac{5 c^{4} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{8 \sqrt{a^{2} c}}"," ",0,"1/8*x*(-a^2*c*x^2+c)^(7/2)+7/48*c*x*(-a^2*c*x^2+c)^(5/2)+35/192*c^2*x*(-a^2*c*x^2+c)^(3/2)+35/128*c^3*x*(-a^2*c*x^2+c)^(1/2)+35/128*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/7/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(7/2)-1/3*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)*x-5/12*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x-5/8*c^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x-5/8*c^4/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
625,1,242,106,0.046000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6}+\frac{5 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}+\frac{5 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{16}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{16 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{5}{2}}}{5 a}-\frac{c \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}} x}{2}-\frac{3 c^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x}{4}-\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"1/6*x*(-a^2*c*x^2+c)^(5/2)+5/24*c*x*(-a^2*c*x^2+c)^(3/2)+5/16*c^2*x*(-a^2*c*x^2+c)^(1/2)+5/16*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/5/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(5/2)-1/2*c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)*x-3/4*c^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x-3/4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
626,1,188,87,0.044000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4}+\frac{3 c x \sqrt{-a^{2} c \,x^{2}+c}}{8}+\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 \sqrt{a^{2} c}}+\frac{2 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)\right)^{\frac{3}{2}}}{3 a}-c \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}\, x -\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/4*x*(-a^2*c*x^2+c)^(3/2)+3/8*c*x*(-a^2*c*x^2+c)^(1/2)+3/8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(3/2)-c*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)*x-c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
627,1,134,70,0.042000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/2*x*(-a^2*c*x^2+c)^(1/2)+1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
628,1,79,51,0.043000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{2} c \left(x -\frac{1}{a}\right)}"," ",0,"1/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^2/c/(x-1/a)*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)","A"
629,1,31,43,0.037000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(a x +1\right)^{2} \left(a x -2\right)}{3 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/3*(a*x+1)^2*(a*x-2)/a/(-a^2*c*x^2+c)^(3/2)","A"
630,1,47,62,0.038000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x +1\right)^{2} \left(2 x^{3} a^{3}-4 a^{2} x^{2}+a x +2\right)}{5 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-1/5*(a*x+1)^2*(2*a^3*x^3-4*a^2*x^2+a*x+2)/a/(-a^2*c*x^2+c)^(5/2)","A"
631,1,64,81,0.040000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\left(a x +1\right)^{2} \left(8 x^{5} a^{5}-16 x^{4} a^{4}-4 x^{3} a^{3}+24 a^{2} x^{2}-9 a x -6\right)}{21 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/21*(a*x+1)^2*(8*a^5*x^5-16*a^4*x^4-4*a^3*x^3+24*a^2*x^2-9*a*x-6)/a/(-a^2*c*x^2+c)^(7/2)","A"
632,1,80,100,0.045000," ","int((a*x+1)/(a*x-1)/(-a^2*c*x^2+c)^(9/2),x)","-\frac{\left(a x +1\right)^{2} \left(16 a^{7} x^{7}-32 x^{6} a^{6}-24 x^{5} a^{5}+80 x^{4} a^{4}-10 x^{3} a^{3}-60 a^{2} x^{2}+25 a x +10\right)}{45 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}"," ",0,"-1/45*(a*x+1)^2*(16*a^7*x^7-32*a^6*x^6-24*a^5*x^5+80*a^4*x^4-10*a^3*x^3-60*a^2*x^2+25*a*x+10)/a/(-a^2*c*x^2+c)^(9/2)","A"
633,1,100,161,0.046000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(9/2),x)","\frac{x \left(21 a^{9} x^{9}+70 x^{8} a^{8}-240 x^{6} a^{6}-210 x^{5} a^{5}+252 x^{4} a^{4}+420 x^{3} a^{3}-315 a x -210\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}{210 \left(a x -1\right)^{3} \left(a x +1\right)^{6} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/210*x*(21*a^9*x^9+70*a^8*x^8-240*a^6*x^6-210*a^5*x^5+252*a^4*x^4+420*a^3*x^3-315*a*x-210)*(-a^2*c*x^2+c)^(9/2)/(a*x-1)^3/(a*x+1)^6/((a*x-1)/(a*x+1))^(3/2)","A"
634,1,100,121,0.041000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(7/2),x)","\frac{x \left(21 a^{7} x^{7}+72 x^{6} a^{6}+28 x^{5} a^{5}-168 x^{4} a^{4}-210 x^{3} a^{3}+56 a^{2} x^{2}+252 a x +168\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}{168 \left(a x -1\right)^{2} \left(a x +1\right)^{5} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/168*x*(21*a^7*x^7+72*a^6*x^6+28*a^5*x^5-168*a^4*x^4-210*a^3*x^3+56*a^2*x^2+252*a*x+168)*(-a^2*c*x^2+c)^(7/2)/(a*x-1)^2/(a*x+1)^5/((a*x-1)/(a*x+1))^(3/2)","A"
635,1,84,81,0.040000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(5/2),x)","\frac{x \left(5 x^{5} a^{5}+18 x^{4} a^{4}+15 x^{3} a^{3}-20 a^{2} x^{2}-45 a x -30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{30 \left(a x -1\right) \left(a x +1\right)^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/30*x*(5*a^5*x^5+18*a^4*x^4+15*a^3*x^3-20*a^2*x^2-45*a*x-30)*(-a^2*c*x^2+c)^(5/2)/(a*x-1)/(a*x+1)^4/((a*x-1)/(a*x+1))^(3/2)","A"
636,1,60,40,0.038000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(3/2),x)","\frac{x \left(x^{3} a^{3}+4 a^{2} x^{2}+6 a x +4\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 \left(a x +1\right)^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/4*x*(a^3*x^3+4*a^2*x^2+6*a*x+4)*(-a^2*c*x^2+c)^(3/2)/(a*x+1)^3/((a*x-1)/(a*x+1))^(3/2)","A"
637,1,67,99,0.053000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(a^{2} x^{2}+6 a x +8 \ln \left(a x -1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{2 a \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/2*(a^2*x^2+6*a*x+8*ln(a*x-1))*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/a/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
638,1,64,71,0.057000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -\ln \left(a x -1\right)-2\right)}{a c \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-ln(a*x-1)-2)/a/c/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
639,1,39,41,0.037000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{a x -1}{2 a \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-1/2*(a*x-1)/a/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2)","A"
640,1,169,161,0.069000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-9 \ln \left(a x -1\right) x^{2} a^{2}+9 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)-18 a x -3 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)+20\right)}{48 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right) \left(a x +1\right) \left(a^{2} x^{2}-1\right) c^{3} a}"," ",0,"1/48/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)/(a*x+1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-9*ln(a*x-1)*x^2*a^2+9*ln(a*x+1)*x^2*a^2+6*a^2*x^2+9*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)-18*a*x-3*ln(a*x-1)+3*ln(a*x+1)+20)/(a^2*x^2-1)/c^3/a","A"
641,1,241,242,0.068000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}-45 \ln \left(a x -1\right) x^{4} a^{4}+45 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}+30 \ln \left(a x -1\right) x^{3} a^{3}-30 a^{3} x^{3} \ln \left(a x +1\right)-90 x^{3} a^{3}+30 \ln \left(a x -1\right) x^{2} a^{2}-30 \ln \left(a x +1\right) x^{2} a^{2}+70 a^{2} x^{2}-45 \ln \left(a x -1\right) x a +45 a x \ln \left(a x +1\right)+30 a x +15 \ln \left(a x -1\right)-15 \ln \left(a x +1\right)-64\right)}{192 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x -1\right)^{2} \left(a x +1\right)^{2} \left(a^{2} x^{2}-1\right) c^{4} a}"," ",0,"1/192/((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/(a*x+1)^2*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5-45*ln(a*x-1)*x^4*a^4+45*ln(a*x+1)*x^4*a^4+30*x^4*a^4+30*ln(a*x-1)*x^3*a^3-30*a^3*x^3*ln(a*x+1)-90*x^3*a^3+30*ln(a*x-1)*x^2*a^2-30*ln(a*x+1)*x^2*a^2+70*a^2*x^2-45*ln(a*x-1)*x*a+45*a*x*ln(a*x+1)+30*a*x+15*ln(a*x-1)-15*ln(a*x+1)-64)/(a^2*x^2-1)/c^4/a","A"
642,1,116,206,0.041000," ","int((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(63 a^{9} x^{9}-70 x^{8} a^{8}-315 a^{7} x^{7}+360 x^{6} a^{6}+630 x^{5} a^{5}-756 x^{4} a^{4}-630 x^{3} a^{3}+840 a^{2} x^{2}+315 a x -630\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}} \sqrt{\frac{a x -1}{a x +1}}}{630 \left(a x +1\right)^{4} \left(a x -1\right)^{5}}"," ",0,"1/630*x*(63*a^9*x^9-70*a^8*x^8-315*a^7*x^7+360*a^6*x^6+630*a^5*x^5-756*a^4*x^4-630*a^3*x^3+840*a^2*x^2+315*a*x-630)*(-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)^4/(a*x-1)^5","A"
643,1,100,165,0.040000," ","int((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(35 a^{7} x^{7}-40 x^{6} a^{6}-140 x^{5} a^{5}+168 x^{4} a^{4}+210 x^{3} a^{3}-280 a^{2} x^{2}-140 a x +280\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} \sqrt{\frac{a x -1}{a x +1}}}{280 \left(a x +1\right)^{3} \left(a x -1\right)^{4}}"," ",0,"1/280*x*(35*a^7*x^7-40*a^6*x^6-140*a^5*x^5+168*a^4*x^4+210*a^3*x^3-280*a^2*x^2-140*a*x+280)*(-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)^3/(a*x-1)^4","A"
644,1,84,123,0.040000," ","int((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(5 x^{5} a^{5}-6 x^{4} a^{4}-15 x^{3} a^{3}+20 a^{2} x^{2}+15 a x -30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \sqrt{\frac{a x -1}{a x +1}}}{30 \left(a x +1\right)^{2} \left(a x -1\right)^{3}}"," ",0,"1/30*x*(5*a^5*x^5-6*a^4*x^4-15*a^3*x^3+20*a^2*x^2+15*a*x-30)*(-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)^2/(a*x-1)^3","A"
645,1,68,83,0.039000," ","int((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(3 x^{3} a^{3}-4 a^{2} x^{2}-6 a x +12\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \sqrt{\frac{a x -1}{a x +1}}}{12 \left(a x +1\right) \left(a x -1\right)^{2}}"," ",0,"1/12*x*(3*a^3*x^3-4*a^2*x^2-6*a*x+12)*(-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)/(a*x-1)^2","A"
646,1,44,59,0.039000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(a x -2\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\frac{a x -1}{a x +1}}}{2 a x -2}"," ",0,"1/2*x*(a*x-2)*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
647,1,51,33,0.051000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\ln \left(a x +1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}{a c \left(a x -1\right)}"," ",0,"-ln(a*x+1)*(-c*(a^2*x^2-1))^(1/2)*((a*x-1)/(a*x+1))^(1/2)/a/c/(a*x-1)","A"
648,1,84,78,0.062000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)+\ln \left(a x -1\right)-\ln \left(a x +1\right)+2\right)}{4 \left(a^{2} x^{2}-1\right) c^{2} a}"," ",0,"1/4*((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)+ln(a*x-1)-ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a","A"
649,1,169,159,0.069000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)+3 \ln \left(a x -1\right) x^{2} a^{2}-3 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)+6 a x -3 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)-4\right)}{16 \left(a x +1\right) \left(a^{2} x^{2}-1\right) c^{3} a \left(a x -1\right)}"," ",0,"1/16*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)+3*ln(a*x-1)*x^2*a^2-3*ln(a*x+1)*x^2*a^2+6*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)+6*a*x-3*ln(a*x-1)+3*ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a/(a*x-1)","A"
650,1,241,240,0.069000," ","int(((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}+15 \ln \left(a x -1\right) x^{4} a^{4}-15 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}-30 \ln \left(a x -1\right) x^{3} a^{3}+30 a^{3} x^{3} \ln \left(a x +1\right)+30 x^{3} a^{3}-30 \ln \left(a x -1\right) x^{2} a^{2}+30 \ln \left(a x +1\right) x^{2} a^{2}-50 a^{2} x^{2}+15 \ln \left(a x -1\right) x a -15 a x \ln \left(a x +1\right)-50 a x +15 \ln \left(a x -1\right)-15 \ln \left(a x +1\right)+16\right)}{96 \left(a x +1\right)^{2} \left(a^{2} x^{2}-1\right) c^{4} a \left(a x -1\right)^{2}}"," ",0,"1/96*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)^2*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5+15*ln(a*x-1)*x^4*a^4-15*ln(a*x+1)*x^4*a^4+30*x^4*a^4-30*ln(a*x-1)*x^3*a^3+30*a^3*x^3*ln(a*x+1)+30*x^3*a^3-30*ln(a*x-1)*x^2*a^2+30*ln(a*x+1)*x^2*a^2-50*a^2*x^2+15*ln(a*x-1)*x*a-15*a*x*ln(a*x+1)-50*a*x+15*ln(a*x-1)-15*ln(a*x+1)+16)/(a^2*x^2-1)/c^4/a/(a*x-1)^2","A"
651,1,226,107,0.051000," ","int((-a^2*c*x^2+c)^(5/2)/(a*x+1)*(a*x-1),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}{6}+\frac{5 c x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{24}+\frac{5 c^{2} x \sqrt{-a^{2} c \,x^{2}+c}}{16}+\frac{5 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{16 \sqrt{a^{2} c}}-\frac{2 \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c \right)^{\frac{5}{2}}}{5 a}-\frac{c \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c \right)^{\frac{3}{2}} x}{2}-\frac{3 c^{2} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}\, x}{4}-\frac{3 c^{3} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{4 \sqrt{a^{2} c}}"," ",0,"1/6*x*(-a^2*c*x^2+c)^(5/2)+5/24*c*x*(-a^2*c*x^2+c)^(3/2)+5/16*c^2*x*(-a^2*c*x^2+c)^(1/2)+5/16*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/5/a*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(5/2)-1/2*c*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(3/2)*x-3/4*c^2*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)*x-3/4*c^3/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
652,1,176,88,0.046000," ","int((-a^2*c*x^2+c)^(3/2)/(a*x+1)*(a*x-1),x)","\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4}+\frac{3 c x \sqrt{-a^{2} c \,x^{2}+c}}{8}+\frac{3 c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 \sqrt{a^{2} c}}-\frac{2 \left(-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c \right)^{\frac{3}{2}}}{3 a}-c \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}\, x -\frac{c^{2} \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/4*x*(-a^2*c*x^2+c)^(3/2)+3/8*c*x*(-a^2*c*x^2+c)^(1/2)+3/8*c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(3/2)-c*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)*x-c^2/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
653,1,126,71,0.048000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/2*x*(-a^2*c*x^2+c)^(1/2)+1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)-2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
654,1,73,52,0.044000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a^{2} c \left(x +\frac{1}{a}\right)}"," ",0,"1/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^2/c/(x+1/a)*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)","A"
655,1,31,44,0.039000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(a x -1\right)^{2} \left(a x +2\right)}{3 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"1/3*(a*x-1)^2*(a*x+2)/a/(-a^2*c*x^2+c)^(3/2)","A"
656,1,47,63,0.039000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x -1\right)^{2} \left(2 x^{3} a^{3}+4 a^{2} x^{2}+a x -2\right)}{5 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-1/5*(a*x-1)^2*(2*a^3*x^3+4*a^2*x^2+a*x-2)/a/(-a^2*c*x^2+c)^(5/2)","A"
657,1,64,82,0.040000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^(7/2),x)","\frac{\left(a x -1\right)^{2} \left(8 x^{5} a^{5}+16 x^{4} a^{4}-4 x^{3} a^{3}-24 a^{2} x^{2}-9 a x +6\right)}{21 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"1/21*(a*x-1)^2*(8*a^5*x^5+16*a^4*x^4-4*a^3*x^3-24*a^2*x^2-9*a*x+6)/a/(-a^2*c*x^2+c)^(7/2)","A"
658,1,80,101,0.044000," ","int(1/(a*x+1)*(a*x-1)/(-a^2*c*x^2+c)^(9/2),x)","-\frac{\left(a x -1\right)^{2} \left(16 a^{7} x^{7}+32 x^{6} a^{6}-24 x^{5} a^{5}-80 x^{4} a^{4}-10 x^{3} a^{3}+60 a^{2} x^{2}+25 a x -10\right)}{45 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}"," ",0,"-1/45*(a*x-1)^2*(16*a^7*x^7+32*a^6*x^6-24*a^5*x^5-80*a^4*x^4-10*a^3*x^3+60*a^2*x^2+25*a*x-10)/a/(-a^2*c*x^2+c)^(9/2)","A"
659,1,100,165,0.038000," ","int((-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{x \left(21 a^{9} x^{9}-70 x^{8} a^{8}+240 x^{6} a^{6}-210 x^{5} a^{5}-252 x^{4} a^{4}+420 x^{3} a^{3}-315 a x +210\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{210 \left(a x +1\right)^{3} \left(a x -1\right)^{6}}"," ",0,"1/210*x*(21*a^9*x^9-70*a^8*x^8+240*a^6*x^6-210*a^5*x^5-252*a^4*x^4+420*a^3*x^3-315*a*x+210)*(-a^2*c*x^2+c)^(9/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^3/(a*x-1)^6","A"
660,1,100,124,0.039000," ","int((-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{x \left(21 a^{7} x^{7}-72 x^{6} a^{6}+28 x^{5} a^{5}+168 x^{4} a^{4}-210 x^{3} a^{3}-56 a^{2} x^{2}+252 a x -168\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{168 \left(a x +1\right)^{2} \left(a x -1\right)^{5}}"," ",0,"1/168*x*(21*a^7*x^7-72*a^6*x^6+28*a^5*x^5+168*a^4*x^4-210*a^3*x^3-56*a^2*x^2+252*a*x-168)*(-a^2*c*x^2+c)^(7/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^2/(a*x-1)^5","A"
661,1,84,83,0.035000," ","int((-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{x \left(5 x^{5} a^{5}-18 x^{4} a^{4}+15 x^{3} a^{3}+20 a^{2} x^{2}-45 a x +30\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{30 \left(a x +1\right) \left(a x -1\right)^{4}}"," ",0,"1/30*x*(5*a^5*x^5-18*a^4*x^4+15*a^3*x^3+20*a^2*x^2-45*a*x+30)*(-a^2*c*x^2+c)^(5/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/(a*x-1)^4","A"
662,1,60,41,0.041000," ","int((-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{x \left(x^{3} a^{3}-4 a^{2} x^{2}+6 a x -4\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{3}}"," ",0,"1/4*x*(a^3*x^3-4*a^2*x^2+6*a*x-4)*(-a^2*c*x^2+c)^(3/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3","A"
663,1,67,98,0.049000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(a^{2} x^{2}-6 a x +8 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \left(a x -1\right)^{2}}"," ",0,"1/2*(a^2*x^2-6*a*x+8*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^2","A"
664,1,62,69,0.058000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(1/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x \ln \left(a x +1\right)+\ln \left(a x +1\right)+2\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{a c \left(a x -1\right)^{2}}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(a*x*ln(a*x+1)+ln(a*x+1)+2)*((a*x-1)/(a*x+1))^(3/2)/a/c/(a*x-1)^2","A"
665,1,39,40,0.036000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-1/2*(a*x+1)/a*((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(3/2)","A"
666,1,169,158,0.062000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)+9 \ln \left(a x -1\right) x^{2} a^{2}-9 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)+18 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)+20\right)}{48 \left(a x +1\right) \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a}"," ",0,"-1/48*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)+9*ln(a*x-1)*x^2*a^2-9*ln(a*x+1)*x^2*a^2+6*a^2*x^2+9*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)+18*a*x+3*ln(a*x-1)-3*ln(a*x+1)+20)/(a^2*x^2-1)/c^3/a","A"
667,1,241,239,0.067000," ","int(((a*x-1)/(a*x+1))^(3/2)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(15 \ln \left(a x -1\right) x^{5} a^{5}-15 \ln \left(a x +1\right) x^{5} a^{5}+45 \ln \left(a x -1\right) x^{4} a^{4}-45 \ln \left(a x +1\right) x^{4} a^{4}+30 x^{4} a^{4}+30 \ln \left(a x -1\right) x^{3} a^{3}-30 a^{3} x^{3} \ln \left(a x +1\right)+90 x^{3} a^{3}-30 \ln \left(a x -1\right) x^{2} a^{2}+30 \ln \left(a x +1\right) x^{2} a^{2}+70 a^{2} x^{2}-45 \ln \left(a x -1\right) x a +45 a x \ln \left(a x +1\right)-30 a x -15 \ln \left(a x -1\right)+15 \ln \left(a x +1\right)-64\right)}{192 \left(a x +1\right)^{2} \left(a x -1\right)^{2} \left(a^{2} x^{2}-1\right) c^{4} a}"," ",0,"-1/192*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^2/(a*x-1)^2*(-c*(a^2*x^2-1))^(1/2)*(15*ln(a*x-1)*x^5*a^5-15*ln(a*x+1)*x^5*a^5+45*ln(a*x-1)*x^4*a^4-45*ln(a*x+1)*x^4*a^4+30*x^4*a^4+30*ln(a*x-1)*x^3*a^3-30*a^3*x^3*ln(a*x+1)+90*x^3*a^3-30*ln(a*x-1)*x^2*a^2+30*ln(a*x+1)*x^2*a^2+70*a^2*x^2-45*ln(a*x-1)*x*a+45*a*x*ln(a*x+1)-30*a*x-15*ln(a*x-1)+15*ln(a*x+1)-64)/(a^2*x^2-1)/c^4/a","A"
668,1,47,64,0.039000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{3} \left(3 a x +4\right) \sqrt{-a^{2} c \,x^{2}+c}}{12 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/12*x^3*(3*a*x+4)*(-a^2*c*x^2+c)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
669,1,47,62,0.034000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{2} \left(2 a x +3\right) \sqrt{-a^{2} c \,x^{2}+c}}{6 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/6*x^2*(2*a*x+3)*(-a^2*c*x^2+c)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
670,1,44,58,0.034000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \left(a x +2\right) \sqrt{-a^{2} c \,x^{2}+c}}{2 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/2*x*(a*x+2)*(-a^2*c*x^2+c)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
671,1,44,61,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x,x)","\frac{\left(a x +\ln \left(x \right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}}{\left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(a*x+ln(x))*(-c*(a^2*x^2-1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
672,1,48,65,0.054000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","\frac{\left(a \ln \left(x \right) x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}}{x \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(a*ln(x)*x-1)*(-c*(a^2*x^2-1))^(1/2)/x/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
673,1,210,113,0.054000," ","int((a*x+1)/(a*x-1)*x^3*(-a^2*c*x^2+c)^(1/2),x)","-\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 a^{2} c}-\frac{4 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 c \,a^{4}}-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 a^{3} c}+\frac{5 x \sqrt{-a^{2} c \,x^{2}+c}}{4 a^{3}}+\frac{5 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 a^{3} \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{4}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{3} \sqrt{a^{2} c}}"," ",0,"-1/5*x^2*(-a^2*c*x^2+c)^(3/2)/a^2/c-4/5/c/a^4*(-a^2*c*x^2+c)^(3/2)-1/2/a^3*x*(-a^2*c*x^2+c)^(3/2)/c+5/4/a^3*x*(-a^2*c*x^2+c)^(1/2)+5/4/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
674,1,186,92,0.050000," ","int((a*x+1)/(a*x-1)*x^2*(-a^2*c*x^2+c)^(1/2),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 a^{2} c}+\frac{9 x \sqrt{-a^{2} c \,x^{2}+c}}{8 a^{2}}+\frac{9 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a^{2} \sqrt{a^{2} c}}-\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{3} c}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{3}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a^{2} \sqrt{a^{2} c}}"," ",0,"-1/4*x*(-a^2*c*x^2+c)^(3/2)/a^2/c+9/8/a^2*x*(-a^2*c*x^2+c)^(1/2)+9/8/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3/a^3*(-a^2*c*x^2+c)^(3/2)/c+2/a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
675,1,162,71,0.046000," ","int((a*x+1)/(a*x-1)*x*(-a^2*c*x^2+c)^(1/2),x)","-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{2} c}+\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{a}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a^{2}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{a \sqrt{a^{2} c}}"," ",0,"-1/3*(-a^2*c*x^2+c)^(3/2)/a^2/c+x/a*(-a^2*c*x^2+c)^(1/2)+1/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
676,1,134,70,0.043000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2),x)","\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}{a}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/2*x*(-a^2*c*x^2+c)^(1/2)+1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","A"
677,1,129,61,0.049000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2)/x,x)","-\sqrt{-a^{2} c \,x^{2}+c}+\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+2 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}-\frac{2 a c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"-(-a^2*c*x^2+c)^(1/2)+c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
678,1,208,68,0.052000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","2 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a -2 \sqrt{-a^{2} c \,x^{2}+c}\, a +\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+a^{2} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+2 a \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}-\frac{2 a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}"," ",0,"2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a-2*(-a^2*c*x^2+c)^(1/2)*a+1/c/x*(-a^2*c*x^2+c)^(3/2)+a^2*x*(-a^2*c*x^2+c)^(1/2)+a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2*a*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))","B"
679,1,239,64,0.057000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2)/x^3,x)","\frac{3 \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) \sqrt{c}\, a^{2}}{2}-\frac{3 \sqrt{-a^{2} c \,x^{2}+c}\, a^{2}}{2}+\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{3} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+2 a^{2} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}-\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 c \,x^{2}}"," ",0,"3/2*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*c^(1/2)*a^2-3/2*(-a^2*c*x^2+c)^(1/2)*a^2+2*a/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^3*x*(-a^2*c*x^2+c)^(1/2)+2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2*a^2*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))+1/2/c/x^2*(-a^2*c*x^2+c)^(3/2)","B"
680,1,261,83,0.057000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2)/x^4,x)","\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{3}-\sqrt{-a^{2} c \,x^{2}+c}\, a^{3}+\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{4} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}+2 a^{3} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}-\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}+\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c \,x^{2}}"," ",0,"c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^3-(-a^2*c*x^2+c)^(1/2)*a^3+2*a^2/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^4*x*(-a^2*c*x^2+c)^(1/2)+2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+1/3/c/x^3*(-a^2*c*x^2+c)^(3/2)+2*a^3*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))+a/c/x^2*(-a^2*c*x^2+c)^(3/2)","B"
681,1,287,106,0.061000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^(1/2)/x^5,x)","\frac{7 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{4}}{8}-\frac{7 \sqrt{-a^{2} c \,x^{2}+c}\, a^{4}}{8}+\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{5} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}+2 a^{4} \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}-\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2} c -2 a c \left(x -\frac{1}{a}\right)}}\right)}{\sqrt{a^{2} c}}+\frac{9 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{8 c \,x^{2}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 c \,x^{4}}"," ",0,"7/8*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^4-7/8*(-a^2*c*x^2+c)^(1/2)*a^4+2*a^3/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^5*x*(-a^2*c*x^2+c)^(1/2)+2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3*a/c/x^3*(-a^2*c*x^2+c)^(3/2)+2*a^4*(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2)-2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x-1/a)^2*a^2*c-2*a*c*(x-1/a))^(1/2))+9/8*a^2/c/x^2*(-a^2*c*x^2+c)^(3/2)+1/4/c/x^4*(-a^2*c*x^2+c)^(3/2)","B"
682,1,92,198,0.061000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(12 x^{5} a^{5}+45 x^{4} a^{4}+80 x^{3} a^{3}+120 a^{2} x^{2}+240 a x +240 \ln \left(a x -1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{60 a^{4} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/60*(12*x^5*a^5+45*x^4*a^4+80*x^3*a^3+120*a^2*x^2+240*a*x+240*ln(a*x-1))*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/a^4/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
683,1,83,164,0.056000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(x^{4} a^{4}+4 x^{3} a^{3}+8 a^{2} x^{2}+16 a x +16 \ln \left(a x -1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{4 a^{3} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/4*(x^4*a^4+4*x^3*a^3+8*a^2*x^2+16*a*x+16*ln(a*x-1))*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/a^3/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
684,1,76,132,0.053000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(2 x^{3} a^{3}+9 a^{2} x^{2}+24 a x +24 \ln \left(a x -1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{6 a^{2} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/6*(2*x^3*a^3+9*a^2*x^2+24*a*x+24*ln(a*x-1))*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/a^2/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
685,1,67,99,0.052000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2),x)","\frac{\left(a^{2} x^{2}+6 a x +8 \ln \left(a x -1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{2 a \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/2*(a^2*x^2+6*a*x+8*ln(a*x-1))*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/a/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
686,1,59,102,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-a x +\ln \left(x \right)-4 \ln \left(a x -1\right)\right) \left(a x -1\right)}{\left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(-a*x+ln(x)-4*ln(a*x-1))*(a*x-1)/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
687,1,65,102,0.062000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^2,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 a \ln \left(x \right) x -4 \ln \left(a x -1\right) x a -1\right) \left(a x -1\right)}{x \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(3*a*ln(x)*x-4*ln(a*x-1)*x*a-1)*(a*x-1)/x/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
688,1,77,135,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^3,x)","-\frac{\left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x -1\right) x^{2} a^{2}-6 a x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{2 x^{2} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/2*(8*a^2*ln(x)*x^2-8*ln(a*x-1)*x^2*a^2-6*a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/x^2/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
689,1,85,170,0.058000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^4,x)","-\frac{\left(24 a^{3} \ln \left(x \right) x^{3}-24 \ln \left(a x -1\right) x^{3} a^{3}-24 a^{2} x^{2}-9 a x -2\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{6 x^{3} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/6*(24*a^3*ln(x)*x^3-24*ln(a*x-1)*x^3*a^3-24*a^2*x^2-9*a*x-2)*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/x^3/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
690,1,93,202,0.062000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^(1/2)/x^5,x)","-\frac{\left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x -1\right) x^{4} a^{4}-16 x^{3} a^{3}-8 a^{2} x^{2}-4 a x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x -1\right)}{4 x^{4} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/4*(16*a^4*ln(x)*x^4-16*ln(a*x-1)*x^4*a^4-16*x^3*a^3-8*a^2*x^2-4*a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(a*x-1)/x^4/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
691,1,106,183,0.060000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(2 x^{3} a^{3}+2 a^{2} x^{2}+7 \ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-4 a x -7 \ln \left(a x -1\right)-\ln \left(a x +1\right)-2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a^{5}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(2*x^3*a^3+2*a^2*x^2+7*ln(a*x-1)*x*a+a*x*ln(a*x+1)-4*a*x-7*ln(a*x-1)-ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^5","A"
692,1,97,150,0.058000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a^{2} x^{2}+5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 a x -5 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a^{4}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a^2*x^2+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*a*x-5*ln(a*x-1)+ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^4","A"
693,1,86,112,0.057000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-3 \ln \left(a x -1\right)-\ln \left(a x +1\right)-2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a^{3}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x*a+a*x*ln(a*x+1)-3*ln(a*x-1)-ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^3","A"
694,1,84,75,0.058000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-\ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a^{2}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)-ln(a*x-1)+ln(a*x+1)-2)/(a^2*x^2-1)/c^2/a^2","A"
695,1,84,79,0.060000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-\ln \left(a x -1\right)+\ln \left(a x +1\right)+2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} a}"," ",0,"-1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x*a-a*x*ln(a*x+1)-ln(a*x-1)+ln(a*x+1)+2)/(a^2*x^2-1)/c^2/a","A"
696,1,92,155,0.060000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a \ln \left(x \right) x -3 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 \ln \left(x \right)+3 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a*ln(x)*x-3*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*ln(x)+3*ln(a*x-1)+ln(a*x+1)-2)/(a^2*x^2-1)/c^2","A"
697,1,118,188,0.067000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(4 a^{2} \ln \left(x \right) x^{2}-5 \ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}-4 a \ln \left(x \right) x +5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-6 a x +4\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} x}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(4*a^2*ln(x)*x^2-5*ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2-4*a*ln(x)*x+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-6*a*x+4)/(a^2*x^2-1)/c^2/x","A"
698,1,138,220,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^3/(-a^2*c*x^2+c)^(3/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(8 a^{3} \ln \left(x \right) x^{3}-7 \ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-8 a^{2} \ln \left(x \right) x^{2}+7 \ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}-6 a^{2} x^{2}+2 a x +2\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, \left(a^{2} x^{2}-1\right) c^{2} x^{2}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(-c*(a^2*x^2-1))^(1/2)*(8*a^3*ln(x)*x^3-7*ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-8*a^2*ln(x)*x^2+7*ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2-6*a^2*x^2+2*a*x+2)/(a^2*x^2-1)/c^2/x^2","A"
699,1,185,230,0.068000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^5/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 x^{4} a^{4}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-16 x^{3} a^{3}-23 \ln \left(a x -1\right) x^{2} a^{2}+7 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+18 a x +23 \ln \left(a x -1\right)-7 \ln \left(a x +1\right)+12\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a^{6} \left(a x +1\right)}"," ",0,"-1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(16*x^4*a^4+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-16*x^3*a^3-23*ln(a*x-1)*x^2*a^2+7*ln(a*x+1)*x^2*a^2-34*a^2*x^2-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+18*a*x+23*ln(a*x-1)-7*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/a^6/(a*x+1)","A"
700,1,169,187,0.063000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^4/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(11 \ln \left(a x -1\right) x^{3} a^{3}+5 a^{3} x^{3} \ln \left(a x +1\right)-11 \ln \left(a x -1\right) x^{2} a^{2}-5 \ln \left(a x +1\right) x^{2} a^{2}-10 a^{2} x^{2}-11 \ln \left(a x -1\right) x a -5 a x \ln \left(a x +1\right)-6 a x +11 \ln \left(a x -1\right)+5 \ln \left(a x +1\right)+12\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a^{5} \left(a x +1\right)}"," ",0,"-1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(11*ln(a*x-1)*x^3*a^3+5*a^3*x^3*ln(a*x+1)-11*ln(a*x-1)*x^2*a^2-5*ln(a*x+1)*x^2*a^2-10*a^2*x^2-11*ln(a*x-1)*x*a-5*a*x*ln(a*x+1)-6*a*x+11*ln(a*x-1)+5*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/a^5/(a*x+1)","A"
701,1,169,152,0.065000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-3 \ln \left(a x -1\right) x^{2} a^{2}+3 \ln \left(a x +1\right) x^{2} a^{2}-10 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)+2 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)+4\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a^{4} \left(a x +1\right)}"," ",0,"-1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-3*ln(a*x-1)*x^2*a^2+3*ln(a*x+1)*x^2*a^2-10*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)+2*a*x+3*ln(a*x-1)-3*ln(a*x+1)+4)/(a^2*x^2-1)/c^3/a^4/(a*x+1)","A"
702,1,164,160,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-\ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}+2 a^{2} x^{2}-\ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)+6 a x +\ln \left(a x -1\right)-\ln \left(a x +1\right)-4\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a^{3} \left(a x +1\right)}"," ",0,"1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2+2*a^2*x^2-ln(a*x-1)*x*a+a*x*ln(a*x+1)+6*a*x+ln(a*x-1)-ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a^3/(a*x+1)","A"
703,1,164,119,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(\ln \left(a x -1\right) x^{3} a^{3}-a^{3} x^{3} \ln \left(a x +1\right)-\ln \left(a x -1\right) x^{2} a^{2}+\ln \left(a x +1\right) x^{2} a^{2}+2 a^{2} x^{2}-\ln \left(a x -1\right) x a +a x \ln \left(a x +1\right)-2 a x +\ln \left(a x -1\right)-\ln \left(a x +1\right)+4\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a^{2} \left(a x +1\right)}"," ",0,"1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(ln(a*x-1)*x^3*a^3-a^3*x^3*ln(a*x+1)-ln(a*x-1)*x^2*a^2+ln(a*x+1)*x^2*a^2+2*a^2*x^2-ln(a*x-1)*x*a+a*x*ln(a*x+1)-2*a*x+ln(a*x-1)-ln(a*x+1)+4)/(a^2*x^2-1)/c^3/a^2/(a*x+1)","A"
704,1,169,160,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-3 \ln \left(a x -1\right) x^{2} a^{2}+3 \ln \left(a x +1\right) x^{2} a^{2}+6 a^{2} x^{2}-3 \ln \left(a x -1\right) x a +3 a x \ln \left(a x +1\right)-6 a x +3 \ln \left(a x -1\right)-3 \ln \left(a x +1\right)-4\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} a \left(a x +1\right)}"," ",0,"-1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(3*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-3*ln(a*x-1)*x^2*a^2+3*ln(a*x+1)*x^2*a^2+6*a^2*x^2-3*ln(a*x-1)*x*a+3*a*x*ln(a*x+1)-6*a*x+3*ln(a*x-1)-3*ln(a*x+1)-4)/(a^2*x^2-1)/c^3/a/(a*x+1)","A"
705,1,196,237,0.063000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 a^{3} \ln \left(x \right) x^{3}-11 \ln \left(a x -1\right) x^{3} a^{3}-5 a^{3} x^{3} \ln \left(a x +1\right)-16 a^{2} \ln \left(x \right) x^{2}+11 \ln \left(a x -1\right) x^{2} a^{2}+5 \ln \left(a x +1\right) x^{2} a^{2}-6 a^{2} x^{2}-16 a \ln \left(x \right) x +11 \ln \left(a x -1\right) x a +5 a x \ln \left(a x +1\right)-2 a x +16 \ln \left(x \right)-11 \ln \left(a x -1\right)-5 \ln \left(a x +1\right)+12\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} \left(a x +1\right)}"," ",0,"1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(16*a^3*ln(x)*x^3-11*ln(a*x-1)*x^3*a^3-5*a^3*x^3*ln(a*x+1)-16*a^2*ln(x)*x^2+11*ln(a*x-1)*x^2*a^2+5*ln(a*x+1)*x^2*a^2-6*a^2*x^2-16*a*ln(x)*x+11*ln(a*x-1)*x*a+5*a*x*ln(a*x+1)-2*a*x+16*ln(x)-11*ln(a*x-1)-5*ln(a*x+1)+12)/(a^2*x^2-1)/c^3/(a*x+1)","A"
706,1,225,269,0.064000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/x^2/(-a^2*c*x^2+c)^(5/2),x)","\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(16 a^{4} \ln \left(x \right) x^{4}-23 \ln \left(a x -1\right) x^{4} a^{4}+7 \ln \left(a x +1\right) x^{4} a^{4}-16 a^{3} \ln \left(x \right) x^{3}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-30 x^{3} a^{3}-16 a^{2} \ln \left(x \right) x^{2}+23 \ln \left(a x -1\right) x^{2} a^{2}-7 \ln \left(a x +1\right) x^{2} a^{2}+22 a^{2} x^{2}+16 a \ln \left(x \right) x -23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+28 a x -16\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, \left(a x -1\right) \left(a^{2} x^{2}-1\right) c^{3} x \left(a x +1\right)}"," ",0,"1/16/((a*x-1)/(a*x+1))^(1/2)/(a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(16*a^4*ln(x)*x^4-23*ln(a*x-1)*x^4*a^4+7*ln(a*x+1)*x^4*a^4-16*a^3*ln(x)*x^3+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-30*x^3*a^3-16*a^2*ln(x)*x^2+23*ln(a*x-1)*x^2*a^2-7*ln(a*x+1)*x^2*a^2+22*a^2*x^2+16*a*ln(x)*x-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+28*a*x-16)/(a^2*x^2-1)/c^3/x/(a*x+1)","A"
707,1,47,64,0.037000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{3} \left(3 a x -4\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\frac{a x -1}{a x +1}}}{12 a x -12}"," ",0,"1/12*x^3*(3*a*x-4)*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
708,1,47,62,0.036000," ","int(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{2} \left(2 a x -3\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\frac{a x -1}{a x +1}}}{6 a x -6}"," ",0,"1/6*x^2*(2*a*x-3)*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
709,1,44,59,0.034000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x \left(a x -2\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\frac{a x -1}{a x +1}}}{2 a x -2}"," ",0,"1/2*x*(a*x-2)*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
710,1,46,62,0.048000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(-a x +\ln \left(x \right)\right) \sqrt{\frac{a x -1}{a x +1}}}{a x -1}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(-a*x+ln(x))*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
711,1,48,64,0.056000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x)","\frac{\left(a \ln \left(x \right) x +1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}{\left(a x -1\right) x}"," ",0,"(a*ln(x)*x+1)*(-c*(a^2*x^2-1))^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)/x","A"
712,1,202,113,0.056000," ","int(x^3*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{x^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 a^{2} c}-\frac{4 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{5 c \,a^{4}}+\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 a^{3} c}-\frac{5 x \sqrt{-a^{2} c \,x^{2}+c}}{4 a^{3}}-\frac{5 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{4 a^{3} \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a^{4}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{a^{3} \sqrt{a^{2} c}}"," ",0,"-1/5*x^2*(-a^2*c*x^2+c)^(3/2)/a^2/c-4/5/c/a^4*(-a^2*c*x^2+c)^(3/2)+1/2/a^3*x*(-a^2*c*x^2+c)^(3/2)/c-5/4/a^3*x*(-a^2*c*x^2+c)^(1/2)-5/4/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^4*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)+2/a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
713,1,178,92,0.053000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 a^{2} c}+\frac{9 x \sqrt{-a^{2} c \,x^{2}+c}}{8 a^{2}}+\frac{9 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{8 a^{2} \sqrt{a^{2} c}}+\frac{2 \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{3} c}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a^{3}}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{a^{2} \sqrt{a^{2} c}}"," ",0,"-1/4*x*(-a^2*c*x^2+c)^(3/2)/a^2/c+9/8/a^2*x*(-a^2*c*x^2+c)^(1/2)+9/8/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/3/a^3*(-a^2*c*x^2+c)^(3/2)/c-2/a^3*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)-2/a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
714,1,156,70,0.046000," ","int(x*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 a^{2} c}-\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{a}-\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{a \sqrt{a^{2} c}}+\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a^{2}}+\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{a \sqrt{a^{2} c}}"," ",0,"-1/3*(-a^2*c*x^2+c)^(3/2)/a^2/c-x/a*(-a^2*c*x^2+c)^(1/2)-1/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+2/a^2*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)+2/a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
715,1,126,71,0.053000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{x \sqrt{-a^{2} c \,x^{2}+c}}{2}+\frac{c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{2 \sqrt{a^{2} c}}-\frac{2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}{a}-\frac{2 c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"1/2*x*(-a^2*c*x^2+c)^(1/2)+1/2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/a*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)-2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
716,1,121,61,0.051000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1)/x,x)","-\sqrt{-a^{2} c \,x^{2}+c}+\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right)+2 \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}+\frac{2 a c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"-(-a^2*c*x^2+c)^(1/2)+c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)+2*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)+2*a*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","A"
717,1,200,68,0.053000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1)/x^2,x)","-2 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a +2 \sqrt{-a^{2} c \,x^{2}+c}\, a +\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+a^{2} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-2 a \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}-\frac{2 a^{2} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"-2*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a+2*(-a^2*c*x^2+c)^(1/2)*a+1/c/x*(-a^2*c*x^2+c)^(3/2)+a^2*x*(-a^2*c*x^2+c)^(1/2)+a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2*a*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)-2*a^2*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
718,1,231,64,0.052000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1)/x^3,x)","\frac{3 \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) \sqrt{c}\, a^{2}}{2}-\frac{3 \sqrt{-a^{2} c \,x^{2}+c}\, a^{2}}{2}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{3} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{2 c \,x^{2}}+2 a^{2} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}+\frac{2 a^{3} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"3/2*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*c^(1/2)*a^2-3/2*(-a^2*c*x^2+c)^(1/2)*a^2-2*a/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^3*x*(-a^2*c*x^2+c)^(1/2)-2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+1/2/c/x^2*(-a^2*c*x^2+c)^(3/2)+2*a^2*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)+2*a^3*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
719,1,254,85,0.066000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1)/x^4,x)","-\sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{3}+\sqrt{-a^{2} c \,x^{2}+c}\, a^{3}+\frac{2 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}+2 a^{4} x \sqrt{-a^{2} c \,x^{2}+c}+\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}-\frac{a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c \,x^{2}}-2 a^{3} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}-\frac{2 a^{4} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"-c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^3+(-a^2*c*x^2+c)^(1/2)*a^3+2*a^2/c/x*(-a^2*c*x^2+c)^(3/2)+2*a^4*x*(-a^2*c*x^2+c)^(1/2)+2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))+1/3/c/x^3*(-a^2*c*x^2+c)^(3/2)-a/c/x^2*(-a^2*c*x^2+c)^(3/2)-2*a^3*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)-2*a^4*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
720,1,279,106,0.066000," ","int((-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1)/x^5,x)","\frac{7 \sqrt{c}\, \ln \left(\frac{2 c +2 \sqrt{c}\, \sqrt{-a^{2} c \,x^{2}+c}}{x}\right) a^{4}}{8}-\frac{7 \sqrt{-a^{2} c \,x^{2}+c}\, a^{4}}{8}-\frac{2 a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{c x}-2 a^{5} x \sqrt{-a^{2} c \,x^{2}+c}-\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-a^{2} c \,x^{2}+c}}\right)}{\sqrt{a^{2} c}}-\frac{2 a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{3 c \,x^{3}}+\frac{9 a^{2} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{8 c \,x^{2}}+\frac{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}{4 c \,x^{4}}+2 a^{4} \sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}+\frac{2 a^{5} c \arctan \left(\frac{\sqrt{a^{2} c}\, x}{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2} c +2 \left(x +\frac{1}{a}\right) a c}}\right)}{\sqrt{a^{2} c}}"," ",0,"7/8*c^(1/2)*ln((2*c+2*c^(1/2)*(-a^2*c*x^2+c)^(1/2))/x)*a^4-7/8*(-a^2*c*x^2+c)^(1/2)*a^4-2*a^3/c/x*(-a^2*c*x^2+c)^(3/2)-2*a^5*x*(-a^2*c*x^2+c)^(1/2)-2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-a^2*c*x^2+c)^(1/2))-2/3*a/c/x^3*(-a^2*c*x^2+c)^(3/2)+9/8*a^2/c/x^2*(-a^2*c*x^2+c)^(3/2)+1/4/c/x^4*(-a^2*c*x^2+c)^(3/2)+2*a^4*(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2)+2*a^5*c/(a^2*c)^(1/2)*arctan((a^2*c)^(1/2)*x/(-(x+1/a)^2*a^2*c+2*(x+1/a)*a*c)^(1/2))","B"
721,1,92,197,0.056000," ","int(x^3*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-12 x^{5} a^{5}+45 x^{4} a^{4}-80 x^{3} a^{3}+120 a^{2} x^{2}-240 a x +240 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{60 a^{4} \left(a x -1\right)^{2}}"," ",0,"-1/60*(-12*x^5*a^5+45*x^4*a^4-80*x^3*a^3+120*a^2*x^2-240*a*x+240*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a^4/(a*x-1)^2","A"
722,1,83,164,0.054000," ","int(x^2*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(x^{4} a^{4}-4 x^{3} a^{3}+8 a^{2} x^{2}-16 a x +16 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{2} a^{3}}"," ",0,"1/4*(x^4*a^4-4*x^3*a^3+8*a^2*x^2-16*a*x+16*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/a^3","A"
723,1,76,131,0.051000," ","int(x*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-2 x^{3} a^{3}+9 a^{2} x^{2}-24 a x +24 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 a^{2} \left(a x -1\right)^{2}}"," ",0,"-1/6*(-2*x^3*a^3+9*a^2*x^2-24*a*x+24*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a^2/(a*x-1)^2","A"
724,1,67,98,0.049000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(a^{2} x^{2}-6 a x +8 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \left(a x -1\right)^{2}}"," ",0,"1/2*(a^2*x^2-6*a*x+8*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^2","A"
725,1,57,100,0.057000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x)","\frac{\left(a x +\ln \left(x \right)-4 \ln \left(a x +1\right)\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\left(a x -1\right)^{2}}"," ",0,"(a*x+ln(x)-4*ln(a*x+1))*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2","A"
726,1,65,102,0.057000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x)","-\frac{\sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(3 a \ln \left(x \right) x -4 a x \ln \left(a x +1\right)+1\right) \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\left(a x -1\right)^{2} x}"," ",0,"-(-c*(a^2*x^2-1))^(1/2)*(3*a*ln(x)*x-4*a*x*ln(a*x+1)+1)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/x","A"
727,1,77,134,0.059000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x)","\frac{\left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x +1\right) x^{2} a^{2}+6 a x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 x^{2} \left(a x -1\right)^{2}}"," ",0,"1/2*(8*a^2*ln(x)*x^2-8*ln(a*x+1)*x^2*a^2+6*a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/x^2/(a*x-1)^2","A"
728,1,85,169,0.058000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x)","-\frac{\left(24 a^{3} \ln \left(x \right) x^{3}-24 a^{3} x^{3} \ln \left(a x +1\right)+24 a^{2} x^{2}-9 a x +2\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 x^{3} \left(a x -1\right)^{2}}"," ",0,"-1/6*(24*a^3*ln(x)*x^3-24*a^3*x^3*ln(a*x+1)+24*a^2*x^2-9*a*x+2)*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/x^3/(a*x-1)^2","A"
729,1,93,201,0.059000," ","int((-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x)","\frac{\left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x +1\right) x^{4} a^{4}+16 x^{3} a^{3}-8 a^{2} x^{2}+4 a x -1\right) \sqrt{-c \left(a^{2} x^{2}-1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 x^{4} \left(a x -1\right)^{2}}"," ",0,"1/4*(16*a^4*ln(x)*x^4-16*ln(a*x+1)*x^4*a^4+16*x^3*a^3-8*a^2*x^2+4*a*x-1)*(-c*(a^2*x^2-1))^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/x^4/(a*x-1)^2","A"
730,0,0,126,0.386000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\int \frac{x^{m} \sqrt{-a^{2} c \,x^{2}+c}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","F"
731,0,0,154,0.514000," ","int((a*x+1)/(a*x-1)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\int \frac{\left(a x +1\right) x^{m} \sqrt{-a^{2} c \,x^{2}+c}}{a x -1}\, dx"," ",0,"int((a*x+1)/(a*x-1)*x^m*(-a^2*c*x^2+c)^(1/2),x)","F"
732,1,62,74,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(-a^2*c*x^2+c)^(1/2),x)","\frac{x^{1+m} \left(a m x +a x +m +2\right) \sqrt{-a^{2} c \,x^{2}+c}}{\left(2+m \right) \left(1+m \right) \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"x^(1+m)*(a*m*x+a*x+m+2)*(-a^2*c*x^2+c)^(1/2)/(2+m)/(1+m)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
733,1,64,75,0.038000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{1+m} \left(a m x +a x -m -2\right) \sqrt{-a^{2} c \,x^{2}+c}\, \sqrt{\frac{a x -1}{a x +1}}}{\left(2+m \right) \left(1+m \right) \left(a x -1\right)}"," ",0,"x^(1+m)*(a*m*x+a*x-m-2)*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(2+m)/(1+m)/(a*x-1)","A"
734,0,0,154,0.503000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","\int \frac{x^{m} \sqrt{-a^{2} c \,x^{2}+c}\, \left(a x -1\right)}{a x +1}\, dx"," ",0,"int(x^m*(-a^2*c*x^2+c)^(1/2)/(a*x+1)*(a*x-1),x)","F"
735,0,0,127,0.403000," ","int(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\int x^{m} \sqrt{-a^{2} c \,x^{2}+c}\, \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}\, dx"," ",0,"int(x^m*(-a^2*c*x^2+c)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","F"
736,0,0,75,0.393000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^3,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{3}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^3,x)","F"
737,0,0,75,0.378000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^2,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{2}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^2,x)","F"
738,0,0,73,0.057000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c),x)","F"
739,0,0,72,0.033000," ","int(exp(n*arccoth(a*x)),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}\, dx"," ",0,"int(exp(n*arccoth(a*x)),x)","F"
740,1,18,17,0.043000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c),x)","\frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a c n}"," ",0,"exp(n*arccoth(a*x))/a/c/n","A"
741,1,55,70,0.037000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^2,x)","-\frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(2 a^{2} x^{2}-2 x a n +n^{2}-2\right)}{\left(a^{2} x^{2}-1\right) c^{2} a n \left(n^{2}-4\right)}"," ",0,"-exp(n*arccoth(a*x))*(2*a^2*x^2-2*a*n*x+n^2-2)/(a^2*x^2-1)/c^2/a/n/(n^2-4)","A"
742,1,101,118,0.039000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^3,x)","\frac{\left(24 x^{4} a^{4}-24 x^{3} a^{3} n +12 a^{2} n^{2} x^{2}-4 a \,n^{3} x -48 a^{2} x^{2}+n^{4}+40 x a n -16 n^{2}+24\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(a^{2} x^{2}-1\right)^{2} c^{3} a \left(n^{2}-16\right) \left(n^{2}-4\right) n}"," ",0,"(24*a^4*x^4-24*a^3*n*x^3+12*a^2*n^2*x^2-4*a*n^3*x-48*a^2*x^2+n^4+40*a*n*x-16*n^2+24)*exp(n*arccoth(a*x))/(a^2*x^2-1)^2/c^3/a/(n^2-16)/(n^2-4)/n","A"
743,1,167,181,0.045000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^4,x)","-\frac{\left(720 x^{6} a^{6}-720 a^{5} x^{5} n +360 a^{4} n^{2} x^{4}-120 a^{3} n^{3} x^{3}-2160 x^{4} a^{4}+30 a^{2} n^{4} x^{2}+1920 x^{3} a^{3} n -6 a \,n^{5} x -840 a^{2} n^{2} x^{2}+n^{6}+240 a \,n^{3} x +2160 a^{2} x^{2}-50 n^{4}-1584 x a n +544 n^{2}-720\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(a^{2} x^{2}-1\right)^{3} c^{4} a n \left(n^{6}-56 n^{4}+784 n^{2}-2304\right)}"," ",0,"-(720*a^6*x^6-720*a^5*n*x^5+360*a^4*n^2*x^4-120*a^3*n^3*x^3-2160*a^4*x^4+30*a^2*n^4*x^2+1920*a^3*n*x^3-6*a*n^5*x-840*a^2*n^2*x^2+n^6+240*a*n^3*x+2160*a^2*x^2-50*n^4-1584*a*n*x+544*n^2-720)*exp(n*arccoth(a*x))/(a^2*x^2-1)^3/c^4/a/n/(n^6-56*n^4+784*n^2-2304)","A"
744,0,0,100,0.377000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(3/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(3/2),x)","F"
745,0,0,100,0.378000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(1/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \sqrt{-a^{2} c \,x^{2}+c}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^(1/2),x)","F"
746,0,0,95,0.399000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(1/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\sqrt{-a^{2} c \,x^{2}+c}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(1/2),x)","F"
747,1,49,43,0.038000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(a x -n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(n^{2}-1\right) a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(a*x-n)*exp(n*arccoth(a*x))/(n^2-1)/a/(-a^2*c*x^2+c)^(3/2)","A"
748,1,84,90,0.040000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(6 x^{3} a^{3}-6 a^{2} n \,x^{2}+3 a \,n^{2} x -n^{3}-9 a x +7 n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(6*a^3*x^3-6*a^2*n*x^2+3*a*n^2*x-n^3-9*a*x+7*n)*exp(n*arccoth(a*x))/a/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
749,1,140,145,0.040000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(7/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(120 x^{5} a^{5}-120 n \,a^{4} x^{4}+60 a^{3} n^{2} x^{3}-20 a^{2} n^{3} x^{2}-300 x^{3} a^{3}+5 a \,n^{4} x +260 a^{2} n \,x^{2}-n^{5}-110 a \,n^{2} x +30 n^{3}+225 a x -149 n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a \left(n^{6}-35 n^{4}+259 n^{2}-225\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{7}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(120*a^5*x^5-120*a^4*n*x^4+60*a^3*n^2*x^3-20*a^2*n^3*x^2-300*a^3*x^3+5*a*n^4*x+260*a^2*n*x^2-n^5-110*a*n^2*x+30*n^3+225*a*x-149*n)*exp(n*arccoth(a*x))/a/(n^6-35*n^4+259*n^2-225)/(-a^2*c*x^2+c)^(7/2)","A"
750,1,218,203,0.043000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(9/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(5040 a^{7} x^{7}-5040 n \,a^{6} x^{6}+2520 a^{5} n^{2} x^{5}-840 a^{4} n^{3} x^{4}-17640 x^{5} a^{5}+210 a^{3} n^{4} x^{3}+15960 n \,a^{4} x^{4}-42 a^{2} n^{5} x^{2}-7140 a^{3} n^{2} x^{3}+7 a \,n^{6} x +2100 a^{2} n^{3} x^{2}-n^{7}+22050 x^{3} a^{3}-455 a \,n^{4} x -17178 a^{2} n \,x^{2}+77 n^{5}+6433 a \,n^{2} x -1519 n^{3}-11025 a x +6483 n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a \left(n^{8}-84 n^{6}+1974 n^{4}-12916 n^{2}+11025\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{9}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(5040*a^7*x^7-5040*a^6*n*x^6+2520*a^5*n^2*x^5-840*a^4*n^3*x^4-17640*a^5*x^5+210*a^3*n^4*x^3+15960*a^4*n*x^4-42*a^2*n^5*x^2-7140*a^3*n^2*x^3+7*a*n^6*x+2100*a^2*n^3*x^2-n^7+22050*a^3*x^3-455*a*n^4*x-17178*a^2*n*x^2+77*n^5+6433*a*n^2*x-1519*n^3-11025*a*x+6483*n)*exp(n*arccoth(a*x))/a/(n^8-84*n^6+1974*n^4-12916*n^2+11025)/(-a^2*c*x^2+c)^(9/2)","A"
751,0,0,314,0.388000," ","int(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x^{3}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(3/2),x)","F"
752,0,0,145,0.377000," ","int(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x^{2}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(3/2),x)","F"
753,1,49,43,0.037000," ","int(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(x a n -1\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a^{2} \left(n^{2}-1\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(a*n*x-1)*exp(n*arccoth(a*x))/a^2/(n^2-1)/(-a^2*c*x^2+c)^(3/2)","A"
754,1,49,43,0.038000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(3/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(a x -n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(n^{2}-1\right) a \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(a*x-n)*exp(n*arccoth(a*x))/(n^2-1)/a/(-a^2*c*x^2+c)^(3/2)","A"
755,0,0,235,0.400000," ","int(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(3/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(3/2),x)","F"
756,0,0,409,0.382000," ","int(exp(n*arccoth(a*x))*x^4/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} x^{4}}{\left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*x^4/(-a^2*c*x^2+c)^(5/2),x)","F"
757,1,93,291,0.040000," ","int(exp(n*arccoth(a*x))*x^3/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(a^{3} n^{3} x^{3}-7 x^{3} a^{3} n -3 a^{2} n^{2} x^{2}+9 a^{2} x^{2}+6 x a n -6\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a^{4} \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(a^3*n^3*x^3-7*a^3*n*x^3-3*a^2*n^2*x^2+9*a^2*x^2+6*a*n*x-6)*exp(n*arccoth(a*x))/a^4/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
758,1,96,96,0.039000," ","int(exp(n*arccoth(a*x))*x^2/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(a^{3} n^{2} x^{3}-a^{2} n^{3} x^{2}-3 x^{3} a^{3}+3 a^{2} n \,x^{2}+2 a \,n^{2} x -2 n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(n^{4}-10 n^{2}+9\right) a^{3} \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(a^3*n^2*x^3-a^2*n^3*x^2-3*a^3*x^3+3*a^2*n*x^2+2*a*n^2*x-2*n)*exp(n*arccoth(a*x))/(n^4-10*n^2+9)/a^3/(-a^2*c*x^2+c)^(5/2)","A"
759,1,86,91,0.038000," ","int(exp(n*arccoth(a*x))*x/(-a^2*c*x^2+c)^(5/2),x)","-\frac{\left(a x -1\right) \left(a x +1\right) \left(2 x^{3} a^{3} n -2 a^{2} n^{2} x^{2}+a \,n^{3} x -3 x a n -n^{2}+3\right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a^{2} \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"-(a*x-1)*(a*x+1)*(2*a^3*n*x^3-2*a^2*n^2*x^2+a*n^3*x-3*a*n*x-n^2+3)*exp(n*arccoth(a*x))/a^2/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
760,1,84,90,0.040000," ","int(exp(n*arccoth(a*x))/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(6 x^{3} a^{3}-6 a^{2} n \,x^{2}+3 a \,n^{2} x -n^{3}-9 a x +7 n \right) {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{a \left(n^{4}-10 n^{2}+9\right) \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}"," ",0,"(a*x-1)*(a*x+1)*(6*a^3*x^3-6*a^2*n*x^2+3*a*n^2*x-n^3-9*a*x+7*n)*exp(n*arccoth(a*x))/a/(n^4-10*n^2+9)/(-a^2*c*x^2+c)^(5/2)","A"
761,0,0,824,0.404000," ","int(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(5/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{x \left(-a^{2} c \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/x/(-a^2*c*x^2+c)^(5/2),x)","F"
762,0,0,121,0.408000," ","int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^p,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{p}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(-a^2*c*x^2+c)^p,x)","F"
763,1,38,51,0.032000," ","int(exp(2*p*arccoth(a*x))*(-a^2*c*x^2+c)^p,x)","\frac{\left(a x +1\right) {\mathrm e}^{2 p \,\mathrm{arccoth}\left(a x \right)} \left(-a^{2} c \,x^{2}+c \right)^{p}}{a \left(1+2 p \right)}"," ",0,"(a*x+1)/a/(1+2*p)*exp(2*p*arccoth(a*x))*(-a^2*c*x^2+c)^p","A"
764,1,40,52,0.033000," ","int((-a^2*c*x^2+c)^p/exp(2*p*arccoth(a*x)),x)","\frac{\left(a x -1\right) \left(-a^{2} c \,x^{2}+c \right)^{p} {\mathrm e}^{-2 p \,\mathrm{arccoth}\left(a x \right)}}{a \left(1+2 p \right)}"," ",0,"(a*x-1)/a/(1+2*p)*(-a^2*c*x^2+c)^p/exp(2*p*arccoth(a*x))","A"
765,0,0,61,0.631000," ","int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right)^{2} \left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(a x -1\right)^{2}}\, dx"," ",0,"int(1/(a*x-1)^2*(a*x+1)^2*(-a^2*c*x^2+c)^p,x)","F"
766,0,0,112,0.383000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p}}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(3/2)*(-a^2*c*x^2+c)^p,x)","F"
767,0,0,52,0.532000," ","int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(a x +1\right) \left(-a^{2} c \,x^{2}+c \right)^{p}}{a x -1}\, dx"," ",0,"int((a*x+1)/(a*x-1)*(-a^2*c*x^2+c)^p,x)","F"
768,0,0,112,0.391000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^p,x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p}}{\sqrt{\frac{a x -1}{a x +1}}}\, dx"," ",0,"int(1/((a*x-1)/(a*x+1))^(1/2)*(-a^2*c*x^2+c)^p,x)","F"
769,0,0,112,0.418000," ","int((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(1/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{p} \sqrt{\frac{a x -1}{a x +1}}\, dx"," ",0,"int((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(1/2),x)","F"
770,0,0,54,0.599000," ","int((-a^2*c*x^2+c)^p/(a*x+1)*(a*x-1),x)","\int \frac{\left(-a^{2} c \,x^{2}+c \right)^{p} \left(a x -1\right)}{a x +1}\, dx"," ",0,"int((-a^2*c*x^2+c)^p/(a*x+1)*(a*x-1),x)","F"
771,0,0,112,0.399000," ","int((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(3/2),x)","\int \left(-a^{2} c \,x^{2}+c \right)^{p} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}\, dx"," ",0,"int((-a^2*c*x^2+c)^p*((a*x-1)/(a*x+1))^(3/2),x)","F"
772,1,320,290,0.072000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^4,x)","\frac{\left(a x -1\right) c^{4} \left(-1680 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{8} a^{8}+1680 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}+3675 a^{7} x^{7} \sqrt{a^{2}}\, \sqrt{a^{2} x^{2}-1}+3675 a^{7} x^{7} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+1680 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}-1995 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-1136 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+1050 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+816 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -240 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{1680 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{8} x^{7} \sqrt{a^{2}}}"," ",0,"1/1680*(a*x-1)*c^4*(-1680*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^8*a^8+1680*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6+3675*a^7*x^7*(a^2)^(1/2)*(a^2*x^2-1)^(1/2)+3675*a^7*x^7*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+1680*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8-1995*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5-1136*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+1050*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+816*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-240*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^8/x^7/(a^2)^(1/2)","A"
773,1,272,228,0.063000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^3,x)","\frac{\left(a x -1\right) c^{3} \left(-120 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+120 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+225 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+225 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+120 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-105 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-64 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{120 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{6} x^{5} \sqrt{a^{2}}}"," ",0,"1/120*(a*x-1)*c^3*(-120*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+120*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+225*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+225*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+120*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-105*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-64*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^6/x^5/(a^2)^(1/2)","A"
774,1,224,166,0.052000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^2,x)","\frac{\left(a x -1\right) c^{2} \left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+9 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-3 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"1/6*(a*x-1)*c^2*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+9*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-3*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","A"
775,1,163,95,0.049000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2),x)","\frac{\left(a x -1\right) c \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"(a*x-1)*c*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)/(a*x+1))^(1/2)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","A"
776,1,251,92,0.059000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x)","\frac{2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{2 a \sqrt{a^{2}}\, \left(a x -1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/2*(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a^2)^(1/2)/(a*x-1)/c/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
777,1,530,154,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x)","-\frac{-45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+21 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+11 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+90 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-5 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -90 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-19 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{24 a \left(a x -1\right)^{2} \left(a x +1\right)^{2} \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-1/24*(-45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+21*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+11*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+90*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-5*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-90*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-19*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a*x-1)^2/(a*x+1)^2/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
778,1,714,216,0.071000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x)","-\frac{-525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}-240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+285 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}+240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+83 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-218 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-342 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-3 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +1575 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+243 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-240 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{240 a \left(a x +1\right)^{3} \sqrt{a^{2}}\, \left(a x -1\right)^{3} c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-1/240*(-525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+285*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5+525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6+240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+83*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-218*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-342*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-3*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+1575*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+243*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-240*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a*x+1)^3/(a^2)^(1/2)/(a*x-1)^3/c^3/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
779,1,898,278,0.076000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x)","-\frac{-132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}-27673 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+7705 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-198450 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+198450 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}-24295 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +37095 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+2637 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +132300 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-16077 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+13440 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)+53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{9} a^{10}+13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{8} a^{9}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{9} a^{9}+19635 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{7} a^{7}+33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{8} a^{8}+2893 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}+53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}-80640 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+80640 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}}{13440 a \left(a x +1\right)^{4} \sqrt{a^{2}}\, \left(a x -1\right)^{4} c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-1/13440*(-132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7-27673*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5+7705*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-198450*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+198450*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6-24295*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+37095*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+2637*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+132300*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-16077*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+13440*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))+53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^9*a^10+13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^8*a^9-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^9*a^9+19635*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^7*a^7+33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^8*a^8+2893*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^6*a^6+53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7-80640*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+80640*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5)/a/(a*x+1)^4/(a^2)^(1/2)/(a*x-1)^4/c^4/((a*x-1)*(a*x+1))^(1/2)/((a*x-1)/(a*x+1))^(1/2)","B"
780,1,116,115,0.042000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^5,x)","-\frac{c^{5}}{9 a^{10} x^{9}}-\frac{c^{5}}{4 a^{9} x^{8}}+\frac{3 c^{5}}{7 a^{8} x^{7}}+\frac{4 c^{5}}{3 a^{7} x^{6}}-\frac{2 c^{5}}{5 a^{6} x^{5}}-\frac{3 c^{5}}{a^{5} x^{4}}-\frac{2 c^{5}}{3 a^{4} x^{3}}+\frac{4 c^{5}}{x^{2} a^{3}}+\frac{3 c^{5}}{a^{2} x}+c^{5} x +\frac{2 c^{5} \ln \left(x \right)}{a}"," ",0,"-1/9*c^5/a^10/x^9-1/4*c^5/a^9/x^8+3/7*c^5/a^8/x^7+4/3*c^5/a^7/x^6-2/5*c^5/a^6/x^5-3*c^5/a^5/x^4-2/3*c^5/a^4/x^3+4*c^5/x^2/a^3+3*c^5/a^2/x+c^5*x+2*c^5*ln(x)/a","A"
781,1,83,82,0.045000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^4,x)","\frac{c^{4}}{7 a^{8} x^{7}}+\frac{c^{4}}{3 a^{7} x^{6}}-\frac{2 c^{4}}{5 a^{6} x^{5}}-\frac{3 c^{4}}{2 a^{5} x^{4}}+\frac{3 c^{4}}{x^{2} a^{3}}+\frac{2 c^{4}}{a^{2} x}+c^{4} x +\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"1/7*c^4/a^8/x^7+1/3*c^4/a^7/x^6-2/5*c^4/a^6/x^5-3/2*c^4/a^5/x^4+3*c^4/x^2/a^3+2*c^4/a^2/x+c^4*x+2*c^4*ln(x)/a","A"
782,1,71,70,0.041000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^3,x)","-\frac{c^{3}}{5 a^{6} x^{5}}-\frac{c^{3}}{2 a^{5} x^{4}}+\frac{c^{3}}{3 a^{4} x^{3}}+\frac{2 c^{3}}{x^{2} a^{3}}+\frac{c^{3}}{a^{2} x}+c^{3} x +\frac{2 c^{3} \ln \left(x \right)}{a}"," ",0,"-1/5*c^3/a^6/x^5-1/2*c^3/a^5/x^4+1/3*c^3/a^4/x^3+2*c^3/x^2/a^3+c^3/a^2/x+c^3*x+2*c^3*ln(x)/a","A"
783,1,38,37,0.041000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^2,x)","\frac{c^{2}}{3 a^{4} x^{3}}+\frac{c^{2}}{x^{2} a^{3}}+c^{2} x +\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"1/3*c^2/a^4/x^3+c^2/x^2/a^3+c^2*x+2*c^2*ln(x)/a","A"
784,1,22,21,0.037000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2),x)","-\frac{c}{a^{2} x}+c x +\frac{2 c \ln \left(x \right)}{a}"," ",0,"-c/a^2/x+c*x+2*c*ln(x)/a","A"
785,1,36,36,0.039000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2),x)","\frac{x}{c}+\frac{2 \ln \left(a x -1\right)}{a c}-\frac{1}{a c \left(a x -1\right)}"," ",0,"x/c+2/a/c*ln(a*x-1)-1/a/c/(a*x-1)","A"
786,1,65,67,0.045000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^2,x)","\frac{x}{c^{2}}-\frac{1}{4 a \,c^{2} \left(a x -1\right)^{2}}-\frac{7}{4 a \,c^{2} \left(a x -1\right)}+\frac{17 \ln \left(a x -1\right)}{8 a \,c^{2}}-\frac{\ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"x/c^2-1/4/a/c^2/(a*x-1)^2-7/4/a/c^2/(a*x-1)+17/8/a/c^2*ln(a*x-1)-1/8*ln(a*x+1)/a/c^2","A"
787,1,95,98,0.047000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^3,x)","\frac{x}{c^{3}}-\frac{1}{12 c^{3} a \left(a x -1\right)^{3}}-\frac{5}{8 c^{3} a \left(a x -1\right)^{2}}-\frac{39}{16 a \,c^{3} \left(a x -1\right)}+\frac{9 \ln \left(a x -1\right)}{4 c^{3} a}-\frac{1}{16 a \,c^{3} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"x/c^3-1/12/c^3/a/(a*x-1)^3-5/8/c^3/a/(a*x-1)^2-39/16/a/c^3/(a*x-1)+9/4/c^3/a*ln(a*x-1)-1/16/a/c^3/(a*x+1)-1/4*ln(a*x+1)/a/c^3","A"
788,1,125,129,0.048000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^4,x)","\frac{x}{c^{4}}-\frac{1}{32 c^{4} a \left(a x -1\right)^{4}}-\frac{13}{48 c^{4} a \left(a x -1\right)^{3}}-\frac{35}{32 c^{4} a \left(a x -1\right)^{2}}-\frac{99}{32 a \,c^{4} \left(a x -1\right)}+\frac{303 \ln \left(a x -1\right)}{128 c^{4} a}+\frac{1}{64 a \,c^{4} \left(a x +1\right)^{2}}-\frac{11}{64 a \,c^{4} \left(a x +1\right)}-\frac{47 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"x/c^4-1/32/c^4/a/(a*x-1)^4-13/48/c^4/a/(a*x-1)^3-35/32/c^4/a/(a*x-1)^2-99/32/a/c^4/(a*x-1)+303/128/c^4/a*ln(a*x-1)+1/64/a/c^4/(a*x+1)^2-11/64/a/c^4/(a*x+1)-47/128*ln(a*x+1)/a/c^4","A"
789,1,329,291,0.073000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^4,x)","\frac{\left(a x -1\right)^{2} c^{4} \left(-1680 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{8} a^{8}+1680 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}+525 a^{7} x^{7} \sqrt{a^{2}}\, \sqrt{a^{2} x^{2}-1}+525 a^{7} x^{7} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+1680 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+35 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-816 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-490 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+176 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +80 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{560 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{8} x^{7} \sqrt{a^{2}}}"," ",0,"1/560*(a*x-1)^2*c^4*(-1680*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^8*a^8+1680*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6+525*a^7*x^7*(a^2)^(1/2)*(a^2*x^2-1)^(1/2)+525*a^7*x^7*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+1680*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+35*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5-816*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-490*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+176*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+80*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^8/x^7/(a^2)^(1/2)","A"
790,1,281,229,0.061000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^3,x)","\frac{\left(a x -1\right)^{2} c^{3} \left(-120 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+120 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}+15 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+120 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+25 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-32 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -8 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{40 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{6} x^{5} \sqrt{a^{2}}}"," ",0,"1/40*(a*x-1)^2*c^3*(-120*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+120*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5+15*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+120*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+25*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-32*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-8*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^6/x^5/(a^2)^(1/2)","A"
791,1,233,167,0.057000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^2,x)","\frac{\left(a x -1\right)^{2} c^{2} \left(-18 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+18 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+18 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+9 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"1/6*(a*x-1)^2*c^2*(-18*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+18*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+18*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+9*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","A"
792,1,235,68,0.056000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2),x)","-\frac{\left(a x -1\right)^{2} c \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}+3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a +3 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"-(a*x-1)^2*c*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)+3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a+3*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)/(a*x+1))^(3/2)/(a*x+1)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","B"
793,1,346,124,0.060000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x)","\frac{9 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+9 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-6 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+5 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -9 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-9 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{3 a \left(a x -1\right) \sqrt{a^{2}}\, c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/3*(9*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+9*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+5*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-9*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-9*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a/(a*x-1)/(a^2)^(1/2)/c/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
794,1,438,155,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x)","-\frac{-125 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+85 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+500 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-148 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -750 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+67 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+500 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-125 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-120 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{40 a \sqrt{a^{2}}\, \left(a x -1\right)^{2} c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/40*(-125*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+85*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+500*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-148*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-750*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+67*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+500*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-125*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-120*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a^2)^(1/2)/(a*x-1)^2/c^2/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(3/2)","B"
795,1,714,217,0.072000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x)","-\frac{-3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}-3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+2555 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+11025 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}+10080 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}-1873 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-3675 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-4426 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-18375 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-16800 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+3350 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+18375 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+16800 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+2511 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-1957 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-11025 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -10080 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+3360 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{1120 a \sqrt{a^{2}}\, \left(a x -1\right)^{3} c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right)^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/1120*(-3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7-3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+2555*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5+11025*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6+10080*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7-1873*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4-3675*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-4426*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-18375*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-16800*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+3350*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+18375*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+16800*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+2511*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-1957*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-11025*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-10080*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+3360*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a^2)^(1/2)/(a*x-1)^3/c^3/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)^3/((a*x-1)/(a*x+1))^(3/2)","B"
796,1,766,279,0.078000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x)","-\frac{-138915 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{9} a^{9}-120960 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{9} a^{10}+98595 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{7} a^{7}+416745 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{8} a^{8}+362880 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{8} a^{9}-75113 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-240861 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-1111320 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}-967680 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+178863 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+833490 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+725760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+252497 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+833490 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+725760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-182307 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-1111320 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-967680 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-101271 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +74077 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+416745 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +362880 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-138915 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-120960 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)}{40320 a \sqrt{a^{2}}\, \left(a x -1\right)^{4} c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x +1\right)^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/40320*(-138915*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^9*a^9-120960*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^9*a^10+98595*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^7*a^7+416745*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^8*a^8+362880*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^8*a^9-75113*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^6*a^6-240861*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5-1111320*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6-967680*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+178863*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+833490*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+725760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+252497*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+833490*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+725760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-182307*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-1111320*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-967680*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-101271*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+74077*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+416745*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+362880*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-138915*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-120960*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a/(a^2)^(1/2)/(a*x-1)^4/c^4/((a*x-1)*(a*x+1))^(1/2)/(a*x+1)^4/((a*x-1)/(a*x+1))^(3/2)","B"
797,1,105,104,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^5,x)","\frac{c^{5}}{9 a^{10} x^{9}}+\frac{c^{5}}{2 a^{9} x^{8}}+\frac{3 c^{5}}{7 a^{8} x^{7}}-\frac{4 c^{5}}{3 a^{7} x^{6}}-\frac{14 c^{5}}{5 a^{6} x^{5}}+\frac{14 c^{5}}{3 a^{4} x^{3}}+\frac{4 c^{5}}{x^{2} a^{3}}-\frac{3 c^{5}}{a^{2} x}+c^{5} x +\frac{4 c^{5} \ln \left(x \right)}{a}"," ",0,"1/9*c^5/a^10/x^9+1/2*c^5/a^9/x^8+3/7*c^5/a^8/x^7-4/3*c^5/a^7/x^6-14/5*c^5/a^6/x^5+14/3*c^5/a^4/x^3+4*c^5/x^2/a^3-3*c^5/a^2/x+c^5*x+4*c^5*ln(x)/a","A"
798,1,93,92,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^4,x)","-\frac{c^{4}}{7 a^{8} x^{7}}-\frac{2 c^{4}}{3 a^{7} x^{6}}-\frac{4 c^{4}}{5 a^{6} x^{5}}+\frac{c^{4}}{a^{5} x^{4}}+\frac{10 c^{4}}{3 a^{4} x^{3}}+\frac{2 c^{4}}{x^{2} a^{3}}-\frac{4 c^{4}}{a^{2} x}+c^{4} x +\frac{4 c^{4} \ln \left(x \right)}{a}"," ",0,"-1/7*c^4/a^8/x^7-2/3*c^4/a^7/x^6-4/5*c^4/a^6/x^5+c^4/a^5/x^4+10/3*c^4/a^4/x^3+2*c^4/x^2/a^3-4*c^4/a^2/x+c^4*x+4*c^4*ln(x)/a","A"
799,1,60,59,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^3,x)","\frac{c^{3}}{5 a^{6} x^{5}}+\frac{c^{3}}{a^{5} x^{4}}+\frac{5 c^{3}}{3 a^{4} x^{3}}-\frac{5 c^{3}}{a^{2} x}+c^{3} x +\frac{4 c^{3} \ln \left(x \right)}{a}"," ",0,"1/5*c^3/a^6/x^5+c^3/a^5/x^4+5/3*c^3/a^4/x^3-5*c^3/a^2/x+c^3*x+4*c^3*ln(x)/a","A"
800,1,50,49,0.042000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2)^2,x)","-\frac{c^{2}}{3 a^{4} x^{3}}-\frac{2 c^{2}}{x^{2} a^{3}}-\frac{6 c^{2}}{a^{2} x}+c^{2} x +\frac{4 c^{2} \ln \left(x \right)}{a}"," ",0,"-1/3*c^2/a^4/x^3-2*c^2/x^2/a^3-6*c^2/a^2/x+c^2*x+4*c^2*ln(x)/a","A"
801,1,33,33,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2*(c-c/a^2/x^2),x)","c x +\frac{c}{a^{2} x}-\frac{4 c \ln \left(x \right)}{a}+\frac{8 c \ln \left(a x -1\right)}{a}"," ",0,"c*x+c/a^2/x-4*c*ln(x)/a+8*c/a*ln(a*x-1)","A"
802,1,51,53,0.043000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2),x)","\frac{x}{c}+\frac{4 \ln \left(a x -1\right)}{a c}-\frac{5}{a c \left(a x -1\right)}-\frac{1}{a c \left(a x -1\right)^{2}}"," ",0,"x/c+4/a/c*ln(a*x-1)-5/a/c/(a*x-1)-1/a/c/(a*x-1)^2","A"
803,1,66,69,0.041000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^2,x)","\frac{x}{c^{2}}-\frac{1}{3 c^{2} a \left(a x -1\right)^{3}}+\frac{4 \ln \left(a x -1\right)}{a \,c^{2}}-\frac{6}{a \,c^{2} \left(a x -1\right)}-\frac{2}{a \,c^{2} \left(a x -1\right)^{2}}"," ",0,"x/c^2-1/3/c^2/a/(a*x-1)^3+4/a/c^2*ln(a*x-1)-6/a/c^2/(a*x-1)-2/a/c^2/(a*x-1)^2","A"
804,1,95,99,0.044000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^3,x)","\frac{x}{c^{3}}-\frac{1}{8 a \,c^{3} \left(a x -1\right)^{4}}-\frac{11}{12 c^{3} a \left(a x -1\right)^{3}}-\frac{49}{16 c^{3} a \left(a x -1\right)^{2}}-\frac{111}{16 a \,c^{3} \left(a x -1\right)}+\frac{129 \ln \left(a x -1\right)}{32 c^{3} a}-\frac{\ln \left(a x +1\right)}{32 a \,c^{3}}"," ",0,"x/c^3-1/8/a/c^3/(a*x-1)^4-11/12/c^3/a/(a*x-1)^3-49/16/c^3/a/(a*x-1)^2-111/16/a/c^3/(a*x-1)+129/32/c^3/a*ln(a*x-1)-1/32*ln(a*x+1)/a/c^3","A"
805,1,125,130,0.048000," ","int(1/(a*x-1)^2*(a*x+1)^2/(c-c/a^2/x^2)^4,x)","\frac{x}{c^{4}}-\frac{1}{20 c^{4} a \left(a x -1\right)^{5}}-\frac{7}{16 c^{4} a \left(a x -1\right)^{4}}-\frac{83}{48 c^{4} a \left(a x -1\right)^{3}}-\frac{67}{16 c^{4} a \left(a x -1\right)^{2}}-\frac{501}{64 a \,c^{4} \left(a x -1\right)}+\frac{261 \ln \left(a x -1\right)}{64 c^{4} a}-\frac{1}{64 a \,c^{4} \left(a x +1\right)}-\frac{5 \ln \left(a x +1\right)}{64 a \,c^{4}}"," ",0,"x/c^4-1/20/c^4/a/(a*x-1)^5-7/16/c^4/a/(a*x-1)^4-83/48/c^4/a/(a*x-1)^3-67/16/c^4/a/(a*x-1)^2-501/64/a/c^4/(a*x-1)+261/64/c^4/a*ln(a*x-1)-1/64/a/c^4/(a*x+1)-5/64*ln(a*x+1)/a/c^4","A"
806,1,320,291,0.071000," ","int((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{4} \left(-1680 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{8} a^{8}+1680 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-3675 a^{7} x^{7} \sqrt{a^{2}}\, \sqrt{a^{2} x^{2}-1}-3675 a^{7} x^{7} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+1680 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+1995 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-1136 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-1050 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+816 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -240 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{1680 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{8} x^{7} \sqrt{a^{2}}}"," ",0,"-1/1680*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^4*(-1680*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^8*a^8+1680*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6-3675*a^7*x^7*(a^2)^(1/2)*(a^2*x^2-1)^(1/2)-3675*a^7*x^7*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+1680*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+1995*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5-1136*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-1050*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+816*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-240*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^8/x^7/(a^2)^(1/2)","A"
807,1,272,229,0.061000," ","int((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{3} \left(-120 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+120 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-225 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}-225 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+120 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+105 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-64 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +24 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{120 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{6} x^{5} \sqrt{a^{2}}}"," ",0,"-1/120*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^3*(-120*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+120*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-225*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5-225*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+120*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+105*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-64*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+24*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^6/x^5/(a^2)^(1/2)","A"
808,1,224,167,0.054000," ","int((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c^{2} \left(-6 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+6 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-9 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}-9 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+6 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+3 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"-1/6*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c^2*(-6*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+6*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-9*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3-9*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+6*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+3*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","A"
809,1,166,96,0.051000," ","int((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) c \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*c*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","A"
810,1,250,93,0.062000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2),x)","-\frac{\left(2 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+\left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-6 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +2 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-3 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right) \sqrt{\frac{a x -1}{a x +1}}}{2 a \sqrt{a^{2}}\, \left(a x +1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-1/2*(2*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-6*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+2*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-3*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a*((a*x-1)/(a*x+1))^(1/2)/(a^2)^(1/2)/(a*x+1)/c/((a*x-1)*(a*x+1))^(1/2)","B"
811,1,530,155,0.066000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^2,x)","-\frac{\left(-45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+21 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-45 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-11 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+90 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-5 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +90 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}-48 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+19 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +24 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-45 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+24 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \sqrt{\frac{a x -1}{a x +1}}}{24 a \left(a x -1\right)^{2} \left(a x +1\right)^{2} \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-1/24*(-45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+21*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-45*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-11*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+90*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-5*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+90*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2-48*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+19*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+24*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-45*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+24*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^2/(a*x+1)^2/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)","B"
812,1,714,217,0.069000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^3,x)","-\frac{\left(-525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}+240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+285 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}+240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}-83 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-218 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+342 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-1575 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-3 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -1575 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}-243 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -240 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+525 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-240 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \sqrt{\frac{a x -1}{a x +1}}}{240 a \left(a x -1\right)^{3} \left(a x +1\right)^{3} \sqrt{a^{2}}\, c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-1/240*(-525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7+240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+285*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5-525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6+240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7-83*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-218*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+342*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-1575*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-3*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-1575*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3-243*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-240*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+525*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-240*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)^3/(a*x+1)^3/(a^2)^(1/2)/c^3/((a*x-1)*(a*x+1))^(1/2)","B"
813,1,898,279,0.078000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^4,x)","-\frac{\left(132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}-27673 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+7705 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-198450 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-198450 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+132300 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}+24295 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -37095 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+2637 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a +132300 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+16077 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+13440 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{9} a^{10}+13440 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{8} a^{9}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{9} a^{9}+19635 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{7} a^{7}-33075 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{8} a^{8}-2893 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}-53760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+80640 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+80640 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}\right) \sqrt{\frac{a x -1}{a x +1}}}{13440 a \left(a x +1\right)^{4} \sqrt{a^{2}}\, \left(a x -1\right)^{4} c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}}"," ",0,"-1/13440*(132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7-27673*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5+7705*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-198450*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-198450*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+132300*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6+24295*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-37095*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+2637*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a+132300*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+16077*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+13440*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^9*a^10+13440*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^8*a^9-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^9*a^9+19635*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^7*a^7-33075*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^8*a^8-2893*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^6*a^6-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8-53760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+80640*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+80640*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5)/a*((a*x-1)/(a*x+1))^(1/2)/(a*x+1)^4/(a^2)^(1/2)/(a*x-1)^4/c^4/((a*x-1)*(a*x+1))^(1/2)","B"
814,1,83,82,0.043000," ","int((c-c/a^2/x^2)^4/(a*x+1)*(a*x-1),x)","\frac{c^{4}}{7 a^{8} x^{7}}-\frac{c^{4}}{3 a^{7} x^{6}}-\frac{2 c^{4}}{5 a^{6} x^{5}}+\frac{3 c^{4}}{2 a^{5} x^{4}}-\frac{3 c^{4}}{x^{2} a^{3}}+\frac{2 c^{4}}{a^{2} x}+c^{4} x -\frac{2 c^{4} \ln \left(x \right)}{a}"," ",0,"1/7*c^4/a^8/x^7-1/3*c^4/a^7/x^6-2/5*c^4/a^6/x^5+3/2*c^4/a^5/x^4-3*c^4/x^2/a^3+2*c^4/a^2/x+c^4*x-2*c^4*ln(x)/a","A"
815,1,71,70,0.042000," ","int((c-c/a^2/x^2)^3/(a*x+1)*(a*x-1),x)","-\frac{c^{3}}{5 a^{6} x^{5}}+\frac{c^{3}}{2 a^{5} x^{4}}+\frac{c^{3}}{3 a^{4} x^{3}}-\frac{2 c^{3}}{x^{2} a^{3}}+\frac{c^{3}}{a^{2} x}+c^{3} x -\frac{2 c^{3} \ln \left(x \right)}{a}"," ",0,"-1/5*c^3/a^6/x^5+1/2*c^3/a^5/x^4+1/3*c^3/a^4/x^3-2*c^3/x^2/a^3+c^3/a^2/x+c^3*x-2*c^3*ln(x)/a","A"
816,1,39,38,0.042000," ","int((c-c/a^2/x^2)^2/(a*x+1)*(a*x-1),x)","\frac{c^{2}}{3 a^{4} x^{3}}-\frac{c^{2}}{x^{2} a^{3}}+c^{2} x -\frac{2 c^{2} \ln \left(x \right)}{a}"," ",0,"1/3*c^2/a^4/x^3-c^2/x^2/a^3+c^2*x-2*c^2*ln(x)/a","A"
817,1,22,21,0.040000," ","int((c-c/a^2/x^2)/(a*x+1)*(a*x-1),x)","-\frac{c}{a^{2} x}+c x -\frac{2 c \ln \left(x \right)}{a}"," ",0,"-c/a^2/x+c*x-2*c*ln(x)/a","A"
818,1,36,35,0.041000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2),x)","\frac{x}{c}-\frac{1}{a c \left(a x +1\right)}-\frac{2 \ln \left(a x +1\right)}{a c}"," ",0,"x/c-1/a/c/(a*x+1)-2*ln(a*x+1)/a/c","A"
819,1,65,65,0.044000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^2,x)","\frac{x}{c^{2}}+\frac{\ln \left(a x -1\right)}{8 a \,c^{2}}+\frac{1}{4 a \,c^{2} \left(a x +1\right)^{2}}-\frac{7}{4 a \,c^{2} \left(a x +1\right)}-\frac{17 \ln \left(a x +1\right)}{8 a \,c^{2}}"," ",0,"x/c^2+1/8/a/c^2*ln(a*x-1)+1/4/a/c^2/(a*x+1)^2-7/4/a/c^2/(a*x+1)-17/8*ln(a*x+1)/a/c^2","A"
820,1,95,96,0.050000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^3,x)","\frac{x}{c^{3}}-\frac{1}{16 a \,c^{3} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{4 c^{3} a}-\frac{1}{12 a \,c^{3} \left(a x +1\right)^{3}}+\frac{5}{8 a \,c^{3} \left(a x +1\right)^{2}}-\frac{39}{16 a \,c^{3} \left(a x +1\right)}-\frac{9 \ln \left(a x +1\right)}{4 a \,c^{3}}"," ",0,"x/c^3-1/16/a/c^3/(a*x-1)+1/4/c^3/a*ln(a*x-1)-1/12/a/c^3/(a*x+1)^3+5/8/a/c^3/(a*x+1)^2-39/16/a/c^3/(a*x+1)-9/4*ln(a*x+1)/a/c^3","A"
821,1,125,127,0.050000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^4,x)","\frac{x}{c^{4}}-\frac{1}{64 c^{4} a \left(a x -1\right)^{2}}-\frac{11}{64 a \,c^{4} \left(a x -1\right)}+\frac{47 \ln \left(a x -1\right)}{128 c^{4} a}+\frac{1}{32 a \,c^{4} \left(a x +1\right)^{4}}-\frac{13}{48 a \,c^{4} \left(a x +1\right)^{3}}+\frac{35}{32 a \,c^{4} \left(a x +1\right)^{2}}-\frac{99}{32 a \,c^{4} \left(a x +1\right)}-\frac{303 \ln \left(a x +1\right)}{128 a \,c^{4}}"," ",0,"x/c^4-1/64/c^4/a/(a*x-1)^2-11/64/a/c^4/(a*x-1)+47/128/c^4/a*ln(a*x-1)+1/32/a/c^4/(a*x+1)^4-13/48/a/c^4/(a*x+1)^3+35/32/a/c^4/(a*x+1)^2-99/32/a/c^4/(a*x+1)-303/128*ln(a*x+1)/a/c^4","A"
822,1,329,291,0.074000," ","int((c-c/a^2/x^2)^4*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{4} \left(-1680 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{8} a^{8}+1680 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-525 a^{7} x^{7} \sqrt{a^{2}}\, \sqrt{a^{2} x^{2}-1}-525 a^{7} x^{7} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+1680 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}-35 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-816 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+490 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}+176 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}-280 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +80 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{560 \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{8} x^{7} \sqrt{a^{2}}}"," ",0,"-1/560*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^4*(-1680*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^8*a^8+1680*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^6*a^6-525*a^7*x^7*(a^2)^(1/2)*(a^2*x^2-1)^(1/2)-525*a^7*x^7*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+1680*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8-35*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^5*a^5-816*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4+490*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3+176*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2-280*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+80*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/a^8/x^7/(a^2)^(1/2)","A"
823,1,281,229,0.060000," ","int((c-c/a^2/x^2)^3*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{3} \left(-120 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{6} a^{6}+120 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-15 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{5} a^{5}-15 \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right) \sqrt{a^{2}}\, x^{5} a^{5}+120 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-25 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{3} a^{3}-32 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+30 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a -8 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{40 \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{6} x^{5} \sqrt{a^{2}}}"," ",0,"-1/40*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^3*(-120*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^6*a^6+120*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^4*a^4-15*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^5*a^5-15*arctan(1/(a^2*x^2-1)^(1/2))*(a^2)^(1/2)*x^5*a^5+120*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-25*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^3*a^3-32*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+30*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a-8*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/a^6/x^5/(a^2)^(1/2)","A"
824,1,233,167,0.053000," ","int((c-c/a^2/x^2)^2*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c^{2} \left(-18 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{4} a^{4}+18 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{2} a^{2}+3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{3} a^{3}+3 a^{3} x^{3} \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+18 \ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-9 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x a +2 \left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}\right)}{6 \left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{4} x^{3} \sqrt{a^{2}}}"," ",0,"-1/6*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c^2*(-18*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^4*a^4+18*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x^2*a^2+3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^3*a^3+3*a^3*x^3*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+18*ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-9*(a^2*x^2-1)^(3/2)*(a^2)^(1/2)*x*a+2*(a^2*x^2-1)^(3/2)*(a^2)^(1/2))/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/a^4/x^3/(a^2)^(1/2)","A"
825,1,234,68,0.054000," ","int((c-c/a^2/x^2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right)^{2} c \left(-\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x^{2} a^{2}+4 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +\left(a^{2} x^{2}-1\right)^{\frac{3}{2}} \sqrt{a^{2}}-3 \sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}\, x a -3 a x \sqrt{a^{2}}\, \arctan \left(\frac{1}{\sqrt{a^{2} x^{2}-1}}\right)+\ln \left(\frac{a^{2} x +\sqrt{a^{2} x^{2}-1}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-4 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}\right)}{\left(a x -1\right) \sqrt{\left(a x -1\right) \left(a x +1\right)}\, a^{2} x \sqrt{a^{2}}}"," ",0,"((a*x-1)/(a*x+1))^(3/2)*(a*x+1)^2*c*(-(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x^2*a^2+4*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+(a^2*x^2-1)^(3/2)*(a^2)^(1/2)-3*(a^2*x^2-1)^(1/2)*(a^2)^(1/2)*x*a-3*a*x*(a^2)^(1/2)*arctan(1/(a^2*x^2-1)^(1/2))+ln((a^2*x+(a^2*x^2-1)^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-4*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2)/(a*x-1)/((a*x-1)*(a*x+1))^(1/2)/a^2/x/(a^2)^(1/2)","B"
826,1,346,124,0.059000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2),x)","-\frac{\left(9 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-9 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+6 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+27 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+5 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-27 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +9 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)-9 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{3 a \sqrt{a^{2}}\, \left(a x +1\right) c \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/3*(9*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-9*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+6*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+27*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+5*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-27*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+9*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))-9*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/a*((a*x-1)/(a*x+1))^(3/2)/(a^2)^(1/2)/(a*x+1)/c/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
827,1,438,155,0.067000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^2,x)","-\frac{\left(-125 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+120 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+85 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-500 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+148 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -750 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+720 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+67 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-500 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +480 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-125 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+120 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{40 a \left(a x +1\right)^{2} \sqrt{a^{2}}\, c^{2} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)}"," ",0,"-1/40*(-125*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+120*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+85*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-500*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+148*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-750*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+720*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+67*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-500*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+480*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-125*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+120*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^2/(a^2)^(1/2)/c^2/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)","B"
828,1,714,217,0.072000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^3,x)","-\frac{\left(-3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{7} a^{7}+3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{7} a^{8}+2555 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}-11025 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}+10080 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}+1873 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}-3675 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}+3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}-4426 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}+18375 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}-16800 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}-3350 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}+18375 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}-16800 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}+2511 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{2} a^{2}+3360 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{2} a^{3}+1957 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}-11025 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a +10080 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}-3675 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}+3360 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{1120 a \left(a x +1\right)^{3} \sqrt{a^{2}}\, c^{3} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)^{3}}"," ",0,"-1/1120*(-3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^7*a^7+3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^7*a^8+2555*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5-11025*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6+10080*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7+1873*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4-3675*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5+3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6-4426*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3+18375*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4-16800*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5-3350*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2+18375*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3-16800*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4+2511*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^2*a^2+3360*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^2*a^3+1957*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)-11025*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a+10080*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2-3675*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)+3360*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^3/(a^2)^(1/2)/c^3/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)^3","B"
829,1,766,279,0.080000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^4,x)","-\frac{\left(-138915 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{9} a^{9}+120960 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{9} a^{10}+98595 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{7} a^{7}-416745 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{8} a^{8}+362880 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{8} a^{9}+75113 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{6} a^{6}-240861 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{5} a^{5}+1111320 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x^{6} a^{6}-967680 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{6} a^{7}-178863 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}\, x^{4} a^{4}+833490 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{5} a^{5}-725760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{5} a^{6}+252497 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{3} a^{3}-833490 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{4} a^{4}+725760 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{4} a^{5}+182307 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x^{2} a^{2}-1111320 \sqrt{a^{2}}\, \sqrt{\left(a x -1\right) \left(a x +1\right)}\, x^{3} a^{3}+967680 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x^{3} a^{4}-101271 \sqrt{a^{2}}\, \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} x a -74077 \left(\left(a x -1\right) \left(a x +1\right)\right)^{\frac{3}{2}} \sqrt{a^{2}}+416745 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}\, x a -362880 \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right) x \,a^{2}+138915 \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}-120960 a \ln \left(\frac{a^{2} x +\sqrt{\left(a x -1\right) \left(a x +1\right)}\, \sqrt{a^{2}}}{\sqrt{a^{2}}}\right)\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{40320 a \left(a x +1\right)^{4} \sqrt{a^{2}}\, c^{4} \sqrt{\left(a x -1\right) \left(a x +1\right)}\, \left(a x -1\right)^{4}}"," ",0,"-1/40320*(-138915*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^9*a^9+120960*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^9*a^10+98595*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^7*a^7-416745*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^8*a^8+362880*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^8*a^9+75113*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^6*a^6-240861*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^5*a^5+1111320*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x^6*a^6-967680*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^6*a^7-178863*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)*x^4*a^4+833490*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^5*a^5-725760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^5*a^6+252497*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^3*a^3-833490*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^4*a^4+725760*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^4*a^5+182307*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x^2*a^2-1111320*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(1/2)*x^3*a^3+967680*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x^3*a^4-101271*(a^2)^(1/2)*((a*x-1)*(a*x+1))^(3/2)*x*a-74077*((a*x-1)*(a*x+1))^(3/2)*(a^2)^(1/2)+416745*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)*x*a-362880*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2))*x*a^2+138915*((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2)-120960*a*ln((a^2*x+((a*x-1)*(a*x+1))^(1/2)*(a^2)^(1/2))/(a^2)^(1/2)))/a*((a*x-1)/(a*x+1))^(3/2)/(a*x+1)^4/(a^2)^(1/2)/c^4/((a*x-1)*(a*x+1))^(1/2)/(a*x-1)^4","B"
830,1,112,281,0.106000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(7/2),x)","\frac{\left(60 a^{7} x^{7}+60 a^{6} \ln \left(x \right) x^{6}+180 x^{5} a^{5}+90 x^{4} a^{4}-60 x^{3} a^{3}-45 a^{2} x^{2}+12 a x +10\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x}{60 \left(a x +1\right) \left(a^{2} x^{2}-1\right)^{3} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/60*(60*a^7*x^7+60*a^6*ln(x)*x^6+180*x^5*a^5+90*x^4*a^4-60*x^3*a^3-45*a^2*x^2+12*a*x+10)*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a*x+1)/(a^2*x^2-1)^3/((a*x-1)/(a*x+1))^(1/2)","A"
831,1,96,208,0.066000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(5/2),x)","\frac{\left(12 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}+24 x^{3} a^{3}+12 a^{2} x^{2}-4 a x -3\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x}{12 \left(a x +1\right) \left(a^{2} x^{2}-1\right)^{2} \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/12*(12*x^5*a^5+12*a^4*ln(x)*x^4+24*x^3*a^3+12*a^2*x^2-4*a*x-3)*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a*x+1)/(a^2*x^2-1)^2/((a*x-1)/(a*x+1))^(1/2)","A"
832,1,80,128,0.062000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(3/2),x)","\frac{\left(2 x^{3} a^{3}+2 a^{2} \ln \left(x \right) x^{2}+2 a x +1\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x}{2 \left(a x +1\right) \left(a^{2} x^{2}-1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/2*(2*x^3*a^3+2*a^2*ln(x)*x^2+2*a*x+1)*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a*x+1)/(a^2*x^2-1)/((a*x-1)/(a*x+1))^(1/2)","A"
833,1,50,59,0.055000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x)","\frac{\left(a x +\ln \left(x \right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{\left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(a*x+ln(x))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
834,1,57,64,0.052000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x)","\frac{\left(a x -1\right) \left(a x +\ln \left(a x -1\right)\right)}{\sqrt{\frac{a x -1}{a x +1}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"1/((a*x-1)/(a*x+1))^(1/2)*(a*x-1)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2*(a*x+ln(a*x-1))","A"
835,1,101,151,0.067000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(a x -1\right) \left(4 a^{2} x^{2}+5 \ln \left(a x -1\right) x a -a x \ln \left(a x +1\right)-4 a x -5 \ln \left(a x -1\right)+\ln \left(a x +1\right)-2\right) \left(a x +1\right)}{4 \sqrt{\frac{a x -1}{a x +1}}\, a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/4/((a*x-1)/(a*x+1))^(1/2)*(a*x-1)*(4*a^2*x^2+5*ln(a*x-1)*x*a-a*x*ln(a*x+1)-4*a*x-5*ln(a*x-1)+ln(a*x+1)-2)*(a*x+1)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
836,1,175,231,0.069000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(16 x^{4} a^{4}+23 \ln \left(a x -1\right) x^{3} a^{3}-7 a^{3} x^{3} \ln \left(a x +1\right)-16 x^{3} a^{3}-23 \ln \left(a x -1\right) x^{2} a^{2}+7 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-23 \ln \left(a x -1\right) x a +7 a x \ln \left(a x +1\right)+18 a x +23 \ln \left(a x -1\right)-7 \ln \left(a x +1\right)+12\right)}{16 \sqrt{\frac{a x -1}{a x +1}}\, a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/16/((a*x-1)/(a*x+1))^(1/2)*(a*x-1)*(a*x+1)*(16*x^4*a^4+23*ln(a*x-1)*x^3*a^3-7*a^3*x^3*ln(a*x+1)-16*x^3*a^3-23*ln(a*x-1)*x^2*a^2+7*ln(a*x+1)*x^2*a^2-34*a^2*x^2-23*ln(a*x-1)*x*a+7*a*x*ln(a*x+1)+18*a*x+23*ln(a*x-1)-7*ln(a*x+1)+12)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
837,1,247,313,0.072000," ","int(1/((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(96 x^{6} a^{6}+153 \ln \left(a x -1\right) x^{5} a^{5}-57 \ln \left(a x +1\right) x^{5} a^{5}-96 x^{5} a^{5}-153 \ln \left(a x -1\right) x^{4} a^{4}+57 \ln \left(a x +1\right) x^{4} a^{4}-366 x^{4} a^{4}-306 \ln \left(a x -1\right) x^{3} a^{3}+114 a^{3} x^{3} \ln \left(a x +1\right)+222 x^{3} a^{3}+306 \ln \left(a x -1\right) x^{2} a^{2}-114 \ln \left(a x +1\right) x^{2} a^{2}+338 a^{2} x^{2}+153 \ln \left(a x -1\right) x a -57 a x \ln \left(a x +1\right)-122 a x -153 \ln \left(a x -1\right)+57 \ln \left(a x +1\right)-88\right)}{96 \sqrt{\frac{a x -1}{a x +1}}\, a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/96/((a*x-1)/(a*x+1))^(1/2)*(a*x-1)*(a*x+1)*(96*x^6*a^6+153*ln(a*x-1)*x^5*a^5-57*ln(a*x+1)*x^5*a^5-96*x^5*a^5-153*ln(a*x-1)*x^4*a^4+57*ln(a*x+1)*x^4*a^4-366*x^4*a^4-306*ln(a*x-1)*x^3*a^3+114*a^3*x^3*ln(a*x+1)+222*x^3*a^3+306*ln(a*x-1)*x^2*a^2-114*ln(a*x+1)*x^2*a^2+338*a^2*x^2+153*ln(a*x-1)*x*a-57*a*x*ln(a*x+1)-122*a*x-153*ln(a*x-1)+57*ln(a*x+1)-88)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
838,1,795,326,0.117000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(7/2),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \left(-2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{9} c +2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{5} a^{9}+375 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{8} c -480 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{6} a^{8} c +105 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{8}+2352 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{7} c^{2}-560 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7} c^{2}+224 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{3} a^{7}-525 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{6} c^{2}-2940 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{5} c^{3}+700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{7} a^{5} c^{3}+630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{2} a^{6}+875 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c^{3}+672 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x \,a^{5}+4410 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{3} c^{4}-1050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{7} a^{3} c^{4}+280 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}-2625 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{2} c^{4}-4410 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} x^{6} a +1050 \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} x^{6} a -2625 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{6} c^{5}\right)}{1680 a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-1/1680*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/a^2*(-2016*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^7*a^9*c+2016*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^5*a^9+375*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^6*a^8*c-480*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^6*a^8*c+105*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^4*a^8+2352*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^7*a^7*c^2-560*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7*c^2+224*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^3*a^7-525*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^6*a^6*c^2-2940*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^7*a^5*c^3+700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^7*a^5*c^3+630*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^2*a^6+875*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^6*a^4*c^3+672*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x*a^5+4410*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^7*a^3*c^4-1050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^7*a^3*c^4+280*a^4*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)-2625*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^2*c^4-4410*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*(-c/a^2)^(1/2)*c^(9/2)*x^6*a+1050*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*(-c/a^2)^(1/2)*c^(9/2)*x^6*a-2625*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^6*c^5)/(c*(a^2*x^2-1)/a^2)^(7/2)/(-c/a^2)^(1/2)/c","B"
839,1,625,256,0.062000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(5/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \left(-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{7} c +80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{3} a^{7}+48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +60 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-75 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{2} a^{6}+100 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x \,a^{5}-45 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4} c^{2}-90 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c^{3}-150 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c^{3}-30 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}+150 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a +90 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a +135 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c^{3}+135 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{4}\right)}{120 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c}"," ",0,"1/120*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/a^2*(-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^5*a^7*c+80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^3*a^7+48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^6*c+27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^4*a^6*c+60*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5*c^2-75*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^2*a^6+100*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^5*a^5*c^2-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x*a^5-45*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4*c^2-90*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c^3-150*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c^3-30*a^4*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)+150*(-c/a^2)^(1/2)*c^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a+90*(-c/a^2)^(1/2)*c^(7/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a+135*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c^3+135*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^4)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(5/2)/c","B"
840,1,455,185,0.056000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(3/2),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \left(12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{5} c -12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x \,a^{5}+4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c -\sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3} c^{2}-3 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}-18 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c^{2}+18 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c^{2}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{3}\right)}{6 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} c}"," ",0,"1/6*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/a^2*(12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^5*c-12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x*a^5+4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^4*c-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^4*c+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3*c^2-3*a^4*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)-18*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c^2+18*(-c/a^2)^(1/2)*c^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-6*(-c/a^2)^(1/2)*c^(5/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c^2+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^3)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(3/2)/c","B"
841,1,197,98,0.054000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)+2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
842,1,177,101,0.051000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \left(\sqrt{c}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2}+2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a c -2 a \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{c}-\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a \sqrt{c}-2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) c \right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,c^{\frac{3}{2}} a \left(a x -1\right)}"," ",0,"(c*(a^2*x^2-1)/a^2)^(1/2)*(c^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2+2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a*c-2*a*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*c^(1/2)-(c*(a^2*x^2-1)/a^2)^(1/2)*a*c^(1/2)-2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*c)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/c^(3/2)/a/(a*x-1)","A"
843,1,326,109,0.052000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(3 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3}-15 x^{2} a^{2} c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2}+6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c -4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x a -6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a c +12 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}-2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c^{\frac{3}{2}}\right) \left(a x +1\right)}{3 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} a^{4} c^{\frac{3}{2}}}"," ",0,"1/3*(3*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3-15*x^2*a^2*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2+6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a*c+12*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)-2*(c*(a^2*x^2-1)/a^2)^(1/2)*c^(3/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(1/2)/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)/a^4/c^(3/2)","B"
844,1,462,181,0.061000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(15 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5}-45 x^{4} c^{\frac{5}{2}} a^{4} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}-16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4}-60 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{4} c +90 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3} c +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x a -24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x a -50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}-6 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}}\right) \left(a x +1\right)}{15 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} a^{6} c^{\frac{5}{2}}}"," ",0,"1/15*(15*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5-45*x^4*c^(5/2)*a^4*((a*x-1)*(a*x+1)*c/a^2)^(3/2)-16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4-60*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^3*a^3+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^4*c+90*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^2+24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3*c+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x*a-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a-50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)-6*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(3/2)/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)/a^6/c^(5/2)","B"
845,1,572,253,0.075000," ","int((a*x+1)/(a*x-1)/(c-c/a^2/x^2)^(7/2),x)","\frac{\left(105 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{6} a^{6}-553 x^{6} c^{\frac{7}{2}} a^{6} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}-96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{5} a^{5}-392 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{5}-240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{4} a^{4}+1540 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{4}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x \,a^{6} c +240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{3} a^{3}+350 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{3} a^{3}-210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} a^{5} c +180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{2} a^{2}-1470 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{2} a^{2}-180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x a -42 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x a -30 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}}+462 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}\right) \left(a x +1\right)}{105 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} a^{8} c^{\frac{7}{2}}}"," ",0,"1/105*(105*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^6*a^6-553*x^6*c^(7/2)*a^6*((a*x-1)*(a*x+1)*c/a^2)^(5/2)-96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^5*a^5-392*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^5*a^5-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^4*a^4+1540*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^4+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a^6*c+240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^3*a^3+350*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^3*a^3-210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*a^5*c+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^2*a^2-1470*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^2*a^2-180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x*a-42*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a-30*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)+462*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2))*(a*x+1)/((a*x-1)*(a*x+1)*c/a^2)^(5/2)/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)/a^8/c^(7/2)","B"
846,1,112,282,0.063000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(9/2),x)","\frac{\left(280 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}+1120 x^{6} a^{6}+560 x^{5} a^{5}-420 x^{4} a^{4}-448 x^{3} a^{3}+120 a x +35\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} x}{280 \left(a x +1\right)^{3} \left(a^{2} x^{2}-1\right)^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/280*(280*a^9*x^9+840*a^8*ln(x)*x^8+1120*x^6*a^6+560*x^5*a^5-420*x^4*a^4-448*x^3*a^3+120*a*x+35)*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*x/(a*x+1)^3/(a^2*x^2-1)^3/((a*x-1)/(a*x+1))^(3/2)","A"
847,1,112,282,0.063000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(7/2),x)","\frac{\left(60 a^{7} x^{7}+180 a^{6} \ln \left(x \right) x^{6}-60 x^{5} a^{5}+150 x^{4} a^{4}+100 x^{3} a^{3}-15 a^{2} x^{2}-36 a x -10\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x}{60 \left(a x +1\right)^{3} \left(a^{2} x^{2}-1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/60*(60*a^7*x^7+180*a^6*ln(x)*x^6-60*x^5*a^5+150*x^4*a^4+100*x^3*a^3-15*a^2*x^2-36*a*x-10)*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/(a*x+1)^3/(a^2*x^2-1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
848,1,96,208,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(5/2),x)","\frac{\left(4 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}-8 x^{3} a^{3}+4 a^{2} x^{2}+4 a x +1\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x}{4 \left(a x +1\right)^{3} \left(a^{2} x^{2}-1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/4*(4*x^5*a^5+12*a^4*ln(x)*x^4-8*x^3*a^3+4*a^2*x^2+4*a*x+1)*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/(a*x+1)^3/(a^2*x^2-1)/((a*x-1)/(a*x+1))^(3/2)","A"
849,1,69,130,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(3/2),x)","\frac{\left(2 x^{3} a^{3}+6 a^{2} \ln \left(x \right) x^{2}-6 a x -1\right) \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x}{2 \left(a x +1\right)^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/2*(2*x^3*a^3+6*a^2*ln(x)*x^2-6*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/(a*x+1)^3/((a*x-1)/(a*x+1))^(3/2)","A"
850,1,65,97,0.063000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\left(-a x +\ln \left(x \right)-4 \ln \left(a x -1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{\left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(-a*x+ln(x)-4*ln(a*x-1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
851,1,85,103,0.061000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x)","\frac{\left(a x -1\right) \left(a^{2} x^{2}+3 \ln \left(a x -1\right) x a -a x -3 \ln \left(a x -1\right)-2\right)}{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"1/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)/(a*x+1)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2*(a^2*x^2+3*ln(a*x-1)*x*a-a*x-3*ln(a*x-1)-2)","A"
852,1,102,153,0.066000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(a x -1\right) \left(2 x^{3} a^{3}+6 \ln \left(a x -1\right) x^{2} a^{2}-4 a^{2} x^{2}-12 \ln \left(a x -1\right) x a -4 a x +6 \ln \left(a x -1\right)+5\right)}{2 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/2/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)*(2*x^3*a^3+6*ln(a*x-1)*x^2*a^2-4*a^2*x^2-12*ln(a*x-1)*x*a-4*a*x+6*ln(a*x-1)+5)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
853,1,175,233,0.070000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(48 x^{4} a^{4}+147 \ln \left(a x -1\right) x^{3} a^{3}-3 a^{3} x^{3} \ln \left(a x +1\right)-144 x^{3} a^{3}-441 \ln \left(a x -1\right) x^{2} a^{2}+9 \ln \left(a x +1\right) x^{2} a^{2}-42 a^{2} x^{2}+441 \ln \left(a x -1\right) x a -9 a x \ln \left(a x +1\right)+270 a x -147 \ln \left(a x -1\right)+3 \ln \left(a x +1\right)-140\right)}{48 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/48/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)*(a*x+1)*(48*x^4*a^4+147*ln(a*x-1)*x^3*a^3-3*a^3*x^3*ln(a*x+1)-144*x^3*a^3-441*ln(a*x-1)*x^2*a^2+9*ln(a*x+1)*x^2*a^2-42*a^2*x^2+441*ln(a*x-1)*x*a-9*a*x*ln(a*x+1)+270*a*x-147*ln(a*x-1)+3*ln(a*x+1)-140)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
854,1,247,314,0.074000," ","int(1/((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\left(a x -1\right) \left(a x +1\right) \left(64 x^{6} a^{6}+201 \ln \left(a x -1\right) x^{5} a^{5}-9 \ln \left(a x +1\right) x^{5} a^{5}-192 x^{5} a^{5}-603 \ln \left(a x -1\right) x^{4} a^{4}+27 \ln \left(a x +1\right) x^{4} a^{4}-174 x^{4} a^{4}+402 \ln \left(a x -1\right) x^{3} a^{3}-18 a^{3} x^{3} \ln \left(a x +1\right)+618 x^{3} a^{3}+402 \ln \left(a x -1\right) x^{2} a^{2}-18 \ln \left(a x +1\right) x^{2} a^{2}-118 a^{2} x^{2}-603 \ln \left(a x -1\right) x a +27 a x \ln \left(a x +1\right)-414 a x +201 \ln \left(a x -1\right)-9 \ln \left(a x +1\right)+208\right)}{64 \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/64/((a*x-1)/(a*x+1))^(3/2)*(a*x-1)*(a*x+1)*(64*x^6*a^6+201*ln(a*x-1)*x^5*a^5-9*ln(a*x+1)*x^5*a^5-192*x^5*a^5-603*ln(a*x-1)*x^4*a^4+27*ln(a*x+1)*x^4*a^4-174*x^4*a^4+402*ln(a*x-1)*x^3*a^3-18*a^3*x^3*ln(a*x+1)+618*x^3*a^3+402*ln(a*x-1)*x^2*a^2-18*ln(a*x+1)*x^2*a^2-118*a^2*x^2-603*ln(a*x-1)*x*a+27*a*x*ln(a*x+1)-414*a*x+201*ln(a*x-1)-9*ln(a*x+1)+208)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
855,1,112,282,0.063000," ","int((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \left(-60 a^{7} x^{7}+60 a^{6} \ln \left(x \right) x^{6}-180 x^{5} a^{5}+90 x^{4} a^{4}+60 x^{3} a^{3}-45 a^{2} x^{2}-12 a x +10\right)}{60 \left(a x -1\right) \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/60*((a*x-1)/(a*x+1))^(1/2)*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x*(-60*a^7*x^7+60*a^6*ln(x)*x^6-180*x^5*a^5+90*x^4*a^4+60*x^3*a^3-45*a^2*x^2-12*a*x+10)/(a*x-1)/(a^2*x^2-1)^3","A"
856,1,96,210,0.062000," ","int((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \left(-12 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}-24 x^{3} a^{3}+12 a^{2} x^{2}+4 a x -3\right)}{12 \left(a x -1\right) \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/12*((a*x-1)/(a*x+1))^(1/2)*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x*(-12*x^5*a^5+12*a^4*ln(x)*x^4-24*x^3*a^3+12*a^2*x^2+4*a*x-3)/(a*x-1)/(a^2*x^2-1)^2","A"
857,1,80,129,0.063000," ","int((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \left(-2 x^{3} a^{3}+2 a^{2} \ln \left(x \right) x^{2}-2 a x +1\right)}{2 \left(a x -1\right) \left(a^{2} x^{2}-1\right)}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(1/2)*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x*(-2*x^3*a^3+2*a^2*ln(x)*x^2-2*a*x+1)/(a*x-1)/(a^2*x^2-1)","A"
858,1,52,60,0.054000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\left(-a x +\ln \left(x \right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{a x -1}"," ",0,"-(-a*x+ln(x))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
859,1,59,64,0.052000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(-a x +\ln \left(a x +1\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"-((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(-a*x+ln(a*x+1))/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2","A"
860,1,100,150,0.068000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(3/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(4 a^{2} x^{2}+\ln \left(a x -1\right) x a -5 a x \ln \left(a x +1\right)+4 a x +\ln \left(a x -1\right)-5 \ln \left(a x +1\right)-2\right) \left(a x -1\right)}{4 a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"1/4*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(4*a^2*x^2+ln(a*x-1)*x*a-5*a*x*ln(a*x+1)+4*a*x+ln(a*x-1)-5*ln(a*x+1)-2)*(a*x-1)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
861,1,175,231,0.073000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(a x -1\right) \left(16 x^{4} a^{4}+7 \ln \left(a x -1\right) x^{3} a^{3}-23 a^{3} x^{3} \ln \left(a x +1\right)+16 x^{3} a^{3}+7 \ln \left(a x -1\right) x^{2} a^{2}-23 \ln \left(a x +1\right) x^{2} a^{2}-34 a^{2} x^{2}-7 \ln \left(a x -1\right) x a +23 a x \ln \left(a x +1\right)-18 a x -7 \ln \left(a x -1\right)+23 \ln \left(a x +1\right)+12\right)}{16 a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/16*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(a*x-1)*(16*x^4*a^4+7*ln(a*x-1)*x^3*a^3-23*a^3*x^3*ln(a*x+1)+16*x^3*a^3+7*ln(a*x-1)*x^2*a^2-23*ln(a*x+1)*x^2*a^2-34*a^2*x^2-7*ln(a*x-1)*x*a+23*a*x*ln(a*x+1)-18*a*x-7*ln(a*x-1)+23*ln(a*x+1)+12)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
862,1,247,312,0.072000," ","int(((a*x-1)/(a*x+1))^(1/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\sqrt{\frac{a x -1}{a x +1}}\, \left(a x +1\right) \left(a x -1\right) \left(96 x^{6} a^{6}+57 \ln \left(a x -1\right) x^{5} a^{5}-153 \ln \left(a x +1\right) x^{5} a^{5}+96 x^{5} a^{5}+57 \ln \left(a x -1\right) x^{4} a^{4}-153 \ln \left(a x +1\right) x^{4} a^{4}-366 x^{4} a^{4}-114 \ln \left(a x -1\right) x^{3} a^{3}+306 a^{3} x^{3} \ln \left(a x +1\right)-222 x^{3} a^{3}-114 \ln \left(a x -1\right) x^{2} a^{2}+306 \ln \left(a x +1\right) x^{2} a^{2}+338 a^{2} x^{2}+57 \ln \left(a x -1\right) x a -153 a x \ln \left(a x +1\right)+122 a x +57 \ln \left(a x -1\right)-153 \ln \left(a x +1\right)-88\right)}{96 a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/96*((a*x-1)/(a*x+1))^(1/2)*(a*x+1)*(a*x-1)*(96*x^6*a^6+57*ln(a*x-1)*x^5*a^5-153*ln(a*x+1)*x^5*a^5+96*x^5*a^5+57*ln(a*x-1)*x^4*a^4-153*ln(a*x+1)*x^4*a^4-366*x^4*a^4-114*ln(a*x-1)*x^3*a^3+306*a^3*x^3*ln(a*x+1)-222*x^3*a^3-114*ln(a*x-1)*x^2*a^2+306*ln(a*x+1)*x^2*a^2+338*a^2*x^2+57*ln(a*x-1)*x*a-153*a*x*ln(a*x+1)+122*a*x+57*ln(a*x-1)-153*ln(a*x+1)-88)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
863,1,795,329,0.119000," ","int((c-c/a^2/x^2)^(7/2)/(a*x+1)*(a*x-1),x)","\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} x \left(-2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{9} c +2016 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{5} a^{9}-375 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{8} c +480 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{7}{2}} x^{6} a^{8} c -105 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{8}+2352 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{7} c^{2}-560 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7} c^{2}+224 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{3} a^{7}+525 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{6} c^{2}-2940 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{5} c^{3}+700 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{7} a^{5} c^{3}-630 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{2} a^{6}-875 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c^{3}+672 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}\, x \,a^{5}+4410 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{7} a^{3} c^{4}-1050 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{7} a^{3} c^{4}-280 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{9}{2}} \sqrt{-\frac{c}{a^{2}}}+2625 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{2} c^{4}-4410 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} x^{6} a +1050 \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{9}{2}} x^{6} a +2625 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{6} c^{5}\right)}{1680 a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"1/1680*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*x/a^2*(-2016*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^7*a^9*c+2016*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^5*a^9-375*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)*x^6*a^8*c+480*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(7/2)*x^6*a^8*c-105*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^4*a^8+2352*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^7*a^7*c^2-560*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7*c^2+224*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^3*a^7+525*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)*x^6*a^6*c^2-2940*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^7*a^5*c^3+700*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^7*a^5*c^3-630*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x^2*a^6-875*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^6*a^4*c^3+672*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)*x*a^5+4410*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^7*a^3*c^4-1050*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^7*a^3*c^4-280*a^4*(c*(a^2*x^2-1)/a^2)^(9/2)*(-c/a^2)^(1/2)+2625*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^2*c^4-4410*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*(-c/a^2)^(1/2)*c^(9/2)*x^6*a+1050*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*(-c/a^2)^(1/2)*c^(9/2)*x^6*a+2625*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^6*c^5)/(c*(a^2*x^2-1)/a^2)^(7/2)/(-c/a^2)^(1/2)/c","B"
864,1,625,257,0.064000," ","int((c-c/a^2/x^2)^(5/2)/(a*x+1)*(a*x-1),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} x \left(-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{7} c +80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{3} a^{7}-48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c -27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{6} c +60 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}+75 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x^{2} a^{6}+100 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5} c^{2}-80 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} x \,a^{5}+45 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4} c^{2}-90 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c^{3}-150 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c^{3}+30 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{7}{2}} \sqrt{-\frac{c}{a^{2}}}+150 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a +90 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{7}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a -135 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c^{3}-135 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{4}\right)}{120 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c}"," ",0,"-1/120*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*x/a^2*(-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^5*a^7*c+80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^3*a^7-48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^6*c-27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x^4*a^6*c+60*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5*c^2+75*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x^2*a^6+100*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^5*a^5*c^2-80*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(7/2)*x*a^5+45*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4*c^2-90*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c^3-150*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c^3+30*a^4*(c*(a^2*x^2-1)/a^2)^(7/2)*(-c/a^2)^(1/2)+150*(-c/a^2)^(1/2)*c^(7/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a+90*(-c/a^2)^(1/2)*c^(7/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a-135*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c^3-135*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^4)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(5/2)/c","B"
865,1,454,185,0.059000," ","int((c-c/a^2/x^2)^(3/2)/(a*x+1)*(a*x-1),x)","-\frac{\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} x \left(12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{5} c -12 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} x \,a^{5}-4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +\sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{4} c +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3} c^{2}+3 a^{4} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \sqrt{-\frac{c}{a^{2}}}-18 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c^{2}+18 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{5}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c^{2}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{3}\right)}{6 a^{2} \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} c}"," ",0,"-1/6*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*x/a^2*(12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^5*c-12*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(5/2)*x*a^5-4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^4*c+(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^4*c+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3*c^2+3*a^4*(c*(a^2*x^2-1)/a^2)^(5/2)*(-c/a^2)^(1/2)-18*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c^2+18*(-c/a^2)^(1/2)*c^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-6*(-c/a^2)^(1/2)*c^(5/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c^2-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^3)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(3/2)/c","B"
866,1,196,98,0.054000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}+c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)+2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)+c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
867,1,179,102,0.049000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \left(-\sqrt{c}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2}+2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a c -2 a \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{c}-\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a \sqrt{c}+2 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) c \right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,c^{\frac{3}{2}} a \left(a x +1\right)}"," ",0,"-(c*(a^2*x^2-1)/a^2)^(1/2)*(-c^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2+2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a*c-2*a*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*c^(1/2)-(c*(a^2*x^2-1)/a^2)^(1/2)*a*c^(1/2)+2*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*c)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/c^(3/2)/a/(a*x+1)","A"
868,1,326,110,0.052000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^(3/2),x)","\frac{\left(3 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{3}+15 x^{2} a^{2} c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}-4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2}-6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c -4 c^{\frac{3}{2}} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x a -6 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a c -12 c^{\frac{3}{2}} \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c^{\frac{3}{2}}\right) \left(a x -1\right)}{3 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} a^{4} c^{\frac{3}{2}}}"," ",0,"1/3*(3*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^3+15*x^2*a^2*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c-4*c^(3/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a-6*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a*c-12*c^(3/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+2*(c*(a^2*x^2-1)/a^2)^(1/2)*c^(3/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(1/2)/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)/a^4/c^(3/2)","B"
869,1,462,175,0.061000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(15 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} a^{5}+45 x^{4} c^{\frac{5}{2}} a^{4} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{4} a^{4}-60 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+16 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{4} c -90 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-30 \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3} c +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x a -24 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x a +50 c^{\frac{5}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}}+6 c^{\frac{5}{2}} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}}\right) \left(a x -1\right)}{15 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{3}{2}} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} a^{6} c^{\frac{5}{2}}}"," ",0,"1/15*(15*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^5*a^5+45*x^4*c^(5/2)*a^4*((a*x-1)*(a*x+1)*c/a^2)^(3/2)+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^4*a^4-60*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^3*a^3+16*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^4*c-90*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x^2*a^2-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-30*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3*c+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)*x*a-24*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a+50*c^(5/2)*((a*x-1)*(a*x+1)*c/a^2)^(3/2)+6*c^(5/2)*(c*(a^2*x^2-1)/a^2)^(3/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(3/2)/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)/a^6/c^(5/2)","B"
870,1,572,240,0.076000," ","int(1/(a*x+1)*(a*x-1)/(c-c/a^2/x^2)^(7/2),x)","-\frac{\left(-105 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} a^{7}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{6} a^{6}-553 x^{6} c^{\frac{7}{2}} a^{6} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}+96 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{5} a^{5}+392 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{5} a^{5}-240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{4} a^{4}+1540 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{4} a^{4}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x \,a^{6} c -240 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{3} a^{3}-350 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{3} a^{3}+210 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} a^{5} c +180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x^{2} a^{2}-1470 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{2} a^{2}+180 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}} x a +42 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x a -30 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{5}{2}} c^{\frac{7}{2}}+462 c^{\frac{7}{2}} \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}}\right) \left(a x -1\right)}{105 \left(\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}\right)^{\frac{5}{2}} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} a^{8} c^{\frac{7}{2}}}"," ",0,"-1/105*(-105*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^7*a^7+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^6*a^6-553*x^6*c^(7/2)*a^6*((a*x-1)*(a*x+1)*c/a^2)^(5/2)+96*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^5*a^5+392*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^5*a^5-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^4*a^4+1540*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^4*a^4+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a^6*c-240*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^3*a^3-350*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^3*a^3+210*(c*(a^2*x^2-1)/a^2)^(5/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*a^5*c+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x^2*a^2-1470*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x^2*a^2+180*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)*x*a+42*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2)*x*a-30*(c*(a^2*x^2-1)/a^2)^(5/2)*c^(7/2)+462*c^(7/2)*((a*x-1)*(a*x+1)*c/a^2)^(5/2))*(a*x-1)/((a*x-1)*(a*x+1)*c/a^2)^(5/2)/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)/a^8/c^(7/2)","B"
871,1,112,282,0.066000," ","int((c-c/a^2/x^2)^(9/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-280 a^{9} x^{9}+840 a^{8} \ln \left(x \right) x^{8}+1120 x^{6} a^{6}-560 x^{5} a^{5}-420 x^{4} a^{4}+448 x^{3} a^{3}-120 a x +35\right) x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{9}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{280 \left(a x -1\right)^{3} \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/280*(-280*a^9*x^9+840*a^8*ln(x)*x^8+1120*x^6*a^6-560*x^5*a^5-420*x^4*a^4+448*x^3*a^3-120*a*x+35)*x*(c*(a^2*x^2-1)/a^2/x^2)^(9/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3/(a^2*x^2-1)^3","A"
872,1,112,282,0.066000," ","int((c-c/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-60 a^{7} x^{7}+180 a^{6} \ln \left(x \right) x^{6}+60 x^{5} a^{5}+150 x^{4} a^{4}-100 x^{3} a^{3}-15 a^{2} x^{2}+36 a x -10\right) x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{60 \left(a x -1\right)^{3} \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/60*(-60*a^7*x^7+180*a^6*ln(x)*x^6+60*x^5*a^5+150*x^4*a^4-100*x^3*a^3-15*a^2*x^2+36*a*x-10)*x*(c*(a^2*x^2-1)/a^2/x^2)^(7/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3/(a^2*x^2-1)^2","A"
873,1,96,209,0.065000," ","int((c-c/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-4 x^{5} a^{5}+12 a^{4} \ln \left(x \right) x^{4}+8 x^{3} a^{3}+4 a^{2} x^{2}-4 a x +1\right) x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{3} \left(a^{2} x^{2}-1\right)}"," ",0,"-1/4*(-4*x^5*a^5+12*a^4*ln(x)*x^4+8*x^3*a^3+4*a^2*x^2-4*a*x+1)*x*(c*(a^2*x^2-1)/a^2/x^2)^(5/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3/(a^2*x^2-1)","A"
874,1,69,130,0.063000," ","int((c-c/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-2 x^{3} a^{3}+6 a^{2} \ln \left(x \right) x^{2}+6 a x -1\right) x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 \left(a x -1\right)^{3}}"," ",0,"-1/2*(-2*x^3*a^3+6*a^2*ln(x)*x^2+6*a*x-1)*x*(c*(a^2*x^2-1)/a^2/x^2)^(3/2)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^3","A"
875,1,63,95,0.066000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(a x +\ln \left(x \right)-4 \ln \left(a x +1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\left(a x -1\right)^{2}}"," ",0,"(a*x+ln(x)-4*ln(a*x+1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2","A"
876,1,87,101,0.059000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(1/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \left(-a^{2} x^{2}+3 a x \ln \left(a x +1\right)-a x +3 \ln \left(a x +1\right)+2\right)}{\left(a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \,a^{2}}"," ",0,"-((a*x-1)/(a*x+1))^(3/2)*(a*x+1)/(a*x-1)*(-a^2*x^2+3*a*x*ln(a*x+1)-a*x+3*ln(a*x+1)+2)/(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/a^2","A"
877,1,102,150,0.064000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(3/2),x)","-\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \left(-2 x^{3} a^{3}+6 \ln \left(a x +1\right) x^{2} a^{2}-4 a^{2} x^{2}+12 a x \ln \left(a x +1\right)+4 a x +6 \ln \left(a x +1\right)+5\right)}{2 a^{4} x^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{3}{2}}}"," ",0,"-1/2*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*(-2*x^3*a^3+6*ln(a*x+1)*x^2*a^2-4*a^2*x^2+12*a*x*ln(a*x+1)+4*a*x+6*ln(a*x+1)+5)/a^4/x^3/(c*(a^2*x^2-1)/a^2/x^2)^(3/2)","A"
878,1,175,230,0.069000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(5/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \left(a x -1\right) \left(48 x^{4} a^{4}+3 \ln \left(a x -1\right) x^{3} a^{3}-147 a^{3} x^{3} \ln \left(a x +1\right)+144 x^{3} a^{3}+9 \ln \left(a x -1\right) x^{2} a^{2}-441 \ln \left(a x +1\right) x^{2} a^{2}-42 a^{2} x^{2}+9 \ln \left(a x -1\right) x a -441 a x \ln \left(a x +1\right)-270 a x +3 \ln \left(a x -1\right)-147 \ln \left(a x +1\right)-140\right)}{48 a^{6} x^{5} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{5}{2}}}"," ",0,"1/48*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*(a*x-1)*(48*x^4*a^4+3*ln(a*x-1)*x^3*a^3-147*a^3*x^3*ln(a*x+1)+144*x^3*a^3+9*ln(a*x-1)*x^2*a^2-441*ln(a*x+1)*x^2*a^2-42*a^2*x^2+9*ln(a*x-1)*x*a-441*a*x*ln(a*x+1)-270*a*x+3*ln(a*x-1)-147*ln(a*x+1)-140)/a^6/x^5/(c*(a^2*x^2-1)/a^2/x^2)^(5/2)","A"
879,1,247,311,0.073000," ","int(((a*x-1)/(a*x+1))^(3/2)/(c-c/a^2/x^2)^(7/2),x)","\frac{\left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}} \left(a x +1\right) \left(a x -1\right) \left(64 x^{6} a^{6}+9 \ln \left(a x -1\right) x^{5} a^{5}-201 \ln \left(a x +1\right) x^{5} a^{5}+192 x^{5} a^{5}+27 \ln \left(a x -1\right) x^{4} a^{4}-603 \ln \left(a x +1\right) x^{4} a^{4}-174 x^{4} a^{4}+18 \ln \left(a x -1\right) x^{3} a^{3}-402 a^{3} x^{3} \ln \left(a x +1\right)-618 x^{3} a^{3}-18 \ln \left(a x -1\right) x^{2} a^{2}+402 \ln \left(a x +1\right) x^{2} a^{2}-118 a^{2} x^{2}-27 \ln \left(a x -1\right) x a +603 a x \ln \left(a x +1\right)+414 a x -9 \ln \left(a x -1\right)+201 \ln \left(a x +1\right)+208\right)}{64 a^{8} x^{7} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}\right)^{\frac{7}{2}}}"," ",0,"1/64*((a*x-1)/(a*x+1))^(3/2)*(a*x+1)*(a*x-1)*(64*x^6*a^6+9*ln(a*x-1)*x^5*a^5-201*ln(a*x+1)*x^5*a^5+192*x^5*a^5+27*ln(a*x-1)*x^4*a^4-603*ln(a*x+1)*x^4*a^4-174*x^4*a^4+18*ln(a*x-1)*x^3*a^3-402*a^3*x^3*ln(a*x+1)-618*x^3*a^3-18*ln(a*x-1)*x^2*a^2+402*ln(a*x+1)*x^2*a^2-118*a^2*x^2-27*ln(a*x-1)*x*a+603*a*x*ln(a*x+1)+414*a*x-9*ln(a*x-1)+201*ln(a*x+1)+208)/a^8/x^7/(c*(a^2*x^2-1)/a^2/x^2)^(7/2)","A"
880,1,63,72,0.037000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^m*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{1+m} \left(a x m +m +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{\left(1+m \right) m \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"x^(1+m)*(a*m*x+m+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(1+m)/m/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
881,1,53,64,0.035000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x^2*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{3} \left(2 a x +3\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{6 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/6*x^3*(2*a*x+3)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
882,1,52,61,0.034000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*x*(c-c/a^2/x^2)^(1/2),x)","\frac{x^{2} \left(a x +2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{2 \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"1/2*x^2*(a*x+2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
883,1,50,59,0.047000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2),x)","\frac{\left(a x +\ln \left(x \right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{\left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(a*x+ln(x))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
884,1,50,62,0.058000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x,x)","\frac{\left(a \ln \left(x \right) x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{\left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"(a*ln(x)*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
885,1,53,40,0.044000," ","int(1/((a*x-1)/(a*x+1))^(1/2)*(c-c/a^2/x^2)^(1/2)/x^2,x)","-\frac{\left(2 a x +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}}{2 x \left(a x +1\right) \sqrt{\frac{a x -1}{a x +1}}}"," ",0,"-1/2*(2*a*x+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x/(a*x+1)/((a*x-1)/(a*x+1))^(1/2)","A"
886,1,196,136,0.051000," ","int((a*x+1)/(a*x-1)*x^3*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-6 x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{4}-16 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-27 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +27 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-48 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-48 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{24 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c \,a^{4}}"," ",0,"-1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-6*x*(c*(a^2*x^2-1)/a^2)^(3/2)*a^4-16*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-27*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+27*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-48*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-48*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/c/a^4","A"
887,1,174,107,0.052000," ","int((a*x+1)/(a*x-1)*x^2*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +3 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-6 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-6 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{3} c}"," ",0,"-1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-3*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+3*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-6*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-6*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^3/c","A"
888,1,147,82,0.044000," ","int((a*x+1)/(a*x-1)*x*(c-c/a^2/x^2)^(1/2),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}+\sqrt{c}\, \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-4 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-4 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a \right)}{2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-x*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2+c^(1/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-4*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-4*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2","A"
889,1,197,98,0.053000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)+2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
890,1,306,99,0.056000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2)/x,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{3} c +a^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+\sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x \,a^{2} c +2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}\, c x +2 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x \,c^{2}\right)}{a \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/a*(-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^3*c+a^3*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a-2*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x*a-2*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x*a^2*c+2*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)*c*x+2*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x*c^2)/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
891,1,347,91,0.056000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2)/x^2,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c +4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{3}+4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{2} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c +a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{2}\right)}{2 x \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c+4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^3+4*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^2*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c+a^2*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^2)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
892,1,378,117,0.056000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2)/x^3,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a \left(-6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{3} c +6 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{3}+6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{2} c +3 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{2}+3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{3} c^{2}+a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{3 x^{2} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*a*(-6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^3*c+6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^3+6*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^2*c+3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^2+3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^3*c^2+a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
893,1,410,128,0.059000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2)/x^4,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{4} a^{2} c +21 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c +27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+21 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{2}+16 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +6 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{24 x^{3} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*a^2*(-48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+48*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^4*a^2*c+21*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c+27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2+21*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^2+16*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+6*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
894,1,447,149,0.064000," ","int((a*x+1)/(a*x-1)*(c-c/a^2/x^2)^(1/2)/x^5,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-40 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c +40 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{4}+15 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c +25 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+15 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{5} a \,c^{2}+16 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}+10 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +4 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{20 x^{4} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-1/20*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*a^2*(-40*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^4*c+40*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^4*a^4+15*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+40*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c+25*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+15*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^5*a*c^2+16*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2+10*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+4*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
895,1,89,164,0.059000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^3*(c-c/a^2/x^2)^(1/2),x)","\frac{\left(x^{4} a^{4}+4 x^{3} a^{3}+8 a^{2} x^{2}+16 a x +16 \ln \left(a x -1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{4 a^{3} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/4*(x^4*a^4+4*x^3*a^3+8*a^2*x^2+16*a*x+16*ln(a*x-1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/a^3/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
896,1,82,132,0.060000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x^2*(c-c/a^2/x^2)^(1/2),x)","\frac{\left(2 x^{3} a^{3}+9 a^{2} x^{2}+24 a x +24 \ln \left(a x -1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{6 a^{2} \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/6*(2*x^3*a^3+9*a^2*x^2+24*a*x+24*ln(a*x-1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/a^2/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
897,1,73,99,0.059000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*x*(c-c/a^2/x^2)^(1/2),x)","\frac{\left(a^{2} x^{2}+6 a x +8 \ln \left(a x -1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{2 a \left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"1/2*(a^2*x^2+6*a*x+8*ln(a*x-1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/a/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
898,1,65,97,0.060000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2),x)","-\frac{\left(-a x +\ln \left(x \right)-4 \ln \left(a x -1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{\left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(-a*x+ln(x)-4*ln(a*x-1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
899,1,67,96,0.063000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x,x)","-\frac{\left(3 a \ln \left(x \right) x -4 \ln \left(a x -1\right) x a -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{\left(a x +1\right)^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-(3*a*ln(x)*x-4*ln(a*x-1)*x*a-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/((a*x-1)/(a*x+1))^(3/2)","A"
900,1,82,129,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^2,x)","-\frac{\left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x -1\right) x^{2} a^{2}-6 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{2 \left(a x +1\right)^{2} x \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/2*(8*a^2*ln(x)*x^2-8*ln(a*x-1)*x^2*a^2-6*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/x/((a*x-1)/(a*x+1))^(3/2)","A"
901,1,90,164,0.064000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^3,x)","-\frac{\left(24 a^{3} \ln \left(x \right) x^{3}-24 \ln \left(a x -1\right) x^{3} a^{3}-24 a^{2} x^{2}-9 a x -2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{6 \left(a x +1\right)^{2} x^{2} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/6*(24*a^3*ln(x)*x^3-24*ln(a*x-1)*x^3*a^3-24*a^2*x^2-9*a*x-2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/x^2/((a*x-1)/(a*x+1))^(3/2)","A"
902,1,98,196,0.065000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^4,x)","-\frac{\left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x -1\right) x^{4} a^{4}-16 x^{3} a^{3}-8 a^{2} x^{2}-4 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{4 \left(a x +1\right)^{2} x^{3} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/4*(16*a^4*ln(x)*x^4-16*ln(a*x-1)*x^4*a^4-16*x^3*a^3-8*a^2*x^2-4*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/x^3/((a*x-1)/(a*x+1))^(3/2)","A"
903,1,106,230,0.076000," ","int(1/((a*x-1)/(a*x+1))^(3/2)*(c-c/a^2/x^2)^(1/2)/x^5,x)","-\frac{\left(240 a^{5} \ln \left(x \right) x^{5}-240 \ln \left(a x -1\right) x^{5} a^{5}-240 x^{4} a^{4}-120 x^{3} a^{3}-80 a^{2} x^{2}-45 a x -12\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x -1\right)}{60 \left(a x +1\right)^{2} x^{4} \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}"," ",0,"-1/60*(240*a^5*ln(x)*x^5-240*ln(a*x-1)*x^5*a^5-240*x^4*a^4-120*x^3*a^3-80*a^2*x^2-45*a*x-12)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x-1)/(a*x+1)^2/x^4/((a*x-1)/(a*x+1))^(3/2)","A"
904,1,65,73,0.037000," ","int(x^m*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{1+m} \left(a x m -m -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{\left(1+m \right) m \left(a x -1\right)}"," ",0,"x^(1+m)*(a*m*x-m-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(1+m)/m/(a*x-1)","A"
905,1,53,64,0.034000," ","int(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{3} \left(2 a x -3\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{6 a x -6}"," ",0,"1/6*x^3*(2*a*x-3)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
906,1,52,62,0.037000," ","int(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","\frac{x^{2} \left(a x -2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{2 a x -2}"," ",0,"1/2*x^2*(a*x-2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
907,1,52,60,0.050000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2),x)","-\frac{\left(-a x +\ln \left(x \right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{a x -1}"," ",0,"-(-a*x+ln(x))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
908,1,50,61,0.056000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x,x)","\frac{\left(a \ln \left(x \right) x +1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{a x -1}"," ",0,"(a*ln(x)*x+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)","A"
909,1,53,41,0.035000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/x^2,x)","-\frac{\left(2 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \sqrt{\frac{a x -1}{a x +1}}}{2 \left(a x -1\right) x}"," ",0,"-1/2*(2*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(1/2)/(a*x-1)/x","A"
910,1,196,139,0.051000," ","int(x^3*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(-6 x \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{4}+16 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-27 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +27 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-48 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)+48 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{24 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c \,a^{4}}"," ",0,"-1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(-6*x*(c*(a^2*x^2-1)/a^2)^(3/2)*a^4+16*(c*(a^2*x^2-1)/a^2)^(3/2)*a^3-27*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+27*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-48*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))+48*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/c/a^4","A"
911,1,173,108,0.048000," ","int(x^2*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(\left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} a^{3}-3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x \,a^{2} c +3 c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)-6 c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)+6 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a c \right)}{3 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{3} c}"," ",0,"1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*((c*(a^2*x^2-1)/a^2)^(3/2)*a^3-3*(c*(a^2*x^2-1)/a^2)^(1/2)*x*a^2*c+3*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))-6*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))+6*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a*c)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^3/c","A"
912,1,147,83,0.047000," ","int(x*(c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1),x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-\sqrt{c}\, \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right)+4 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right)-4 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a \right)}{2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*(x*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c^(1/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))+4*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))-4*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a)/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2","A"
913,1,196,98,0.050000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1),x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, x \left(\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}+2 \sqrt{c}\, \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) a \sqrt{-\frac{c}{a^{2}}}+c \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right)\right)}{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*x*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-2*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)+2*c^(1/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*a*(-c/a^2)^(1/2)+c*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x))/(c*(a^2*x^2-1)/a^2)^(1/2)/a^2/(-c/a^2)^(1/2)","A"
914,1,306,99,0.055000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1)/x,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-\sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{3} c +a^{3} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}+\sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x a -2 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x a +2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x \,a^{2} c -2 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2} \sqrt{-\frac{c}{a^{2}}}\, c x -2 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x \,c^{2}\right)}{a \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/a*(-(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^3*c+a^3*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)+(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x*a-2*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x*a+2*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x*a^2*c-2*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2*(-c/a^2)^(1/2)*c*x-2*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x*c^2)/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
915,1,348,92,0.060000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1)/x^2,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(-4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{3} c +4 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{3}+4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{2} a -4 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{2} a +4 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{2} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{2} a^{2} c -a^{2} \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{2} c^{2}\right)}{2 x \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/2*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x*(-4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^3*c+4*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^3+4*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^2*a-4*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^2*a+4*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^2*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^2*a^2*c-a^2*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^2*c^2)/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
916,1,378,120,0.057000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1)/x^3,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a \left(-6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{3} c +6 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{3}+6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{3} a -6 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{3} a +6 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{3} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{3} a^{2} c -3 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x \,a^{2}-3 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{3} c^{2}+a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{3 x^{2} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"-1/3*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^2*a*(-6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^3*c+6*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^3+6*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^3*a-6*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^3*a+6*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^3*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^3*a^2*c-3*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x*a^2-3*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^3*c^2+a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
917,1,410,128,0.058000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1)/x^4,x)","\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +48 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}+48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{4} a -48 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{4} a +48 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{4} a^{2} c -21 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{4} a^{2} c -27 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-21 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{4} c^{2}+16 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x -6 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{24 x^{3} \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, c}"," ",0,"1/24*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^3*a^2*(-48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+48*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3+48*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^4*a-48*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^4*a+48*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^4*a^2*c-21*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^4*a^2*c-27*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-21*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^4*c^2+16*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x-6*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(-c/a^2)^(1/2)/(c*(a^2*x^2-1)/a^2)^(1/2)/c","B"
918,1,447,149,0.063000," ","int((c-c/a^2/x^2)^(1/2)/(a*x+1)*(a*x-1)/x^5,x)","-\frac{\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, a^{2} \left(-40 \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, x^{6} a^{4} c +40 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x^{4} a^{4}-15 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, x^{5} a^{3} c +40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(x \sqrt{c}+\sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\right) x^{5} a^{2}-40 \sqrt{-\frac{c}{a^{2}}}\, c^{\frac{3}{2}} \ln \left(\frac{\sqrt{c}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}+c x}{\sqrt{c}}\right) x^{5} a^{2}+40 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{\left(a x -1\right) \left(a x +1\right) c}{a^{2}}}\, x^{5} a^{3} c -25 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{3} a^{3}-15 \ln \left(\frac{2 \sqrt{-\frac{c}{a^{2}}}\, \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, a^{2}-2 c}{a^{2} x}\right) x^{5} a \,c^{2}+16 \sqrt{-\frac{c}{a^{2}}}\, \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} x^{2} a^{2}-10 a \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\, x +4 \left(\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}\right)^{\frac{3}{2}} \sqrt{-\frac{c}{a^{2}}}\right)}{20 x^{4} \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2}}}\, \sqrt{-\frac{c}{a^{2}}}\, c}"," ",0,"-1/20*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)/x^4*a^2*(-40*(c*(a^2*x^2-1)/a^2)^(1/2)*(-c/a^2)^(1/2)*x^6*a^4*c+40*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x^4*a^4-15*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*x^5*a^3*c+40*(-c/a^2)^(1/2)*c^(3/2)*ln(x*c^(1/2)+(c*(a^2*x^2-1)/a^2)^(1/2))*x^5*a^2-40*(-c/a^2)^(1/2)*c^(3/2)*ln((c^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)+c*x)/c^(1/2))*x^5*a^2+40*(-c/a^2)^(1/2)*((a*x-1)*(a*x+1)*c/a^2)^(1/2)*x^5*a^3*c-25*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^3*a^3-15*ln(2*((-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(1/2)*a^2-c)/a^2/x)*x^5*a*c^2+16*(-c/a^2)^(1/2)*(c*(a^2*x^2-1)/a^2)^(3/2)*x^2*a^2-10*a*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2)*x+4*(c*(a^2*x^2-1)/a^2)^(3/2)*(-c/a^2)^(1/2))/(c*(a^2*x^2-1)/a^2)^(1/2)/(-c/a^2)^(1/2)/c","B"
919,1,89,164,0.058000," ","int(x^3*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(x^{4} a^{4}-4 x^{3} a^{3}+8 a^{2} x^{2}-16 a x +16 \ln \left(a x +1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{2} a^{3}}"," ",0,"1/4*(x^4*a^4-4*x^3*a^3+8*a^2*x^2-16*a*x+16*ln(a*x+1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/a^3","A"
920,1,82,131,0.056000," ","int(x^2*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","-\frac{\left(-2 x^{3} a^{3}+9 a^{2} x^{2}-24 a x +24 \ln \left(a x +1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 a^{2} \left(a x -1\right)^{2}}"," ",0,"-1/6*(-2*x^3*a^3+9*a^2*x^2-24*a*x+24*ln(a*x+1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a^2/(a*x-1)^2","A"
921,1,73,98,0.056000," ","int(x*(c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(a^{2} x^{2}-6 a x +8 \ln \left(a x +1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 a \left(a x -1\right)^{2}}"," ",0,"1/2*(a^2*x^2-6*a*x+8*ln(a*x+1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/a/(a*x-1)^2","A"
922,1,63,95,0.053000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2),x)","\frac{\left(a x +\ln \left(x \right)-4 \ln \left(a x +1\right)\right) x \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\left(a x -1\right)^{2}}"," ",0,"(a*x+ln(x)-4*ln(a*x+1))*x*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2","A"
923,1,67,96,0.063000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x,x)","-\frac{\left(3 a \ln \left(x \right) x -4 a x \ln \left(a x +1\right)+1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{\left(a x -1\right)^{2}}"," ",0,"-(3*a*ln(x)*x-4*a*x*ln(a*x+1)+1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2","A"
924,1,82,128,0.063000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^2,x)","\frac{\left(8 a^{2} \ln \left(x \right) x^{2}-8 \ln \left(a x +1\right) x^{2} a^{2}+6 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{2 \left(a x -1\right)^{2} x}"," ",0,"1/2*(8*a^2*ln(x)*x^2-8*ln(a*x+1)*x^2*a^2+6*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/x","A"
925,1,90,163,0.064000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^3,x)","-\frac{\left(24 a^{3} \ln \left(x \right) x^{3}-24 a^{3} x^{3} \ln \left(a x +1\right)+24 a^{2} x^{2}-9 a x +2\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{6 \left(a x -1\right)^{2} x^{2}}"," ",0,"-1/6*(24*a^3*ln(x)*x^3-24*a^3*x^3*ln(a*x+1)+24*a^2*x^2-9*a*x+2)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/x^2","A"
926,1,98,195,0.065000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^4,x)","\frac{\left(16 a^{4} \ln \left(x \right) x^{4}-16 \ln \left(a x +1\right) x^{4} a^{4}+16 x^{3} a^{3}-8 a^{2} x^{2}+4 a x -1\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{4 \left(a x -1\right)^{2} x^{3}}"," ",0,"1/4*(16*a^4*ln(x)*x^4-16*ln(a*x+1)*x^4*a^4+16*x^3*a^3-8*a^2*x^2+4*a*x-1)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/x^3","A"
927,1,106,229,0.066000," ","int((c-c/a^2/x^2)^(1/2)*((a*x-1)/(a*x+1))^(3/2)/x^5,x)","-\frac{\left(240 a^{5} \ln \left(x \right) x^{5}-240 \ln \left(a x +1\right) x^{5} a^{5}+240 x^{4} a^{4}-120 x^{3} a^{3}+80 a^{2} x^{2}-45 a x +12\right) \sqrt{\frac{c \left(a^{2} x^{2}-1\right)}{a^{2} x^{2}}}\, \left(a x +1\right) \left(\frac{a x -1}{a x +1}\right)^{\frac{3}{2}}}{60 \left(a x -1\right)^{2} x^{4}}"," ",0,"-1/60*(240*a^5*ln(x)*x^5-240*ln(a*x+1)*x^5*a^5+240*x^4*a^4-120*x^3*a^3+80*a^2*x^2-45*a*x+12)*(c*(a^2*x^2-1)/a^2/x^2)^(1/2)*(a*x+1)*((a*x-1)/(a*x+1))^(3/2)/(a*x-1)^2/x^4","A"
928,0,0,138,0.058000," ","int(exp(n*arccoth(a*x))*(c-c/a^2/x^2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a^2/x^2),x)","F"
929,0,0,142,0.056000," ","int(exp(n*arccoth(a*x))/(c-c/a^2/x^2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{c -\frac{c}{a^{2} x^{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a^2/x^2),x)","F"
930,0,0,268,0.064000," ","int(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^2,x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\left(c -\frac{c}{a^{2} x^{2}}\right)^{2}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^2,x)","F"
931,0,0,247,0.050000," ","int(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^(1/2),x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \sqrt{c -\frac{c}{a^{2} x^{2}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^(1/2),x)","F"
932,0,0,157,0.056000," ","int(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^(1/2),x)","\int \frac{{\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)}}{\sqrt{c -\frac{c}{a^{2} x^{2}}}}\, dx"," ",0,"int(exp(n*arccoth(a*x))/(c-c/a^2/x^2)^(1/2),x)","F"
933,0,0,104,0.128000," ","int(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^p,x)","\int {\mathrm e}^{n \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}\, dx"," ",0,"int(exp(n*arccoth(a*x))*(c-c/a^2/x^2)^p,x)","F"
934,0,0,78,0.105000," ","int((c-c/a^2/x^2)^p/exp(2*p*arccoth(a*x)),x)","\int \left(c -\frac{c}{a^{2} x^{2}}\right)^{p} {\mathrm e}^{-2 p \,\mathrm{arccoth}\left(a x \right)}\, dx"," ",0,"int((c-c/a^2/x^2)^p/exp(2*p*arccoth(a*x)),x)","F"
935,0,0,77,0.097000," ","int(exp(2*p*arccoth(a*x))*(c-c/a^2/x^2)^p,x)","\int {\mathrm e}^{2 p \,\mathrm{arccoth}\left(a x \right)} \left(c -\frac{c}{a^{2} x^{2}}\right)^{p}\, dx"," ",0,"int(exp(2*p*arccoth(a*x))*(c-c/a^2/x^2)^p,x)","F"