1,1,250,183,0.102000," ","int(x^3*arcsech(b*x+a),x)","\frac{\frac{\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right)^{4}}{4}-\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right)^{3} a +\frac{3 \,\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right)^{2} a^{2}}{2}-\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right) a^{3}+\frac{\mathrm{arcsech}\left(b x +a \right) a^{4}}{4}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \left(b x +a \right) \sqrt{\frac{b x +a +1}{b x +a}}\, \left(3 a^{4} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)+12 a^{3} \arcsin \left(b x +a \right)+\left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}-6 a \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+18 a^{2} \sqrt{1-\left(b x +a \right)^{2}}+6 a \arcsin \left(b x +a \right)+2 \sqrt{1-\left(b x +a \right)^{2}}\right)}{12 \sqrt{1-\left(b x +a \right)^{2}}}}{b^{4}}"," ",0,"1/b^4*(1/4*arcsech(b*x+a)*(b*x+a)^4-arcsech(b*x+a)*(b*x+a)^3*a+3/2*arcsech(b*x+a)*(b*x+a)^2*a^2-arcsech(b*x+a)*(b*x+a)*a^3+1/4*arcsech(b*x+a)*a^4-1/12*(-(b*x+a-1)/(b*x+a))^(1/2)*(b*x+a)*((b*x+a+1)/(b*x+a))^(1/2)*(3*a^4*arctanh(1/(1-(b*x+a)^2)^(1/2))+12*a^3*arcsin(b*x+a)+(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-6*a*(b*x+a)*(1-(b*x+a)^2)^(1/2)+18*a^2*(1-(b*x+a)^2)^(1/2)+6*a*arcsin(b*x+a)+2*(1-(b*x+a)^2)^(1/2))/(1-(b*x+a)^2)^(1/2))","A"
2,1,189,137,0.070000," ","int(x^2*arcsech(b*x+a),x)","\frac{\frac{\left(b x +a \right)^{3} \mathrm{arcsech}\left(b x +a \right)}{3}-\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right)^{2} a +\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right) a^{2}-\frac{\mathrm{arcsech}\left(b x +a \right) a^{3}}{3}+\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \left(b x +a \right) \sqrt{\frac{b x +a +1}{b x +a}}\, \left(2 a^{3} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)+6 a^{2} \arcsin \left(b x +a \right)-\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+6 a \sqrt{1-\left(b x +a \right)^{2}}+\arcsin \left(b x +a \right)\right)}{6 \sqrt{1-\left(b x +a \right)^{2}}}}{b^{3}}"," ",0,"1/b^3*(1/3*(b*x+a)^3*arcsech(b*x+a)-arcsech(b*x+a)*(b*x+a)^2*a+arcsech(b*x+a)*(b*x+a)*a^2-1/3*arcsech(b*x+a)*a^3+1/6*(-(b*x+a-1)/(b*x+a))^(1/2)*(b*x+a)*((b*x+a+1)/(b*x+a))^(1/2)*(2*a^3*arctanh(1/(1-(b*x+a)^2)^(1/2))+6*a^2*arcsin(b*x+a)-(b*x+a)*(1-(b*x+a)^2)^(1/2)+6*a*(1-(b*x+a)^2)^(1/2)+arcsin(b*x+a))/(1-(b*x+a)^2)^(1/2))","A"
3,1,111,97,0.070000," ","int(x*arcsech(b*x+a),x)","\frac{\frac{\mathrm{arcsech}\left(b x +a \right) \left(b x +a \right)^{2}}{2}-\mathrm{arcsech}\left(b x +a \right) a \left(b x +a \right)-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \left(b x +a \right) \sqrt{\frac{b x +a +1}{b x +a}}\, \left(2 a \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{2 \sqrt{1-\left(b x +a \right)^{2}}}}{b^{2}}"," ",0,"1/b^2*(1/2*arcsech(b*x+a)*(b*x+a)^2-arcsech(b*x+a)*a*(b*x+a)-1/2*(-(b*x+a-1)/(b*x+a))^(1/2)*(b*x+a)*((b*x+a+1)/(b*x+a))^(1/2)*(2*a*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))/(1-(b*x+a)^2)^(1/2))","A"
4,1,50,42,0.047000," ","int(arcsech(b*x+a),x)","x \,\mathrm{arcsech}\left(b x +a \right)+\frac{\mathrm{arcsech}\left(b x +a \right) a}{b}-\frac{\arctan \left(\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)}{b}"," ",0,"x*arcsech(b*x+a)+1/b*arcsech(b*x+a)*a-1/b*arctan((1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))","A"
5,1,886,298,0.955000," ","int(arcsech(b*x+a)/x,x)","\frac{\mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{2}+\frac{\mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{2}-\frac{\sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{2 \left(a^{2}-1\right)}+\frac{\sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{2 a^{2}-2}+\dilog \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)+\dilog \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)-\mathrm{arcsech}\left(b x +a \right) \ln \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)-\mathrm{arcsech}\left(b x +a \right) \ln \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)-\dilog \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)-\dilog \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)+\frac{\left(a^{2}-1-\sqrt{-a^{2}+1}\right) \mathrm{arcsech}\left(b x +a \right) \left(\ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right) a^{2}+\ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right) a^{2}-2 \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)+2 \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right) \sqrt{-a^{2}+1}\right)}{2 a^{2} \left(a^{2}-1\right)}"," ",0,"1/2*arcsech(b*x+a)*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+1/2*arcsech(b*x+a)*ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))-1/2*(-a^2+1)^(1/2)/(a^2-1)*arcsech(b*x+a)*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+1/2*(-a^2+1)^(1/2)/(a^2-1)*arcsech(b*x+a)*ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))+dilog((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+dilog((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))-arcsech(b*x+a)*ln(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-arcsech(b*x+a)*ln(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-dilog(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-dilog(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+1/2*(a^2-1-(-a^2+1)^(1/2))/a^2/(a^2-1)*arcsech(b*x+a)*(ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))*a^2+ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))*a^2-2*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+2*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))*(-a^2+1)^(1/2))","C"
6,1,542,62,0.084000," ","int(arcsech(b*x+a)/x^2,x)","-\frac{\mathrm{arcsech}\left(b x +a \right)}{x}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right) x \,b^{2}}{\sqrt{1-\left(b x +a \right)^{2}}\, \left(a -1\right) \left(1+a \right)}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) x \,b^{2}}{\sqrt{1-\left(b x +a \right)^{2}}\, a \left(a -1\right) \left(1+a \right)}-\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\sqrt{1-\left(b x +a \right)^{2}}\, \left(a -1\right) \left(1+a \right)}-\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right)}{\sqrt{1-\left(b x +a \right)^{2}}\, \left(a -1\right) \left(1+a \right)}+\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right) x \,b^{2}}{\sqrt{1-\left(b x +a \right)^{2}}\, a \left(a -1\right) \left(1+a \right)}+\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\sqrt{1-\left(b x +a \right)^{2}}\, \left(a -1\right) \left(1+a \right)}"," ",0,"-arcsech(b*x+a)/x-(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)*a/(a-1)/(1+a)*arctanh(1/(1-(b*x+a)^2)^(1/2))*x*b^2-(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)/a/(a-1)/(1+a)*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*x*b^2-b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)*a^2/(a-1)/(1+a)*arctanh(1/(1-(b*x+a)^2)^(1/2))-b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)/(a-1)/(1+a)*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)+(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)/a/(a-1)/(1+a)*arctanh(1/(1-(b*x+a)^2)^(1/2))*x*b^2+b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(1-(b*x+a)^2)^(1/2)/(a-1)/(1+a)*arctanh(1/(1-(b*x+a)^2)^(1/2))","B"
7,1,1233,117,0.090000," ","int(arcsech(b*x+a)/x^3,x)","-\frac{\mathrm{arcsech}\left(b x +a \right)}{2 x^{2}}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \,a^{2} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right)}{\left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{3} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right)}{\left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{2}}-\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right)}-\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \sqrt{-a^{2}+1}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{2}}-\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2}}{2 x \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right)}+\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a}+\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{2 \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right) a}+\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{2 x \left(a^{2}-1\right) \left(1+a \right) \left(a -1\right)}"," ",0,"-1/2*arcsech(b*x+a)/x^2+1/2*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^2*arctanh(1/(1-(b*x+a)^2)^(1/2))+b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)+1/2*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^3*arctanh(1/(1-(b*x+a)^2)^(1/2))+b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)-b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*arctanh(1/(1-(b*x+a)^2)^(1/2))-1/2*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^2*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)-b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a*arctanh(1/(1-(b*x+a)^2)^(1/2))-1/2*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)*a-1/2*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a*(-a^2+1)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)+1/2*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^2*arctanh(1/(1-(b*x+a)^2)^(1/2))-1/2*b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x/(a^2-1)/(1+a)/(a-1)*a^2+1/2*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a*arctanh(1/(1-(b*x+a)^2)^(1/2))+1/2*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)/(1+a)/(a-1)/a+1/2*b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x/(a^2-1)/(1+a)/(a-1)","B"
8,1,1946,175,0.099000," ","int(arcsech(b*x+a)/x^4,x)","-\frac{\mathrm{arcsech}\left(b x +a \right)}{3 x^{3}}-\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \,a^{3} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x a \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{4} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2} \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x a \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{5 b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{6 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2} \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}+\frac{5 b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2}}{6 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}+\frac{5 b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{6 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a}+\frac{2 b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{3}}{3 x \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{3}}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{\left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}}-\frac{7 b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{6 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{4}}{6 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}-\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \ln \left(\frac{2 \sqrt{-a^{2}+1}\, \sqrt{1-\left(b x +a \right)^{2}}-2 a \left(b x +a \right)+2}{b x}\right) \sqrt{-a^{2}+1}}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{2}}+\frac{b^{4} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, x \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{3}}-\frac{5 b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a}{6 x \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \arctanh \left(\frac{1}{\sqrt{1-\left(b x +a \right)^{2}}}\right)}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) \sqrt{1-\left(b x +a \right)^{2}}\, a^{2}}+\frac{b^{3} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{3 \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) a^{2}}+\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, a^{2}}{3 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}+\frac{b^{2} \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{6 x \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right) a}-\frac{b \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{6 x^{2} \left(a^{2}-1\right)^{2} \left(1+a \right) \left(a -1\right)}"," ",0,"-1/3*arcsech(b*x+a)/x^3-1/3*b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^3*arctanh(1/(1-(b*x+a)^2)^(1/2))-b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)-1/3*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^4*arctanh(1/(1-(b*x+a)^2)^(1/2))-b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^2*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)+b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a*arctanh(1/(1-(b*x+a)^2)^(1/2))+5/6*b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)+b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*a^2*arctanh(1/(1-(b*x+a)^2)^(1/2))+5/6*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)*a^2+5/6*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)-b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a*arctanh(1/(1-(b*x+a)^2)^(1/2))+2/3*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x/(a^2-1)^2/(1+a)/(a-1)*a^3-1/3*b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^3*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)-b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)*arctanh(1/(1-(b*x+a)^2)^(1/2))-7/6*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)-1/6*b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)*a^4-1/3*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^2*ln(2*((-a^2+1)^(1/2)*(1-(b*x+a)^2)^(1/2)-a*(b*x+a)+1)/b/x)*(-a^2+1)^(1/2)+1/3*b^4*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*x/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^3*arctanh(1/(1-(b*x+a)^2)^(1/2))-5/6*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x/(a^2-1)^2/(1+a)/(a-1)*a+1/3*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/(1-(b*x+a)^2)^(1/2)/a^2*arctanh(1/(1-(b*x+a)^2)^(1/2))+1/3*b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/(a^2-1)^2/(1+a)/(a-1)/a^2+1/3*b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)*a^2+1/6*b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x/(a^2-1)^2/(1+a)/(a-1)/a-1/6*b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)/x^2/(a^2-1)^2/(1+a)/(a-1)","B"
9,1,655,391,1.678000," ","int(x^2*arcsech(b*x+a)^2,x)","-\frac{a}{3 b^{3}}-\frac{x}{3 b^{2}}-\frac{2 a \ln \left(1+\left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)^{2}\right)}{b^{3}}+\frac{4 a \ln \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)}{b^{3}}+\frac{2 i a^{2} \dilog \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{3}}+\frac{a^{3} \mathrm{arcsech}\left(b x +a \right)^{2}}{3 b^{3}}+\frac{4 \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \mathrm{arcsech}\left(b x +a \right) x a}{3 b^{2}}-\frac{2 a \,\mathrm{arcsech}\left(b x +a \right)}{b^{3}}-\frac{2 i a^{2} \dilog \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{3}}-\frac{i \mathrm{arcsech}\left(b x +a \right) \ln \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{3 b^{3}}+\frac{2 i a^{2} \mathrm{arcsech}\left(b x +a \right) \ln \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{3}}+\frac{x^{3} \mathrm{arcsech}\left(b x +a \right)^{2}}{3}-\frac{2 i a^{2} \mathrm{arcsech}\left(b x +a \right) \ln \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{3}}+\frac{i \dilog \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{3 b^{3}}+\frac{5 \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \mathrm{arcsech}\left(b x +a \right) a^{2}}{3 b^{3}}-\frac{i \dilog \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{3 b^{3}}+\frac{i \mathrm{arcsech}\left(b x +a \right) \ln \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{3 b^{3}}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \mathrm{arcsech}\left(b x +a \right) x^{2}}{3 b}"," ",0,"-1/3/b^3*a-1/3*x/b^2-2/b^3*a*ln(1+(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))^2)+4/b^3*a*ln(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))-2*I/b^3*a^2*dilog(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+1/3*a^3*arcsech(b*x+a)^2/b^3+4/3/b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*arcsech(b*x+a)*x*a-2/b^3*a*arcsech(b*x+a)-1/3*I/b^3*dilog(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-1/3*I/b^3*arcsech(b*x+a)*ln(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+2*I/b^3*a^2*arcsech(b*x+a)*ln(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+1/3*x^3*arcsech(b*x+a)^2-2*I/b^3*a^2*arcsech(b*x+a)*ln(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+1/3*I/b^3*dilog(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+5/3/b^3*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*arcsech(b*x+a)*a^2+2*I/b^3*a^2*dilog(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+1/3*I/b^3*arcsech(b*x+a)*ln(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-1/3/b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*arcsech(b*x+a)*x^2","A"
10,1,396,208,1.310000," ","int(x*arcsech(b*x+a)^2,x)","\frac{x^{2} \mathrm{arcsech}\left(b x +a \right)^{2}}{2}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \mathrm{arcsech}\left(b x +a \right) x}{b}-\frac{\sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}\, \mathrm{arcsech}\left(b x +a \right) a}{b^{2}}-\frac{a^{2} \mathrm{arcsech}\left(b x +a \right)^{2}}{2 b^{2}}+\frac{\mathrm{arcsech}\left(b x +a \right)}{b^{2}}-\frac{2 \ln \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)}{b^{2}}+\frac{\ln \left(1+\left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)^{2}\right)}{b^{2}}-\frac{2 i a \,\mathrm{arcsech}\left(b x +a \right) \ln \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{2}}+\frac{2 i a \,\mathrm{arcsech}\left(b x +a \right) \ln \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{2}}-\frac{2 i a \dilog \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{2}}+\frac{2 i a \dilog \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b^{2}}"," ",0,"1/2*x^2*arcsech(b*x+a)^2-1/b*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*arcsech(b*x+a)*x-1/b^2*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)*arcsech(b*x+a)*a-1/2*a^2*arcsech(b*x+a)^2/b^2+1/b^2*arcsech(b*x+a)-2/b^2*ln(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+1/b^2*ln(1+(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))^2)-2*I/b^2*a*arcsech(b*x+a)*ln(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+2*I/b^2*a*arcsech(b*x+a)*ln(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-2*I/b^2*a*dilog(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+2*I/b^2*a*dilog(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))","A"
11,1,209,145,0.339000," ","int(arcsech(b*x+a)^2,x)","x \mathrm{arcsech}\left(b x +a \right)^{2}+\frac{\mathrm{arcsech}\left(b x +a \right)^{2} a}{b}+\frac{2 i \mathrm{arcsech}\left(b x +a \right) \ln \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b}-\frac{2 i \mathrm{arcsech}\left(b x +a \right) \ln \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b}+\frac{2 i \dilog \left(1+i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b}-\frac{2 i \dilog \left(1-i \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)\right)}{b}"," ",0,"x*arcsech(b*x+a)^2+1/b*arcsech(b*x+a)^2*a+2*I/b*arcsech(b*x+a)*ln(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-2*I/b*arcsech(b*x+a)*ln(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))+2*I/b*dilog(1+I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))-2*I/b*dilog(1-I*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2)))","A"
12,0,0,467,0.801000," ","int(arcsech(b*x+a)^2/x,x)","\int \frac{\mathrm{arcsech}\left(b x +a \right)^{2}}{x}\, dx"," ",0,"int(arcsech(b*x+a)^2/x,x)","F"
13,1,367,300,0.751000," ","int(arcsech(b*x+a)^2/x^2,x)","-\frac{b \mathrm{arcsech}\left(b x +a \right)^{2}}{a}-\frac{\mathrm{arcsech}\left(b x +a \right)^{2}}{x}+\frac{2 b \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{a \left(a^{2}-1\right)}-\frac{2 b \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{a \left(a^{2}-1\right)}+\frac{2 b \sqrt{-a^{2}+1}\, \dilog \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{a \left(a^{2}-1\right)}-\frac{2 b \sqrt{-a^{2}+1}\, \dilog \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{a \left(a^{2}-1\right)}"," ",0,"-b*arcsech(b*x+a)^2/a-arcsech(b*x+a)^2/x+2*b*(-a^2+1)^(1/2)/a/(a^2-1)*arcsech(b*x+a)*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))-2*b*(-a^2+1)^(1/2)/a/(a^2-1)*arcsech(b*x+a)*ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))+2*b*(-a^2+1)^(1/2)/a/(a^2-1)*dilog((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))-2*b*(-a^2+1)^(1/2)/a/(a^2-1)*dilog((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))","A"
14,1,1026,683,1.292000," ","int(arcsech(b*x+a)^2/x^3,x)","\frac{b^{2} \mathrm{arcsech}\left(b x +a \right)^{2}}{2 a^{2}-2}-\frac{b^{2} \mathrm{arcsech}\left(b x +a \right) \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{a \left(a^{2}-1\right)}-\frac{b \,\mathrm{arcsech}\left(b x +a \right) \sqrt{-\frac{b x +a -1}{b x +a}}\, \sqrt{\frac{b x +a +1}{b x +a}}}{\left(a^{2}-1\right) x}-\frac{b^{2} \mathrm{arcsech}\left(b x +a \right)^{2}}{2 a^{2} \left(a^{2}-1\right)}-\frac{\mathrm{arcsech}\left(b x +a \right)^{2} a^{2}}{2 \left(a^{2}-1\right) x^{2}}-\frac{b^{2} \mathrm{arcsech}\left(b x +a \right)}{a^{2} \left(a^{2}-1\right)}+\frac{\mathrm{arcsech}\left(b x +a \right)^{2}}{2 \left(a^{2}-1\right) x^{2}}+\frac{2 b^{2} \ln \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)}{a^{2} \left(a^{2}-1\right)}-\frac{b^{2} \ln \left(a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)^{2}+a -\frac{2}{b x +a}-2 \sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)}{a^{2} \left(a^{2}-1\right)}+\frac{b^{2} \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{a^{2} \left(a^{2}-1\right)^{2}}-\frac{b^{2} \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{a^{2} \left(a^{2}-1\right)^{2}}+\frac{b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{a^{2} \left(a^{2}-1\right)^{2}}-\frac{b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{a^{2} \left(a^{2}-1\right)^{2}}-\frac{2 b^{2} \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}+\frac{2 b^{2} \sqrt{-a^{2}+1}\, \mathrm{arcsech}\left(b x +a \right) \ln \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}-\frac{2 b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{-a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}+1}{1+\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}+\frac{2 b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{a \left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)+\sqrt{-a^{2}+1}-1}{-1+\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}"," ",0,"1/2*b^2*arcsech(b*x+a)^2/(a^2-1)-b^2*arcsech(b*x+a)/a/(a^2-1)*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)-b*arcsech(b*x+a)/(a^2-1)/x*(-(b*x+a-1)/(b*x+a))^(1/2)*((b*x+a+1)/(b*x+a))^(1/2)-1/2*b^2*arcsech(b*x+a)^2/a^2/(a^2-1)-1/2*arcsech(b*x+a)^2*a^2/(a^2-1)/x^2-b^2*arcsech(b*x+a)/a^2/(a^2-1)+1/2*arcsech(b*x+a)^2/(a^2-1)/x^2+2*b^2/a^2/(a^2-1)*ln(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))-b^2/a^2/(a^2-1)*ln(a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))^2+a-2/(b*x+a)-2*(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+b^2*(-a^2+1)^(1/2)/a^2/(a^2-1)^2*arcsech(b*x+a)*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))-b^2*(-a^2+1)^(1/2)/a^2/(a^2-1)^2*arcsech(b*x+a)*ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))+b^2*(-a^2+1)^(1/2)/a^2/(a^2-1)^2*dilog((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))-b^2*(-a^2+1)^(1/2)/a^2/(a^2-1)^2*dilog((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))-2*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*arcsech(b*x+a)*ln((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+2*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*arcsech(b*x+a)*ln((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))-2*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*dilog((-a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)+1)/(1+(-a^2+1)^(1/2)))+2*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*dilog((a*(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))+(-a^2+1)^(1/2)-1)/(-1+(-a^2+1)^(1/2)))","A"
15,0,0,401,1.885000," ","int(x*arcsech(b*x+a)^3,x)","\int x \mathrm{arcsech}\left(b x +a \right)^{3}\, dx"," ",0,"int(x*arcsech(b*x+a)^3,x)","F"
16,0,0,243,0.610000," ","int(arcsech(b*x+a)^3,x)","\int \mathrm{arcsech}\left(b x +a \right)^{3}\, dx"," ",0,"int(arcsech(b*x+a)^3,x)","F"
17,0,0,632,0.810000," ","int(arcsech(b*x+a)^3/x,x)","\int \frac{\mathrm{arcsech}\left(b x +a \right)^{3}}{x}\, dx"," ",0,"int(arcsech(b*x+a)^3/x,x)","F"
18,0,0,444,0.896000," ","int(arcsech(b*x+a)^3/x^2,x)","\int \frac{\mathrm{arcsech}\left(b x +a \right)^{3}}{x^{2}}\, dx"," ",0,"int(arcsech(b*x+a)^3/x^2,x)","F"
19,0,0,1263,1.667000," ","int(arcsech(b*x+a)^3/x^3,x)","\int \frac{\mathrm{arcsech}\left(b x +a \right)^{3}}{x^{3}}\, dx"," ",0,"int(arcsech(b*x+a)^3/x^3,x)","F"
20,1,54,110,0.074000," ","int(x^3*arcsech(x^(1/2)),x)","\frac{x^{4} \mathrm{arcsech}\left(\sqrt{x}\right)}{4}-\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{x}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(5 x^{3}+6 x^{2}+8 x +16\right)}{140}"," ",0,"1/4*x^4*arcsech(x^(1/2))-1/140*(-(-1+x^(1/2))/x^(1/2))^(1/2)*x^(1/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(5*x^3+6*x^2+8*x+16)","A"
21,1,49,84,0.069000," ","int(x^2*arcsech(x^(1/2)),x)","\frac{x^{3} \mathrm{arcsech}\left(\sqrt{x}\right)}{3}-\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{x}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(3 x^{2}+4 x +8\right)}{45}"," ",0,"1/3*x^3*arcsech(x^(1/2))-1/45*(-(-1+x^(1/2))/x^(1/2))^(1/2)*x^(1/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(3*x^2+4*x+8)","A"
22,1,42,58,0.062000," ","int(x*arcsech(x^(1/2)),x)","\frac{x^{2} \mathrm{arcsech}\left(\sqrt{x}\right)}{2}-\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{x}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(x +2\right)}{6}"," ",0,"1/2*x^2*arcsech(x^(1/2))-1/6*(-(-1+x^(1/2))/x^(1/2))^(1/2)*x^(1/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(x+2)","A"
23,1,36,28,0.059000," ","int(arcsech(x^(1/2)),x)","x \,\mathrm{arcsech}\left(\sqrt{x}\right)-\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{x}"," ",0,"x*arcsech(x^(1/2))-(-(-1+x^(1/2))/x^(1/2))^(1/2)*((1+x^(1/2))/x^(1/2))^(1/2)*x^(1/2)","A"
24,1,65,64,0.101000," ","int(arcsech(x^(1/2))/x,x)","\mathrm{arcsech}\left(\sqrt{x}\right)^{2}-2 \,\mathrm{arcsech}\left(\sqrt{x}\right) \ln \left(1+\left(\frac{1}{\sqrt{x}}+\sqrt{-1+\frac{1}{\sqrt{x}}}\, \sqrt{1+\frac{1}{\sqrt{x}}}\right)^{2}\right)-\polylog \left(2, -\left(\frac{1}{\sqrt{x}}+\sqrt{-1+\frac{1}{\sqrt{x}}}\, \sqrt{1+\frac{1}{\sqrt{x}}}\right)^{2}\right)"," ",0,"arcsech(x^(1/2))^2-2*arcsech(x^(1/2))*ln(1+(1/x^(1/2)+(-1+1/x^(1/2))^(1/2)*(1+1/x^(1/2))^(1/2))^2)-polylog(2,-(1/x^(1/2)+(-1+1/x^(1/2))^(1/2)*(1+1/x^(1/2))^(1/2))^2)","A"
25,1,64,68,0.072000," ","int(arcsech(x^(1/2))/x^2,x)","-\frac{\mathrm{arcsech}\left(\sqrt{x}\right)}{x}+\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(\arctanh \left(\frac{1}{\sqrt{1-x}}\right) x +\sqrt{1-x}\right)}{2 \sqrt{x}\, \sqrt{1-x}}"," ",0,"-arcsech(x^(1/2))/x+1/2*(-(-1+x^(1/2))/x^(1/2))^(1/2)/x^(1/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(arctanh(1/(1-x)^(1/2))*x+(1-x)^(1/2))/(1-x)^(1/2)","A"
26,1,79,92,0.073000," ","int(arcsech(x^(1/2))/x^3,x)","-\frac{\mathrm{arcsech}\left(\sqrt{x}\right)}{2 x^{2}}+\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{1-x}}\right) x^{2}+3 x \sqrt{1-x}+2 \sqrt{1-x}\right)}{16 x^{\frac{3}{2}} \sqrt{1-x}}"," ",0,"-1/2*arcsech(x^(1/2))/x^2+1/16*(-(-1+x^(1/2))/x^(1/2))^(1/2)/x^(3/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(3*arctanh(1/(1-x)^(1/2))*x^2+3*x*(1-x)^(1/2)+2*(1-x)^(1/2))/(1-x)^(1/2)","A"
27,1,91,116,0.072000," ","int(arcsech(x^(1/2))/x^4,x)","-\frac{\mathrm{arcsech}\left(\sqrt{x}\right)}{3 x^{3}}+\frac{\sqrt{-\frac{-1+\sqrt{x}}{\sqrt{x}}}\, \sqrt{\frac{1+\sqrt{x}}{\sqrt{x}}}\, \left(15 \arctanh \left(\frac{1}{\sqrt{1-x}}\right) x^{3}+15 \sqrt{1-x}\, x^{2}+10 x \sqrt{1-x}+8 \sqrt{1-x}\right)}{144 x^{\frac{5}{2}} \sqrt{1-x}}"," ",0,"-1/3*arcsech(x^(1/2))/x^3+1/144*(-(-1+x^(1/2))/x^(1/2))^(1/2)/x^(5/2)*((1+x^(1/2))/x^(1/2))^(1/2)*(15*arctanh(1/(1-x)^(1/2))*x^3+15*(1-x)^(1/2)*x^2+10*x*(1-x)^(1/2)+8*(1-x)^(1/2))/(1-x)^(1/2)","A"
28,1,29,17,0.061000," ","int(arcsech(1/x),x)","x \,\mathrm{arcsech}\left(\frac{1}{x}\right)-\sqrt{-\left(\frac{1}{x}-1\right) x}\, \sqrt{\left(\frac{1}{x}+1\right) x}"," ",0,"x*arcsech(1/x)-(-(1/x-1)*x)^(1/2)*((1/x+1)*x)^(1/2)","A"
29,1,116,115,0.150000," ","int(arcsech(a*x^n)/x,x)","\frac{\mathrm{arcsech}\left(a \,x^{n}\right)^{2}}{2 n}-\frac{\mathrm{arcsech}\left(a \,x^{n}\right) \ln \left(1+\left(\frac{x^{-n}}{a}+\sqrt{\frac{x^{-n}}{a}-1}\, \sqrt{\frac{x^{-n}}{a}+1}\right)^{2}\right)}{n}-\frac{\polylog \left(2, -\left(\frac{x^{-n}}{a}+\sqrt{\frac{x^{-n}}{a}-1}\, \sqrt{\frac{x^{-n}}{a}+1}\right)^{2}\right)}{2 n}"," ",0,"1/2*arcsech(a*x^n)^2/n-arcsech(a*x^n)*ln(1+(1/a/(x^n)+(1/a/(x^n)-1)^(1/2)*(1/a/(x^n)+1)^(1/2))^2)/n-1/2*polylog(2,-(1/a/(x^n)+(1/a/(x^n)-1)^(1/2)*(1/a/(x^n)+1)^(1/2))^2)/n","A"
30,0,0,94,0.180000," ","int(arcsech(a*x^5)/x,x)","\int \frac{\mathrm{arcsech}\left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arcsech(a*x^5)/x,x)","F"
31,1,140,139,0.148000," ","int(arcsech(c*exp(b*x+a)),x)","\frac{\mathrm{arcsech}\left(c \,{\mathrm e}^{b x +a}\right)^{2}}{2 b}-\frac{\mathrm{arcsech}\left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1+\left(\frac{{\mathrm e}^{-b x -a}}{c}+\sqrt{\frac{{\mathrm e}^{-b x -a}}{c}-1}\, \sqrt{\frac{{\mathrm e}^{-b x -a}}{c}+1}\right)^{2}\right)}{b}-\frac{\polylog \left(2, -\left(\frac{{\mathrm e}^{-b x -a}}{c}+\sqrt{\frac{{\mathrm e}^{-b x -a}}{c}-1}\, \sqrt{\frac{{\mathrm e}^{-b x -a}}{c}+1}\right)^{2}\right)}{2 b}"," ",0,"1/2*arcsech(c*exp(b*x+a))^2/b-arcsech(c*exp(b*x+a))*ln(1+(1/c/exp(b*x+a)+(1/c/exp(b*x+a)-1)^(1/2)*(1/c/exp(b*x+a)+1)^(1/2))^2)/b-1/2*polylog(2,-(1/c/exp(b*x+a)+(1/c/exp(b*x+a)-1)^(1/2)*(1/c/exp(b*x+a)+1)^(1/2))^2)/b","A"
32,1,64,129,0.057000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^4,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right) \left(3 a^{2} x^{2}+2\right)}{15 a^{4}}+\frac{x^{4}}{4 a}"," ",0,"1/15*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)*(3*a^2*x^2+2)/a^4+1/4*x^4/a","A"
33,1,118,93,0.058000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^3,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(2 \,\mathrm{csgn}\left(a \right) x^{3} a^{3} \sqrt{-a^{2} x^{2}+1}-x \sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right) a +\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(a \right)}{8 \sqrt{-a^{2} x^{2}+1}\, a^{3}}+\frac{x^{3}}{3 a}"," ",0,"1/8*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(2*csgn(a)*x^3*a^3*(-a^2*x^2+1)^(1/2)-x*(-a^2*x^2+1)^(1/2)*csgn(a)*a+arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2)))*csgn(a)/(-a^2*x^2+1)^(1/2)/a^3+1/3*x^3/a","C"
34,1,54,82,0.049000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^2,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right)}{3 a^{2}}+\frac{x^{2}}{2 a}"," ",0,"1/3*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)/a^2+1/2*x^2/a","A"
35,1,92,68,0.052000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(x \sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right) a +\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(a \right)}{2 \sqrt{-a^{2} x^{2}+1}\, a}+\frac{x}{a}"," ",0,"1/2*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(x*(-a^2*x^2+1)^(1/2)*csgn(a)*a+arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2)))/(-a^2*x^2+1)^(1/2)*csgn(a)/a+x/a","C"
36,1,80,49,0.056000," ","int(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2),x)","\frac{\ln \left(x \right)}{a}-\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(-\sqrt{-a^{2} x^{2}+1}+\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)}{\sqrt{-a^{2} x^{2}+1}}"," ",0,"ln(x)/a-(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(-(-a^2*x^2+1)^(1/2)+arctanh(1/(-a^2*x^2+1)^(1/2)))/(-a^2*x^2+1)^(1/2)","A"
37,1,92,44,0.056000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x)","-\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right) x a +\sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{\sqrt{-a^{2} x^{2}+1}}-\frac{1}{a x}"," ",0,"-(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*(arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2))*x*a+(-a^2*x^2+1)^(1/2)*csgn(a))*csgn(a)/(-a^2*x^2+1)^(1/2)-1/a/x","C"
38,1,91,56,0.054000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\sqrt{-a^{2} x^{2}+1}\right)}{2 x \sqrt{-a^{2} x^{2}+1}}-\frac{1}{2 a \,x^{2}}"," ",0,"1/2*(-(a*x-1)/a/x)^(1/2)/x*((a*x+1)/a/x)^(1/2)*(a^2*x^2*arctanh(1/(-a^2*x^2+1)^(1/2))-(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/2/a/x^2","A"
39,1,53,47,0.053000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right)}{3 x^{2}}-\frac{1}{3 x^{3} a}"," ",0,"1/3*(-(a*x-1)/a/x)^(1/2)/x^2*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)-1/3/x^3/a","A"
40,1,110,131,0.056000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) x^{4} a^{4}+a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-2 \sqrt{-a^{2} x^{2}+1}\right)}{8 x^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{1}{4 x^{4} a}"," ",0,"1/8*(-(a*x-1)/a/x)^(1/2)/x^3*((a*x+1)/a/x)^(1/2)*(arctanh(1/(-a^2*x^2+1)^(1/2))*x^4*a^4+a^2*x^2*(-a^2*x^2+1)^(1/2)-2*(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/4/x^4/a","A"
41,1,63,118,0.059000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right) \left(2 a^{2} x^{2}+3\right)}{15 x^{4}}-\frac{1}{5 a \,x^{5}}"," ",0,"1/15*(-(a*x-1)/a/x)^(1/2)/x^4*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)*(2*a^2*x^2+3)-1/5/a/x^5","A"
42,1,132,156,0.065000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) x^{6} a^{6}+3 \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+2 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-8 \sqrt{-a^{2} x^{2}+1}\right)}{48 x^{5} \sqrt{-a^{2} x^{2}+1}}-\frac{1}{6 x^{6} a}"," ",0,"1/48*(-(a*x-1)/a/x)^(1/2)/x^5*((a*x+1)/a/x)^(1/2)*(3*arctanh(1/(-a^2*x^2+1)^(1/2))*x^6*a^6+3*(-a^2*x^2+1)^(1/2)*x^4*a^4+2*a^2*x^2*(-a^2*x^2+1)^(1/2)-8*(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/6/x^6/a","A"
43,1,71,143,0.075000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right) \left(8 x^{4} a^{4}+12 a^{2} x^{2}+15\right)}{105 x^{6}}-\frac{1}{7 a \,x^{7}}"," ",0,"1/105*(-(a*x-1)/a/x)^(1/2)/x^6*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)*(8*a^4*x^4+12*a^2*x^2+15)-1/7/a/x^7","A"
44,1,152,181,0.087000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^8,x)","\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(15 \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) x^{8} a^{8}+15 \sqrt{-a^{2} x^{2}+1}\, x^{6} a^{6}+10 \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+8 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-48 \sqrt{-a^{2} x^{2}+1}\right)}{384 x^{7} \sqrt{-a^{2} x^{2}+1}}-\frac{1}{8 a \,x^{8}}"," ",0,"1/384*(-(a*x-1)/a/x)^(1/2)/x^7*((a*x+1)/a/x)^(1/2)*(15*arctanh(1/(-a^2*x^2+1)^(1/2))*x^8*a^8+15*(-a^2*x^2+1)^(1/2)*x^6*a^6+10*(-a^2*x^2+1)^(1/2)*x^4*a^4+8*a^2*x^2*(-a^2*x^2+1)^(1/2)-48*(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/8/a/x^8","A"
45,1,137,116,0.216000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^7,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(2 x^{6} \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, a^{4}-x^{2} \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, a^{2}+\arctan \left(\frac{x^{2}}{\sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}\right)\right)}{16 \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, a^{4}}+\frac{x^{6}}{6 a}"," ",0,"1/16*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(2*x^6*(-(a^2*x^4-1)/a^2)^(1/2)*a^4-x^2*(-(a^2*x^4-1)/a^2)^(1/2)*a^2+arctan(x^2/(-(a^2*x^4-1)/a^2)^(1/2)))/(-(a^2*x^4-1)/a^2)^(1/2)/a^4+1/6*x^6/a","A"
46,1,114,116,0.055000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^6,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(3 x^{9} a^{\frac{9}{2}}-5 x^{5} a^{\frac{5}{2}}-2 \EllipticF \left(x \sqrt{a}, i\right) \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}+2 x \sqrt{a}\right)}{21 a^{\frac{5}{2}} \left(a^{2} x^{4}-1\right)}+\frac{x^{5}}{5 a}"," ",0,"1/21*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(3*x^9*a^(9/2)-5*x^5*a^(5/2)-2*EllipticF(x*a^(1/2),I)*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)+2*x*a^(1/2))/a^(5/2)/(a^2*x^4-1)+1/5*x^5/a","A"
47,1,60,71,0.051000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^5,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(a^{2} x^{4}-1\right)}{6 a^{2}}+\frac{x^{4}}{4 a}"," ",0,"1/6*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(a^2*x^4-1)/a^2+1/4*x^4/a","A"
48,1,136,111,0.057000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^4,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(a^{\frac{7}{2}} x^{7}-x^{3} a^{\frac{3}{2}}+2 \EllipticF \left(x \sqrt{a}, i\right) \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}-2 \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}\, \EllipticE \left(x \sqrt{a}, i\right)\right)}{5 \left(a^{2} x^{4}-1\right) a^{\frac{3}{2}}}+\frac{x^{3}}{3 a}"," ",0,"1/5*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(a^(7/2)*x^7-x^3*a^(3/2)+2*EllipticF(x*a^(1/2),I)*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)-2*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)*EllipticE(x*a^(1/2),I))/(a^2*x^4-1)/a^(3/2)+1/3*x^3/a","A"
49,1,112,76,0.154000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^3,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(x^{2} \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, a^{2}+\arctan \left(\frac{x^{2}}{\sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}\right)\right)}{4 \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, a^{2}}+\frac{x^{2}}{2 a}"," ",0,"1/4*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(x^2*(-(a^2*x^4-1)/a^2)^(1/2)*a^2+arctan(x^2/(-(a^2*x^4-1)/a^2)^(1/2)))/(-(a^2*x^4-1)/a^2)^(1/2)/a^2+1/2*x^2/a","A"
50,1,102,76,0.056000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^2,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(x^{5} a^{\frac{5}{2}}-2 \EllipticF \left(x \sqrt{a}, i\right) \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}-x \sqrt{a}\right)}{3 \left(a^{2} x^{4}-1\right) \sqrt{a}}+\frac{x}{a}"," ",0,"1/3*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(x^5*a^(5/2)-2*EllipticF(x*a^(1/2),I)*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)-x*a^(1/2))/(a^2*x^4-1)/a^(1/2)+x/a","A"
51,1,127,81,0.188000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x^{2} \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(\mathrm{csgn}\left(\frac{1}{a}\right) a \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}-\ln \left(\frac{2 \,\mathrm{csgn}\left(\frac{1}{a}\right) a \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}+2}{a^{2} x^{2}}\right)\right) \mathrm{csgn}\left(\frac{1}{a}\right)}{2 a \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}+\frac{\ln \left(x \right)}{a}"," ",0,"1/2*(-(a*x^2-1)/a/x^2)^(1/2)*x^2*((a*x^2+1)/a/x^2)^(1/2)*(csgn(1/a)*a*(-(a^2*x^4-1)/a^2)^(1/2)-ln(2*(csgn(1/a)*a*(-(a^2*x^4-1)/a^2)^(1/2)+1)/a^2/x^2))*csgn(1/a)/a/(-(a^2*x^4-1)/a^2)^(1/2)+ln(x)/a","C"
52,1,132,148,0.066000," ","int(1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2),x)","-\frac{1}{a x}-\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, x \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(a^{2} x^{4}+2 \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}\, x \EllipticF \left(x \sqrt{a}, i\right) \sqrt{a}-2 \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}\, x \EllipticE \left(x \sqrt{a}, i\right) \sqrt{a}-1\right)}{a^{2} x^{4}-1}"," ",0,"-1/a/x-(-(a*x^2-1)/a/x^2)^(1/2)*x*((a*x^2+1)/a/x^2)^(1/2)*(a^2*x^4+2*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)*x*EllipticF(x*a^(1/2),I)*a^(1/2)-2*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)*x*EllipticE(x*a^(1/2),I)*a^(1/2)-1)/(a^2*x^4-1)","A"
53,1,103,66,0.160000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x,x)","-\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(\arctan \left(\frac{x^{2}}{\sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}\right) x^{2}+\sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\right)}{2 \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2*(-(a*x^2-1)/a/x^2)^(1/2)*((a*x^2+1)/a/x^2)^(1/2)*(arctan(x^2/(-(a^2*x^4-1)/a^2)^(1/2))*x^2+(-(a^2*x^4-1)/a^2)^(1/2))/(-(a^2*x^4-1)/a^2)^(1/2)-1/2/a/x^2","A"
54,1,104,118,0.066000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^2,x)","\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(2 \sqrt{-a \,x^{2}+1}\, \sqrt{a \,x^{2}+1}\, \EllipticF \left(x \sqrt{a}, i\right) x^{3} a^{\frac{3}{2}}-a^{2} x^{4}+1\right)}{3 x \left(a^{2} x^{4}-1\right)}-\frac{1}{3 x^{3} a}"," ",0,"1/3*(-(a*x^2-1)/a/x^2)^(1/2)/x*((a*x^2+1)/a/x^2)^(1/2)*(2*(-a*x^2+1)^(1/2)*(a*x^2+1)^(1/2)*EllipticF(x*a^(1/2),I)*x^3*a^(3/2)-a^2*x^4+1)/(a^2*x^4-1)-1/3/x^3/a","A"
55,1,129,121,0.176000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^3,x)","-\frac{\sqrt{-\frac{a \,x^{2}-1}{a \,x^{2}}}\, \sqrt{\frac{a \,x^{2}+1}{a \,x^{2}}}\, \left(-\ln \left(\frac{2 \,\mathrm{csgn}\left(\frac{1}{a}\right) a \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}+2}{a^{2} x^{2}}\right) x^{4} a +\sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}\, \mathrm{csgn}\left(\frac{1}{a}\right)\right) \mathrm{csgn}\left(\frac{1}{a}\right)}{4 x^{2} \sqrt{-\frac{a^{2} x^{4}-1}{a^{2}}}}-\frac{1}{4 x^{4} a}"," ",0,"-1/4*(-(a*x^2-1)/a/x^2)^(1/2)/x^2*((a*x^2+1)/a/x^2)^(1/2)*(-ln(2*(csgn(1/a)*a*(-(a^2*x^4-1)/a^2)^(1/2)+1)/a^2/x^2)*x^4*a+(-(a^2*x^4-1)/a^2)^(1/2)*csgn(1/a))*csgn(1/a)/(-(a^2*x^4-1)/a^2)^(1/2)-1/4/x^4/a","C"
56,0,0,124,0.094000," ","int((1/x^3/a+(1/x^3/a-1)^(1/2)*(1/x^3/a+1)^(1/2))*x^m,x)","\int \left(\frac{1}{x^{3} a}+\sqrt{\frac{1}{x^{3} a}-1}\, \sqrt{\frac{1}{x^{3} a}+1}\right) x^{m}\, dx"," ",0,"int((1/x^3/a+(1/x^3/a-1)^(1/2)*(1/x^3/a+1)^(1/2))*x^m,x)","F"
57,0,0,122,0.070000," ","int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^m,x)","\int \left(\frac{1}{a \,x^{2}}+\sqrt{\frac{1}{a \,x^{2}}-1}\, \sqrt{\frac{1}{a \,x^{2}}+1}\right) x^{m}\, dx"," ",0,"int((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^m,x)","F"
58,0,0,108,0.044000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^m,x)","\int \left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{m}\, dx"," ",0,"int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^m,x)","F"
59,0,0,116,0.641000," ","int((x/a+(-1+x/a)^(1/2)*(1+x/a)^(1/2))*x^m,x)","\int \left(\frac{x}{a}+\sqrt{-1+\frac{x}{a}}\, \sqrt{1+\frac{x}{a}}\right) x^{m}\, dx"," ",0,"int((x/a+(-1+x/a)^(1/2)*(1+x/a)^(1/2))*x^m,x)","F"
60,0,0,154,1.085000," ","int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x^m,x)","\int \left(\frac{x^{-p}}{a}+\sqrt{\frac{x^{-p}}{a}-1}\, \sqrt{\frac{x^{-p}}{a}+1}\right) x^{m}\, dx"," ",0,"int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x^m,x)","F"
61,0,0,126,1.061000," ","int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x,x)","\int \left(\frac{x^{-p}}{a}+\sqrt{\frac{x^{-p}}{a}-1}\, \sqrt{\frac{x^{-p}}{a}+1}\right) x\, dx"," ",0,"int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x,x)","F"
62,0,0,126,1.069000," ","int(1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2),x)","\int \frac{x^{-p}}{a}+\sqrt{\frac{x^{-p}}{a}-1}\, \sqrt{\frac{x^{-p}}{a}+1}\, dx"," ",0,"int(1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2),x)","F"
63,1,145,79,0.147000," ","int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x,x)","-\frac{\sqrt{-\frac{\left(a \,x^{p}-1\right) x^{-p}}{a}}\, \sqrt{\frac{\left(1+a \,x^{p}\right) x^{-p}}{a}}\, \mathrm{csgn}\left(a \right) \arctan \left(\frac{\mathrm{csgn}\left(a \right) a \,x^{p}}{\sqrt{1-a^{2} x^{2 p}}}\right) x^{p} a}{p \sqrt{1-a^{2} x^{2 p}}}-\frac{\sqrt{-\frac{\left(a \,x^{p}-1\right) x^{-p}}{a}}\, \sqrt{\frac{\left(1+a \,x^{p}\right) x^{-p}}{a}}\, \mathrm{csgn}\left(a \right)^{2}}{p}-\frac{x^{-p}}{a p}"," ",0,"-1/p*(-(a*x^p-1)/a/(x^p))^(1/2)*((1+a*x^p)/a/(x^p))^(1/2)*csgn(a)/(-(x^p)^2*a^2+1)^(1/2)*arctan(csgn(a)*a*x^p/(-(x^p)^2*a^2+1)^(1/2))*x^p*a-1/p*(-(a*x^p-1)/a/(x^p))^(1/2)*((1+a*x^p)/a/(x^p))^(1/2)*csgn(a)^2-1/a/p/(x^p)","C"
64,0,0,128,1.071000," ","int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x^2,x)","\int \frac{\frac{x^{-p}}{a}+\sqrt{\frac{x^{-p}}{a}-1}\, \sqrt{\frac{x^{-p}}{a}+1}}{x^{2}}\, dx"," ",0,"int((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x^2,x)","F"
65,1,123,179,0.064000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^4,x)","-\frac{x^{5}}{5}+\frac{2 x^{3}}{3 a^{2}}+\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(2 \,\mathrm{csgn}\left(a \right) x^{3} a^{3} \sqrt{-a^{2} x^{2}+1}-x \sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right) a +\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(a \right)}{4 a^{4} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/5*x^5+2/3*x^3/a^2+1/4/a^4*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(2*csgn(a)*x^3*a^3*(-a^2*x^2+1)^(1/2)-x*(-a^2*x^2+1)^(1/2)*csgn(a)*a+arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2)))*csgn(a)/(-a^2*x^2+1)^(1/2)","C"
66,1,72,105,0.047000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^3,x)","\frac{-\frac{1}{4} a^{2} x^{4}+\frac{1}{2} x^{2}}{a^{2}}+\frac{2 \sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right)}{3 a^{3}}+\frac{x^{2}}{2 a^{2}}"," ",0,"1/a^2*(-1/4*a^2*x^4+1/2*x^2)+2/3/a^3*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)+1/2*x^2/a^2","A"
67,1,97,151,0.061000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^2,x)","-\frac{x^{3}}{3}+\frac{2 x}{a^{2}}+\frac{\sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(x \sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right) a +\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(a \right)}{a^{2} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/3*x^3+2*x/a^2+1/a^2*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(x*(-a^2*x^2+1)^(1/2)*csgn(a)*a+arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2)))/(-a^2*x^2+1)^(1/2)*csgn(a)","C"
68,1,89,79,0.055000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x,x)","-\frac{x^{2}}{2}+\frac{2 \ln \left(x \right)}{a^{2}}-\frac{2 \sqrt{-\frac{a x -1}{a x}}\, x \sqrt{\frac{a x +1}{a x}}\, \left(-\sqrt{-a^{2} x^{2}+1}+\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)\right)}{a \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/2*x^2+2*ln(x)/a^2-2/a*(-(a*x-1)/a/x)^(1/2)*x*((a*x+1)/a/x)^(1/2)*(-(-a^2*x^2+1)^(1/2)+arctanh(1/(-a^2*x^2+1)^(1/2)))/(-a^2*x^2+1)^(1/2)","A"
69,1,98,53,0.061000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2,x)","-x -\frac{2}{a^{2} x}-\frac{2 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(\arctan \left(\frac{\mathrm{csgn}\left(a \right) a x}{\sqrt{-a^{2} x^{2}+1}}\right) x a +\sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{a \sqrt{-a^{2} x^{2}+1}}"," ",0,"-x-2/a^2/x-2/a*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)*(arctan(csgn(a)*a*x/(-a^2*x^2+1)^(1/2))*x*a+(-a^2*x^2+1)^(1/2)*csgn(a))*csgn(a)/(-a^2*x^2+1)^(1/2)","C"
70,1,97,80,0.061000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x,x)","-\ln \left(x \right)-\frac{1}{x^{2} a^{2}}-\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(-a^{2} x^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\sqrt{-a^{2} x^{2}+1}\right)}{a x \sqrt{-a^{2} x^{2}+1}}"," ",0,"-ln(x)-1/x^2/a^2-1/a*(-(a*x-1)/a/x)^(1/2)/x*((a*x+1)/a/x)^(1/2)*(-a^2*x^2*arctanh(1/(-a^2*x^2+1)^(1/2))+(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)","A"
71,1,73,51,0.058000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^2,x)","\frac{\frac{a^{2}}{x}-\frac{1}{3 x^{3}}}{a^{2}}+\frac{2 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right)}{3 a \,x^{2}}-\frac{1}{3 a^{2} x^{3}}"," ",0,"1/a^2*(a^2/x-1/3/x^3)+2/3/a*(-(a*x-1)/a/x)^(1/2)/x^2*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)-1/3/a^2/x^3","A"
72,1,131,131,0.057000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^3,x)","\frac{\frac{a^{2}}{2 x^{2}}-\frac{1}{4 x^{4}}}{a^{2}}+\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) x^{4} a^{4}+a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-2 \sqrt{-a^{2} x^{2}+1}\right)}{4 a \,x^{3} \sqrt{-a^{2} x^{2}+1}}-\frac{1}{4 a^{2} x^{4}}"," ",0,"1/a^2*(1/2*a^2/x^2-1/4/x^4)+1/4/a*(-(a*x-1)/a/x)^(1/2)/x^3*((a*x+1)/a/x)^(1/2)*(arctanh(1/(-a^2*x^2+1)^(1/2))*x^4*a^4+a^2*x^2*(-a^2*x^2+1)^(1/2)-2*(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/4/a^2/x^4","A"
73,1,84,161,0.059000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^4,x)","\frac{\frac{a^{2}}{3 x^{3}}-\frac{1}{5 x^{5}}}{a^{2}}+\frac{2 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right) \left(2 a^{2} x^{2}+3\right)}{15 a \,x^{4}}-\frac{1}{5 a^{2} x^{5}}"," ",0,"1/a^2*(1/3*a^2/x^3-1/5/x^5)+2/15/a*(-(a*x-1)/a/x)^(1/2)/x^4*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)*(2*a^2*x^2+3)-1/5/a^2/x^5","A"
74,1,153,235,0.093000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^5,x)","\frac{-\frac{1}{6 x^{6}}+\frac{a^{2}}{4 x^{4}}}{a^{2}}+\frac{\sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(3 \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) x^{6} a^{6}+3 \sqrt{-a^{2} x^{2}+1}\, x^{4} a^{4}+2 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-8 \sqrt{-a^{2} x^{2}+1}\right)}{24 a \,x^{5} \sqrt{-a^{2} x^{2}+1}}-\frac{1}{6 a^{2} x^{6}}"," ",0,"1/a^2*(-1/6/x^6+1/4*a^2/x^4)+1/24/a*(-(a*x-1)/a/x)^(1/2)/x^5*((a*x+1)/a/x)^(1/2)*(3*arctanh(1/(-a^2*x^2+1)^(1/2))*x^6*a^6+3*(-a^2*x^2+1)^(1/2)*x^4*a^4+2*a^2*x^2*(-a^2*x^2+1)^(1/2)-8*(-a^2*x^2+1)^(1/2))/(-a^2*x^2+1)^(1/2)-1/6/a^2/x^6","A"
75,1,92,265,0.072000," ","int((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^6,x)","\frac{-\frac{1}{7 x^{7}}+\frac{a^{2}}{5 x^{5}}}{a^{2}}+\frac{2 \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}\, \left(a^{2} x^{2}-1\right) \left(8 x^{4} a^{4}+12 a^{2} x^{2}+15\right)}{105 a \,x^{6}}-\frac{1}{7 a^{2} x^{7}}"," ",0,"1/a^2*(-1/7/x^7+1/5*a^2/x^5)+2/105/a*(-(a*x-1)/a/x)^(1/2)/x^6*((a*x+1)/a/x)^(1/2)*(a^2*x^2-1)*(8*a^4*x^4+12*a^2*x^2+15)-1/7/a^2/x^7","A"
76,1,531,131,0.362000," ","int(x^4/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","-\frac{\left(a x -1\right) \left(15 a^{10} x^{10} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{5}{2}}+30 a^{8} x^{8} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{5}{2}}+30 \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} x^{8} a^{8}+30 x^{6} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{5}{2}} a^{6}-30 a^{7} x^{7} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}}+60 \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \ln \left(a^{2} x^{2}\right) x^{6} a^{6}+12 x^{11} a^{11}-60 x^{5} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}} a^{5}+30 \sqrt{-\frac{a x -1}{a x}}\, \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \ln \left(a^{2} x^{2}\right) x^{6} a^{6}+12 x^{10} a^{10}-60 \sqrt{-\frac{a x -1}{a x}}\, \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \ln \left(a^{2} x^{2}\right) x^{5} a^{5}-40 x^{9} a^{9}+30 x^{4} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \sqrt{-\frac{a x -1}{a x}}\, a^{4}-40 x^{8} a^{8}+40 x^{7} a^{7}+40 x^{6} a^{6}-20 x^{3} a^{3}-20 a^{2} x^{2}+8 a x +8\right)}{60 x^{7} a^{12} \left(\frac{a x +1}{a x}\right)^{\frac{7}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{7}{2}}}"," ",0,"-1/60*(a*x-1)/x^7*(15*a^10*x^10*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(5/2)+30*a^8*x^8*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(5/2)+30*(-(a*x-1)/a/x)^(3/2)*((a*x+1)/a/x)^(7/2)*x^8*a^8+30*x^6*ln(a^2*x^2)*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(5/2)*a^6-30*a^7*x^7*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(3/2)+60*(-(a*x-1)/a/x)^(3/2)*((a*x+1)/a/x)^(7/2)*ln(a^2*x^2)*x^6*a^6+12*x^11*a^11-60*x^5*ln(a^2*x^2)*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(3/2)*a^5+30*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(7/2)*ln(a^2*x^2)*x^6*a^6+12*x^10*a^10-60*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(7/2)*ln(a^2*x^2)*x^5*a^5-40*x^9*a^9+30*x^4*ln(a^2*x^2)*((a*x+1)/a/x)^(7/2)*(-(a*x-1)/a/x)^(1/2)*a^4-40*x^8*a^8+40*x^7*a^7+40*x^6*a^6-20*x^3*a^3-20*a^2*x^2+8*a*x+8)/a^12/((a*x+1)/a/x)^(7/2)/(-(a*x-1)/a/x)^(7/2)","C"
77,-2,0,143,180.000000," ","int(x^3/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","\int \frac{x^{3}}{\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}}\, dx"," ",0,"int(x^3/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","F"
78,1,269,67,0.315000," ","int(x^2/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","-\frac{\left(a x -1\right) \left(3 a^{6} x^{6} \left(\frac{a x +1}{a x}\right)^{\frac{5}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}}+3 x^{4} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{5}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}} a^{4}+3 \ln \left(a^{2} x^{2}\right) \sqrt{-\frac{a x -1}{a x}}\, \left(\frac{a x +1}{a x}\right)^{\frac{5}{2}} x^{4} a^{4}-2 x^{7} a^{7}-3 x^{3} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{5}{2}} \sqrt{-\frac{a x -1}{a x}}\, a^{3}-2 x^{6} a^{6}+6 x^{5} a^{5}+6 x^{4} a^{4}-6 x^{3} a^{3}-6 a^{2} x^{2}+2 a x +2\right)}{6 x^{5} a^{8} \left(\frac{a x +1}{a x}\right)^{\frac{5}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{5}{2}}}"," ",0,"-1/6*(a*x-1)/x^5*(3*a^6*x^6*((a*x+1)/a/x)^(5/2)*(-(a*x-1)/a/x)^(3/2)+3*x^4*ln(a^2*x^2)*((a*x+1)/a/x)^(5/2)*(-(a*x-1)/a/x)^(3/2)*a^4+3*ln(a^2*x^2)*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(5/2)*x^4*a^4-2*x^7*a^7-3*x^3*ln(a^2*x^2)*((a*x+1)/a/x)^(5/2)*(-(a*x-1)/a/x)^(1/2)*a^3-2*x^6*a^6+6*x^5*a^5+6*x^4*a^4-6*x^3*a^3-6*a^2*x^2+2*a*x+2)/a^8/((a*x+1)/a/x)^(5/2)/(-(a*x-1)/a/x)^(5/2)","C"
79,-2,0,84,180.000000," ","int(x/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","\int \frac{x}{\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}}\, dx"," ",0,"int(x/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","F"
80,1,2612,61,0.308000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x)","-\frac{\left(a x -1\right) \left(x^{2} \ln \left(a^{2} x^{2}\right) \left(\frac{a x +1}{a x}\right)^{\frac{3}{2}} \sqrt{-\frac{a x -1}{a x}}\, \sqrt{-a^{2} x^{2}+1}\, a^{2}+2 \sqrt{-a^{2} x^{2}+1}\, x^{3} a^{3}-\ln \left(\frac{2 \left(\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) x^{3} a^{3}-\ln \left(-\frac{2 \left(-\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{-a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) x^{3} a^{3}+2 a^{2} x^{2} \sqrt{-a^{2} x^{2}+1}-x^{2} \ln \left(\frac{2 \left(\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) a^{2}-x^{2} \ln \left(-\frac{2 \left(-\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{-a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) a^{2}-2 a x \sqrt{-a^{2} x^{2}+1}+x \ln \left(\frac{2 \left(\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) a +x \ln \left(-\frac{2 \left(-\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{-a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right) a -2 \sqrt{-a^{2} x^{2}+1}+\ln \left(\frac{2 \left(\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right)+\ln \left(-\frac{2 \left(-\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}\, x +\sqrt{-a^{2} x^{2}+1}+1\right) a^{2}}{-a^{2} x +\sqrt{\frac{\left(-\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) \left(\sqrt{\frac{a x +1}{a x}}\, x^{2} \sqrt{-\frac{a x -1}{a x}}\, a +\sqrt{\left(a x +1\right) x}\, \sqrt{-\left(a x -1\right) x}\right) a^{2}}{\left(a x +1\right) \left(a x -1\right) x^{2}}}}\right)\right)}{2 x^{3} a^{4} \left(\frac{a x +1}{a x}\right)^{\frac{3}{2}} \left(-\frac{a x -1}{a x}\right)^{\frac{3}{2}} \sqrt{-a^{2} x^{2}+1}}"," ",0,"-1/2*(a*x-1)/x^3*(x^2*ln(a^2*x^2)*((a*x+1)/a/x)^(3/2)*(-(a*x-1)/a/x)^(1/2)*(-a^2*x^2+1)^(1/2)*a^2+2*(-a^2*x^2+1)^(1/2)*x^3*a^3-ln(2*(((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*x^3*a^3-ln(-2*(-((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(-a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*x^3*a^3+2*a^2*x^2*(-a^2*x^2+1)^(1/2)-x^2*ln(2*(((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*a^2-x^2*ln(-2*(-((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(-a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*a^2-2*a*x*(-a^2*x^2+1)^(1/2)+x*ln(2*(((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*a+x*ln(-2*(-((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(-a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))*a-2*(-a^2*x^2+1)^(1/2)+ln(2*(((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)))+ln(-2*(-((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2)*x+(-a^2*x^2+1)^(1/2)+1)*a^2/(-a^2*x+((-((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*(((a*x+1)/a/x)^(1/2)*x^2*(-(a*x-1)/a/x)^(1/2)*a+((a*x+1)*x)^(1/2)*(-(a*x-1)*x)^(1/2))*a^2/(a*x+1)/(a*x-1)/x^2)^(1/2))))/a^4/((a*x+1)/a/x)^(3/2)/(-(a*x-1)/a/x)^(3/2)/(-a^2*x^2+1)^(1/2)","B"
81,-2,0,42,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x)","F"
82,-2,0,66,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{2}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x)","F"
83,-2,0,102,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{3}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x)","F"
84,-2,0,176,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{4}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x)","F"
85,-2,0,205,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{5}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x)","F"
86,-2,0,280,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{6}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x)","F"
87,-2,0,309,180.000000," ","int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x)","\int \frac{1}{\left(\frac{1}{a x}+\sqrt{\frac{1}{a x}-1}\, \sqrt{1+\frac{1}{a x}}\right) x^{7}}\, dx"," ",0,"int(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x)","F"
88,0,0,79,0.439000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*(d*x)^m/(-c^2*x^2+1),x)","\int \frac{\left(\frac{1}{c x}+\sqrt{-1+\frac{1}{c x}}\, \sqrt{1+\frac{1}{c x}}\right) \left(d x \right)^{m}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*(d*x)^m/(-c^2*x^2+1),x)","F"
89,1,69,72,0.102000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^4/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \left(c^{2} x^{2}+2\right)}{3 c^{4}}-\frac{x^{2}}{2 c^{3}}-\frac{\ln \left(c^{2} x^{2}-1\right)}{2 c^{5}}"," ",0,"-1/3*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*(c^2*x^2+2)/c^4-1/2*x^2/c^3-1/2/c^5*ln(c^2*x^2-1)","A"
90,1,117,63,0.080000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^3/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \left(x \sqrt{-c^{2} x^{2}+1}\, \mathrm{csgn}\left(c \right) c -\arctan \left(\frac{\mathrm{csgn}\left(c \right) c x}{\sqrt{-c^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(c \right)}{2 c^{3} \sqrt{-c^{2} x^{2}+1}}-\frac{x}{c^{3}}+\frac{\ln \left(c x +1\right)}{2 c^{4}}-\frac{\ln \left(c x -1\right)}{2 c^{4}}"," ",0,"-1/2*(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/c^3*(x*(-c^2*x^2+1)^(1/2)*csgn(c)*c-arctan(csgn(c)*c*x/(-c^2*x^2+1)^(1/2)))/(-c^2*x^2+1)^(1/2)*csgn(c)-x/c^3+1/2/c^4*ln(c*x+1)-1/2/c^4*ln(c*x-1)","C"
91,1,52,39,0.070000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^2/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}}{c^{2}}-\frac{\ln \left(c^{2} x^{2}-1\right)}{2 c^{3}}"," ",0,"-(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)/c^2-1/2/c^3*ln(c^2*x^2-1)","A"
92,1,92,33,0.076000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x/(-c^2*x^2+1),x)","\frac{\sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctan \left(\frac{\mathrm{csgn}\left(c \right) c x}{\sqrt{-\left(c x -1\right) \left(c x +1\right)}}\right) \mathrm{csgn}\left(c \right)}{\sqrt{-c^{2} x^{2}+1}\, c}+\frac{\ln \left(c x +1\right)}{2 c^{2}}-\frac{\ln \left(c x -1\right)}{2 c^{2}}"," ",0,"(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*arctan(csgn(c)*c*x/(-(c*x-1)*(c*x+1))^(1/2))/(-c^2*x^2+1)^(1/2)*csgn(c)/c+1/2/c^2*ln(c*x+1)-1/2/c^2*ln(c*x-1)","C"
93,1,87,61,0.077000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, x \sqrt{\frac{c x +1}{c x}}\, \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right)}{\sqrt{-c^{2} x^{2}+1}}+\frac{\ln \left(x \right)}{c}-\frac{\ln \left(c x +1\right)}{2 c}-\frac{\ln \left(c x -1\right)}{2 c}"," ",0,"-(-(c*x-1)/c/x)^(1/2)*x*((c*x+1)/c/x)^(1/2)*arctanh(1/(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)+ln(x)/c-1/2/c*ln(c*x+1)-1/2/c*ln(c*x-1)","A"
94,1,61,38,0.083000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x/(-c^2*x^2+1),x)","-\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \mathrm{csgn}\left(c \right)^{2}-\frac{1}{c x}+\frac{\ln \left(c x +1\right)}{2}-\frac{\ln \left(c x -1\right)}{2}"," ",0,"-(-(c*x-1)/c/x)^(1/2)*((c*x+1)/c/x)^(1/2)*csgn(c)^2-1/c/x+1/2*ln(c*x+1)-1/2*ln(c*x-1)","C"
95,1,111,88,0.090000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x^2/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \left(\arctanh \left(\frac{1}{\sqrt{-c^{2} x^{2}+1}}\right) c^{2} x^{2}+\sqrt{-c^{2} x^{2}+1}\right)}{2 x \sqrt{-c^{2} x^{2}+1}}-\frac{1}{2 c \,x^{2}}+c \ln \left(x \right)-\frac{c \ln \left(c x +1\right)}{2}-\frac{c \ln \left(c x -1\right)}{2}"," ",0,"-1/2*(-(c*x-1)/c/x)^(1/2)/x*((c*x+1)/c/x)^(1/2)*(arctanh(1/(-c^2*x^2+1)^(1/2))*c^2*x^2+(-c^2*x^2+1)^(1/2))/(-c^2*x^2+1)^(1/2)-1/2/c/x^2+c*ln(x)-1/2*c*ln(c*x+1)-1/2*c*ln(c*x-1)","A"
96,1,86,71,0.099000," ","int((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x^3/(-c^2*x^2+1),x)","-\frac{\sqrt{-\frac{c x -1}{c x}}\, \sqrt{\frac{c x +1}{c x}}\, \mathrm{csgn}\left(c \right)^{2} \left(2 c^{2} x^{2}+1\right)}{3 x^{2}}-\frac{1}{3 c \,x^{3}}-\frac{c}{x}+\frac{c^{2} \ln \left(c x +1\right)}{2}-\frac{c^{2} \ln \left(c x -1\right)}{2}"," ",0,"-1/3*(-(c*x-1)/c/x)^(1/2)/x^2*((c*x+1)/c/x)^(1/2)*csgn(c)^2*(2*c^2*x^2+1)-1/3/c/x^3-c/x+1/2*c^2*ln(c*x+1)-1/2*c^2*ln(c*x-1)","C"
97,1,36,37,0.048000," ","int(x*(-1+a*(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x)/(-a^2*x^2+1),x)","-\frac{x \sqrt{-\frac{a x -1}{a x}}\, \sqrt{\frac{a x +1}{a x}}}{a}"," ",0,"-1/a*x*(-(a*x-1)/a/x)^(1/2)*((a*x+1)/a/x)^(1/2)","A"
98,1,104,103,0.341000," ","int(arcsech(b*x+a)/(a*d/b+d*x),x)","\frac{\mathrm{arcsech}\left(b x +a \right)^{2}}{2 d}-\frac{\mathrm{arcsech}\left(b x +a \right) \ln \left(1+\left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)^{2}\right)}{d}-\frac{\polylog \left(2, -\left(\frac{1}{b x +a}+\sqrt{\frac{1}{b x +a}-1}\, \sqrt{\frac{1}{b x +a}+1}\right)^{2}\right)}{2 d}"," ",0,"1/2*arcsech(b*x+a)^2/d-arcsech(b*x+a)*ln(1+(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))^2)/d-1/2*polylog(2,-(1/(b*x+a)+(1/(b*x+a)-1)^(1/2)*(1/(b*x+a)+1)^(1/2))^2)/d","A"
99,1,62,51,0.103000," ","int(x^3*arcsech(b*x^4+a),x)","\frac{\mathrm{arcsech}\left(b \,x^{4}+a \right) x^{4}}{4}+\frac{\mathrm{arcsech}\left(b \,x^{4}+a \right) a}{4 b}-\frac{\arctan \left(\sqrt{\frac{1}{b \,x^{4}+a}-1}\, \sqrt{\frac{1}{b \,x^{4}+a}+1}\right)}{4 b}"," ",0,"1/4*arcsech(b*x^4+a)*x^4+1/4/b*arcsech(b*x^4+a)*a-1/4/b*arctan((1/(b*x^4+a)-1)^(1/2)*(1/(b*x^4+a)+1)^(1/2))","A"
100,0,0,56,0.247000," ","int(x^(-1+n)*arcsech(a+b*x^n),x)","\int x^{-1+n} \mathrm{arcsech}\left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(-1+n)*arcsech(a+b*x^n),x)","F"