1,1,345,0,0.483332," ","integrate(x^3*arcsech(b*x+a),x, algorithm=""fricas"")","\frac{6 \, b^{4} x^{4} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - 3 \, a^{4} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) + 3 \, a^{4} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 12 \, {\left(2 \, a^{3} + a\right)} \arctan\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - 2 \, {\left(b^{3} x^{3} - 3 \, a b^{2} x^{2} + 13 \, a^{3} + {\left(9 \, a^{2} + 2\right)} b x + 2 \, a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{24 \, b^{4}}"," ",0,"1/24*(6*b^4*x^4*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - 3*a^4*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) + 3*a^4*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 12*(2*a^3 + a)*arctan((b^2*x^2 + 2*a*b*x + a^2)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*x^2 + 2*a*b*x + a^2 - 1)) - 2*(b^3*x^3 - 3*a*b^2*x^2 + 13*a^3 + (9*a^2 + 2)*b*x + 2*a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^4","A",0
2,1,327,0,1.920576," ","integrate(x^2*arcsech(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) + a^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - a^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) - {\left(6 \, a^{2} + 1\right)} \arctan\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - {\left(b^{2} x^{2} - 4 \, a b x - 5 \, a^{2}\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) + a^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - a^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) - (6*a^2 + 1)*arctan((b^2*x^2 + 2*a*b*x + a^2)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*x^2 + 2*a*b*x + a^2 - 1)) - (b^2*x^2 - 4*a*b*x - 5*a^2)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^3","B",0
3,1,308,0,1.393433," ","integrate(x*arcsech(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - a^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) + a^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 4 \, a \arctan\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right) - 2 \, {\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - a^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) + a^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 4*a*arctan((b^2*x^2 + 2*a*b*x + a^2)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*x^2 + 2*a*b*x + a^2 - 1)) - 2*(b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/b^2","B",0
4,1,253,0,0.762020," ","integrate(arcsech(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) + a \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - a \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) - 2 \, \arctan\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) + a*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - a*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) - 2*arctan((b^2*x^2 + 2*a*b*x + a^2)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*x^2 + 2*a*b*x + a^2 - 1)))/b","B",0
5,0,0,0,0.665910," ","integrate(arcsech(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arcsech(b*x + a)/x, x)","F",0
6,1,651,0,0.707126," ","integrate(arcsech(b*x+a)/x^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} - 1\right)} b x \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - {\left(a^{2} - 1\right)} b x \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + \sqrt{-a^{2} + 1} b x \log\left(\frac{{\left(2 \, a^{2} - 1\right)} b^{2} x^{2} + 2 \, a^{4} + 4 \, {\left(a^{3} - a\right)} b x - 4 \, a^{2} - 2 \, {\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{-a^{2} + 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 2}{x^{2}}\right) + 2 \, {\left(a^{3} - a\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right)}{2 \, {\left(a^{3} - a\right)} x}, -\frac{{\left(a^{2} - 1\right)} b x \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - {\left(a^{2} - 1\right)} b x \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 2 \, \sqrt{a^{2} - 1} b x \arctan\left(\frac{{\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{a^{2} - 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{{\left(a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 2 \, {\left(a^{3} - a\right)} b x - 2 \, a^{2} + 1}\right) + 2 \, {\left(a^{3} - a\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right)}{2 \, {\left(a^{3} - a\right)} x}\right]"," ",0,"[-1/2*((a^2 - 1)*b*x*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - (a^2 - 1)*b*x*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + sqrt(-a^2 + 1)*b*x*log(((2*a^2 - 1)*b^2*x^2 + 2*a^4 + 4*(a^3 - a)*b*x - 4*a^2 - 2*(a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(-a^2 + 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 2)/x^2) + 2*(a^3 - a)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)))/((a^3 - a)*x), -1/2*((a^2 - 1)*b*x*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - (a^2 - 1)*b*x*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 2*sqrt(a^2 - 1)*b*x*arctan((a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(a^2 - 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/((a^2 - 1)*b^2*x^2 + a^4 + 2*(a^3 - a)*b*x - 2*a^2 + 1)) + 2*(a^3 - a)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)))/((a^3 - a)*x)]","B",0
7,1,865,0,0.688808," ","integrate(arcsech(b*x+a)/x^3,x, algorithm=""fricas"")","\left[-\frac{{\left(2 \, a^{2} - 1\right)} \sqrt{-a^{2} + 1} b^{2} x^{2} \log\left(\frac{{\left(2 \, a^{2} - 1\right)} b^{2} x^{2} + 2 \, a^{4} + 4 \, {\left(a^{3} - a\right)} b x - 4 \, a^{2} + 2 \, {\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{-a^{2} + 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 2}{x^{2}}\right) - {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) + {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) + 2 \, {\left({\left(a^{3} - a\right)} b^{2} x^{2} + {\left(a^{4} - a^{2}\right)} b x\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{4 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} x^{2}}, \frac{2 \, {\left(2 \, a^{2} - 1\right)} \sqrt{a^{2} - 1} b^{2} x^{2} \arctan\left(\frac{{\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{a^{2} - 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{{\left(a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 2 \, {\left(a^{3} - a\right)} b x - 2 \, a^{2} + 1}\right) + {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - {\left(a^{4} - 2 \, a^{2} + 1\right)} b^{2} x^{2} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) - 2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - 2 \, {\left({\left(a^{3} - a\right)} b^{2} x^{2} + {\left(a^{4} - a^{2}\right)} b x\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{4 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} x^{2}}\right]"," ",0,"[-1/4*((2*a^2 - 1)*sqrt(-a^2 + 1)*b^2*x^2*log(((2*a^2 - 1)*b^2*x^2 + 2*a^4 + 4*(a^3 - a)*b*x - 4*a^2 + 2*(a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(-a^2 + 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 2)/x^2) - (a^4 - 2*a^2 + 1)*b^2*x^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) + (a^4 - 2*a^2 + 1)*b^2*x^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 2*(a^6 - 2*a^4 + a^2)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) + 2*((a^3 - a)*b^2*x^2 + (a^4 - a^2)*b*x)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/((a^6 - 2*a^4 + a^2)*x^2), 1/4*(2*(2*a^2 - 1)*sqrt(a^2 - 1)*b^2*x^2*arctan((a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(a^2 - 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/((a^2 - 1)*b^2*x^2 + a^4 + 2*(a^3 - a)*b*x - 2*a^2 + 1)) + (a^4 - 2*a^2 + 1)*b^2*x^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - (a^4 - 2*a^2 + 1)*b^2*x^2*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) - 2*(a^6 - 2*a^4 + a^2)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - 2*((a^3 - a)*b^2*x^2 + (a^4 - a^2)*b*x)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/((a^6 - 2*a^4 + a^2)*x^2)]","B",0
8,1,987,0,0.694522," ","integrate(arcsech(b*x+a)/x^4,x, algorithm=""fricas"")","\left[-\frac{{\left(6 \, a^{4} - 5 \, a^{2} + 2\right)} \sqrt{-a^{2} + 1} b^{3} x^{3} \log\left(\frac{{\left(2 \, a^{2} - 1\right)} b^{2} x^{2} + 2 \, a^{4} + 4 \, {\left(a^{3} - a\right)} b x - 4 \, a^{2} - 2 \, {\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{-a^{2} + 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 2}{x^{2}}\right) + 2 \, {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - 2 \, {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 4 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - 2 \, {\left({\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{3} x^{3} + {\left(4 \, a^{6} - 5 \, a^{4} + a^{2}\right)} b^{2} x^{2} - {\left(a^{7} - 2 \, a^{5} + a^{3}\right)} b x\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{12 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} x^{3}}, -\frac{{\left(6 \, a^{4} - 5 \, a^{2} + 2\right)} \sqrt{a^{2} - 1} b^{3} x^{3} \arctan\left(\frac{{\left(a b^{2} x^{2} + a^{3} + {\left(2 \, a^{2} - 1\right)} b x - a\right)} \sqrt{a^{2} - 1} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{{\left(a^{2} - 1\right)} b^{2} x^{2} + a^{4} + 2 \, {\left(a^{3} - a\right)} b x - 2 \, a^{2} + 1}\right) + {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{x}\right) - {\left(a^{6} - 3 \, a^{4} + 3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} - 1}{x}\right) + 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \log\left(\frac{{\left(b x + a\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}} + 1}{b x + a}\right) - {\left({\left(5 \, a^{5} - 7 \, a^{3} + 2 \, a\right)} b^{3} x^{3} + {\left(4 \, a^{6} - 5 \, a^{4} + a^{2}\right)} b^{2} x^{2} - {\left(a^{7} - 2 \, a^{5} + a^{3}\right)} b x\right)} \sqrt{-\frac{b^{2} x^{2} + 2 \, a b x + a^{2} - 1}{b^{2} x^{2} + 2 \, a b x + a^{2}}}}{6 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} x^{3}}\right]"," ",0,"[-1/12*((6*a^4 - 5*a^2 + 2)*sqrt(-a^2 + 1)*b^3*x^3*log(((2*a^2 - 1)*b^2*x^2 + 2*a^4 + 4*(a^3 - a)*b*x - 4*a^2 - 2*(a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(-a^2 + 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 2)/x^2) + 2*(a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - 2*(a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 4*(a^9 - 3*a^7 + 3*a^5 - a^3)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - 2*((5*a^5 - 7*a^3 + 2*a)*b^3*x^3 + (4*a^6 - 5*a^4 + a^2)*b^2*x^2 - (a^7 - 2*a^5 + a^3)*b*x)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/((a^9 - 3*a^7 + 3*a^5 - a^3)*x^3), -1/6*((6*a^4 - 5*a^2 + 2)*sqrt(a^2 - 1)*b^3*x^3*arctan((a*b^2*x^2 + a^3 + (2*a^2 - 1)*b*x - a)*sqrt(a^2 - 1)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2))/((a^2 - 1)*b^2*x^2 + a^4 + 2*(a^3 - a)*b*x - 2*a^2 + 1)) + (a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/x) - (a^6 - 3*a^4 + 3*a^2 - 1)*b^3*x^3*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) - 1)/x) + 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*log(((b*x + a)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)) + 1)/(b*x + a)) - ((5*a^5 - 7*a^3 + 2*a)*b^3*x^3 + (4*a^6 - 5*a^4 + a^2)*b^2*x^2 - (a^7 - 2*a^5 + a^3)*b*x)*sqrt(-(b^2*x^2 + 2*a*b*x + a^2 - 1)/(b^2*x^2 + 2*a*b*x + a^2)))/((a^9 - 3*a^7 + 3*a^5 - a^3)*x^3)]","B",0
9,0,0,0,1.287818," ","integrate(x^2*arcsech(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arsech}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^2*arcsech(b*x + a)^2, x)","F",0
10,0,0,0,0.621197," ","integrate(x*arcsech(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arsech}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x*arcsech(b*x + a)^2, x)","F",0
11,0,0,0,0.786012," ","integrate(arcsech(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arsech}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(arcsech(b*x + a)^2, x)","F",0
12,0,0,0,0.966296," ","integrate(arcsech(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(arcsech(b*x + a)^2/x, x)","F",0
13,0,0,0,0.559244," ","integrate(arcsech(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(arcsech(b*x + a)^2/x^2, x)","F",0
14,0,0,0,0.512638," ","integrate(arcsech(b*x+a)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(arcsech(b*x + a)^2/x^3, x)","F",0
15,0,0,0,0.605821," ","integrate(x*arcsech(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arsech}\left(b x + a\right)^{3}, x\right)"," ",0,"integral(x*arcsech(b*x + a)^3, x)","F",0
16,0,0,0,0.568268," ","integrate(arcsech(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arsech}\left(b x + a\right)^{3}, x\right)"," ",0,"integral(arcsech(b*x + a)^3, x)","F",0
17,0,0,0,0.577073," ","integrate(arcsech(b*x+a)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{3}}{x}, x\right)"," ",0,"integral(arcsech(b*x + a)^3/x, x)","F",0
18,0,0,0,1.036250," ","integrate(arcsech(b*x+a)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(arcsech(b*x + a)^3/x^2, x)","F",0
19,0,0,0,0.557786," ","integrate(arcsech(b*x+a)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(b x + a\right)^{3}}{x^{3}}, x\right)"," ",0,"integral(arcsech(b*x + a)^3/x^3, x)","F",0
20,1,57,0,0.636490," ","integrate(x^3*arcsech(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{4} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right) - \frac{1}{140} \, {\left(5 \, x^{3} + 6 \, x^{2} + 8 \, x + 16\right)} \sqrt{x} \sqrt{-\frac{x - 1}{x}}"," ",0,"1/4*x^4*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x) - 1/140*(5*x^3 + 6*x^2 + 8*x + 16)*sqrt(x)*sqrt(-(x - 1)/x)","A",0
21,1,52,0,0.518558," ","integrate(x^2*arcsech(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right) - \frac{1}{45} \, {\left(3 \, x^{2} + 4 \, x + 8\right)} \sqrt{x} \sqrt{-\frac{x - 1}{x}}"," ",0,"1/3*x^3*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x) - 1/45*(3*x^2 + 4*x + 8)*sqrt(x)*sqrt(-(x - 1)/x)","A",0
22,1,45,0,0.630061," ","integrate(x*arcsech(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right) - \frac{1}{6} \, {\left(x + 2\right)} \sqrt{x} \sqrt{-\frac{x - 1}{x}}"," ",0,"1/2*x^2*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x) - 1/6*(x + 2)*sqrt(x)*sqrt(-(x - 1)/x)","A",0
23,1,39,0,0.561502," ","integrate(arcsech(x^(1/2)),x, algorithm=""fricas"")","x \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right) - \sqrt{x} \sqrt{-\frac{x - 1}{x}}"," ",0,"x*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x) - sqrt(x)*sqrt(-(x - 1)/x)","A",0
24,0,0,0,0.569731," ","integrate(arcsech(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arcsech(sqrt(x))/x, x)","F",0
25,1,45,0,0.607958," ","integrate(arcsech(x^(1/2))/x^2,x, algorithm=""fricas"")","\frac{{\left(x - 2\right)} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right) + \sqrt{x} \sqrt{-\frac{x - 1}{x}}}{2 \, x}"," ",0,"1/2*((x - 2)*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x) + sqrt(x)*sqrt(-(x - 1)/x))/x","A",0
26,1,54,0,1.085860," ","integrate(arcsech(x^(1/2))/x^3,x, algorithm=""fricas"")","\frac{{\left(3 \, x + 2\right)} \sqrt{x} \sqrt{-\frac{x - 1}{x}} + {\left(3 \, x^{2} - 8\right)} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right)}{16 \, x^{2}}"," ",0,"1/16*((3*x + 2)*sqrt(x)*sqrt(-(x - 1)/x) + (3*x^2 - 8)*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x))/x^2","A",0
27,1,60,0,1.385088," ","integrate(arcsech(x^(1/2))/x^4,x, algorithm=""fricas"")","\frac{{\left(15 \, x^{2} + 10 \, x + 8\right)} \sqrt{x} \sqrt{-\frac{x - 1}{x}} + 3 \, {\left(5 \, x^{3} - 16\right)} \log\left(\frac{x \sqrt{-\frac{x - 1}{x}} + \sqrt{x}}{x}\right)}{144 \, x^{3}}"," ",0,"1/144*((15*x^2 + 10*x + 8)*sqrt(x)*sqrt(-(x - 1)/x) + 3*(5*x^3 - 16)*log((x*sqrt(-(x - 1)/x) + sqrt(x))/x))/x^3","A",0
28,1,22,0,0.634626," ","integrate(arcsech(1/x),x, algorithm=""fricas"")","x \log\left(x + \sqrt{x^{2} - 1}\right) - \sqrt{x^{2} - 1}"," ",0,"x*log(x + sqrt(x^2 - 1)) - sqrt(x^2 - 1)","A",0
29,-2,0,0,0.000000," ","integrate(arcsech(a*x^n)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
30,0,0,0,0.696355," ","integrate(arcsech(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arsech}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arcsech(a*x^5)/x, x)","F",0
31,-2,0,0,0.000000," ","integrate(arcsech(c*exp(b*x+a)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
32,1,65,0,0.552233," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^4,x, algorithm=""fricas"")","\frac{15 \, a^{3} x^{4} + 4 \, {\left(3 \, a^{4} x^{5} - a^{2} x^{3} - 2 \, x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{60 \, a^{4}}"," ",0,"1/60*(15*a^3*x^4 + 4*(3*a^4*x^5 - a^2*x^3 - 2*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)))/a^4","A",0
33,1,95,0,0.511783," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} + 3 \, {\left(2 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 3 \, \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{24 \, a^{4}}"," ",0,"1/24*(8*a^3*x^3 + 3*(2*a^4*x^4 - a^2*x^2)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 3*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^4","A",0
34,1,54,0,0.758091," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^2,x, algorithm=""fricas"")","\frac{3 \, a x^{2} + 2 \, {\left(a^{2} x^{3} - x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{6 \, a^{2}}"," ",0,"1/6*(3*a*x^2 + 2*(a^2*x^3 - x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)))/a^2","A",0
35,1,79,0,0.618837," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 2 \, a x - \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{2 \, a^{2}}"," ",0,"1/2*(a^2*x^2*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 2*a*x - arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^2","A",0
36,1,115,0,0.695917," ","integrate(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) + \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, \log\left(x\right)}{2 \, a}"," ",0,"1/2*(2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) + log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*log(x))/a","B",0
37,1,77,0,0.697610," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x, algorithm=""fricas"")","-\frac{a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - a x \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right) + 1}{a x}"," ",0,"-(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - a*x*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))) + 1)/(a*x)","A",0
38,1,128,0,0.807674," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) - 2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 2}{4 \, a x^{2}}"," ",0,"1/4*(a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) - 2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 2)/(a*x^2)","B",0
39,1,52,0,0.662947," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} x^{3} - a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1}{3 \, a x^{3}}"," ",0,"1/3*((a^3*x^3 - a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1)/(a*x^3)","A",0
40,1,138,0,0.652189," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x, algorithm=""fricas"")","\frac{a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, {\left(a^{3} x^{3} - 2 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 4}{16 \, a x^{4}}"," ",0,"1/16*(a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*(a^3*x^3 - 2*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 4)/(a*x^4)","A",0
41,1,60,0,0.486608," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{5} x^{5} + a^{3} x^{3} - 3 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 3}{15 \, a x^{5}}"," ",0,"1/15*((2*a^5*x^5 + a^3*x^3 - 3*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 3)/(a*x^5)","A",0
42,1,148,0,0.860380," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x, algorithm=""fricas"")","\frac{3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - 3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, {\left(3 \, a^{5} x^{5} + 2 \, a^{3} x^{3} - 8 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 16}{96 \, a x^{6}}"," ",0,"1/96*(3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - 3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*(3*a^5*x^5 + 2*a^3*x^3 - 8*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 16)/(a*x^6)","A",0
43,1,69,0,0.494542," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{7} x^{7} + 4 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - 15 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 15}{105 \, a x^{7}}"," ",0,"1/105*((8*a^7*x^7 + 4*a^5*x^5 + 3*a^3*x^3 - 15*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 15)/(a*x^7)","A",0
44,1,156,0,0.545193," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^8,x, algorithm=""fricas"")","\frac{15 \, a^{8} x^{8} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - 15 \, a^{8} x^{8} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, {\left(15 \, a^{7} x^{7} + 10 \, a^{5} x^{5} + 8 \, a^{3} x^{3} - 48 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 96}{768 \, a x^{8}}"," ",0,"1/768*(15*a^8*x^8*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - 15*a^8*x^8*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*(15*a^7*x^7 + 10*a^5*x^5 + 8*a^3*x^3 - 48*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 96)/(a*x^8)","A",0
45,1,116,0,0.497613," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^7,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{6} + 3 \, {\left(2 \, a^{4} x^{8} - a^{2} x^{4}\right)} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 6 \, \arctan\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 1}{a x^{2}}\right)}{48 \, a^{4}}"," ",0,"1/48*(8*a^3*x^6 + 3*(2*a^4*x^8 - a^2*x^4)*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 6*arctan((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 1)/(a*x^2)))/a^4","A",0
46,0,0,0,0.728050," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{6} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + x^{4}}{a}, x\right)"," ",0,"integral((a*x^6*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + x^4)/a, x)","F",0
47,1,60,0,0.535607," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^5,x, algorithm=""fricas"")","\frac{3 \, a x^{4} + 2 \, {\left(a^{2} x^{6} - x^{2}\right)} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}}}{12 \, a^{2}}"," ",0,"1/12*(3*a*x^4 + 2*(a^2*x^6 - x^2)*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)))/a^2","A",0
48,0,0,0,1.733548," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{4} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + x^{2}}{a}, x\right)"," ",0,"integral((a*x^4*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + x^2)/a, x)","F",0
49,1,102,0,0.756165," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{4} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 2 \, a x^{2} - 2 \, \arctan\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 1}{a x^{2}}\right)}{4 \, a^{2}}"," ",0,"1/4*(a^2*x^4*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 2*a*x^2 - 2*arctan((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 1)/(a*x^2)))/a^2","A",0
50,0,0,0,1.847850," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 1}{a}, x\right)"," ",0,"integral((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 1)/a, x)","F",0
51,1,133,0,1.592336," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x,x, algorithm=""fricas"")","\frac{2 \, a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - \log\left(a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 1\right) + \log\left(a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 1\right) + 4 \, \log\left(x\right)}{4 \, a}"," ",0,"1/4*(2*a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - log(a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 1) + log(a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 1) + 4*log(x))/a","B",0
52,0,0,0,0.740915," ","integrate(1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 1}{a x^{2}}, x\right)"," ",0,"integral((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 1)/(a*x^2), x)","F",0
53,1,102,0,0.973930," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x,x, algorithm=""fricas"")","-\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 2 \, a x^{2} \arctan\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 1}{a x^{2}}\right) + 1}{2 \, a x^{2}}"," ",0,"-1/2*(a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 2*a*x^2*arctan((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 1)/(a*x^2)) + 1)/(a*x^2)","B",0
54,0,0,0,0.772827," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 1}{a x^{4}}, x\right)"," ",0,"integral((a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 1)/(a*x^4), x)","F",0
55,1,146,0,0.861521," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^3,x, algorithm=""fricas"")","\frac{a^{2} x^{4} \log\left(a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + 1\right) - a^{2} x^{4} \log\left(a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 1\right) - 2 \, a x^{2} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} - 2}{8 \, a x^{4}}"," ",0,"1/8*(a^2*x^4*log(a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + 1) - a^2*x^4*log(a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 1) - 2*a*x^2*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) - 2)/(a*x^4)","A",0
56,0,0,0,2.367697," ","integrate((1/a/x^3+(1/a/x^3-1)^(1/2)*(1/a/x^3+1)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{3} x^{m} \sqrt{\frac{a x^{3} + 1}{a x^{3}}} \sqrt{-\frac{a x^{3} - 1}{a x^{3}}} + x^{m}}{a x^{3}}, x\right)"," ",0,"integral((a*x^3*x^m*sqrt((a*x^3 + 1)/(a*x^3))*sqrt(-(a*x^3 - 1)/(a*x^3)) + x^m)/(a*x^3), x)","F",0
57,0,0,0,1.633786," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{2} x^{m} \sqrt{\frac{a x^{2} + 1}{a x^{2}}} \sqrt{-\frac{a x^{2} - 1}{a x^{2}}} + x^{m}}{a x^{2}}, x\right)"," ",0,"integral((a*x^2*x^m*sqrt((a*x^2 + 1)/(a*x^2))*sqrt(-(a*x^2 - 1)/(a*x^2)) + x^m)/(a*x^2), x)","F",0
58,0,0,0,0.637097," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x x^{m} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + x^{m}}{a x}, x\right)"," ",0,"integral((a*x*x^m*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + x^m)/(a*x), x)","F",0
59,0,0,0,2.072463," ","integrate((x/a+(-1+x/a)^(1/2)*(1+x/a)^(1/2))*x^m,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a x^{m} \sqrt{\frac{a + x}{a}} \sqrt{-\frac{a - x}{a}} + x x^{m}}{a}, x\right)"," ",0,"integral((a*x^m*sqrt((a + x)/a)*sqrt(-(a - x)/a) + x*x^m)/a, x)","F",0
60,-2,0,0,0.000000," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x^m,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
61,-2,0,0,0.000000," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))*x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
62,-2,0,0,0.000000," ","integrate(1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
63,1,102,0,0.699876," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x,x, algorithm=""fricas"")","-\frac{a x^{p} \sqrt{\frac{a x^{p} + 1}{a x^{p}}} \sqrt{-\frac{a x^{p} - 1}{a x^{p}}} - a x^{p} \arctan\left(\sqrt{\frac{a x^{p} + 1}{a x^{p}}} \sqrt{-\frac{a x^{p} - 1}{a x^{p}}}\right) + 1}{a p x^{p}}"," ",0,"-(a*x^p*sqrt((a*x^p + 1)/(a*x^p))*sqrt(-(a*x^p - 1)/(a*x^p)) - a*x^p*arctan(sqrt((a*x^p + 1)/(a*x^p))*sqrt(-(a*x^p - 1)/(a*x^p))) + 1)/(a*p*x^p)","A",0
64,-2,0,0,0.000000," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
65,1,103,0,0.887513," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^4,x, algorithm=""fricas"")","-\frac{12 \, a^{5} x^{5} - 40 \, a^{3} x^{3} - 15 \, {\left(2 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 15 \, \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{60 \, a^{5}}"," ",0,"-1/60*(12*a^5*x^5 - 40*a^3*x^3 - 15*(2*a^4*x^4 - a^2*x^2)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 15*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^5","A",0
66,1,62,0,1.539140," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} x^{4} - 12 \, a x^{2} - 8 \, {\left(a^{2} x^{3} - x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{12 \, a^{3}}"," ",0,"-1/12*(3*a^3*x^4 - 12*a*x^2 - 8*(a^2*x^3 - x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)))/a^3","A",0
67,1,87,0,1.532663," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^2,x, algorithm=""fricas"")","-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 6 \, a x + 3 \, \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{3 \, a^{3}}"," ",0,"-1/3*(a^3*x^3 - 3*a^2*x^2*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 6*a*x + 3*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^3","A",0
68,1,124,0,0.502492," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} - 4 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 2 \, \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - 2 \, \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) - 4 \, \log\left(x\right)}{2 \, a^{2}}"," ",0,"-1/2*(a^2*x^2 - 4*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - 2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) - 4*log(x))/a^2","A",0
69,1,85,0,1.015948," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} + 2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 2 \, a x \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right) + 2}{a^{2} x}"," ",0,"-(a^2*x^2 + 2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 2*a*x*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))) + 2)/(a^2*x)","A",0
70,1,138,0,0.849931," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x,x, algorithm=""fricas"")","\frac{a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) - 2 \, a^{2} x^{2} \log\left(x\right) - 2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 2}{2 \, a^{2} x^{2}}"," ",0,"1/2*(a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) - 2*a^2*x^2*log(x) - 2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 2)/(a^2*x^2)","A",0
71,1,61,0,1.060925," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 2}{3 \, a^{2} x^{3}}"," ",0,"1/3*(3*a^2*x^2 + 2*(a^3*x^3 - a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 2)/(a^2*x^3)","A",0
72,1,146,0,1.016245," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^3,x, algorithm=""fricas"")","\frac{a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 4 \, a^{2} x^{2} + 2 \, {\left(a^{3} x^{3} - 2 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 4}{8 \, a^{2} x^{4}}"," ",0,"1/8*(a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 4*a^2*x^2 + 2*(a^3*x^3 - 2*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 4)/(a^2*x^4)","A",0
73,1,69,0,0.744745," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^4,x, algorithm=""fricas"")","\frac{5 \, a^{2} x^{2} + 2 \, {\left(2 \, a^{5} x^{5} + a^{3} x^{3} - 3 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 6}{15 \, a^{2} x^{5}}"," ",0,"1/15*(5*a^2*x^2 + 2*(2*a^5*x^5 + a^3*x^3 - 3*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 6)/(a^2*x^5)","A",0
74,1,156,0,0.549327," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^5,x, algorithm=""fricas"")","\frac{3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - 3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 12 \, a^{2} x^{2} + 2 \, {\left(3 \, a^{5} x^{5} + 2 \, a^{3} x^{3} - 8 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 16}{48 \, a^{2} x^{6}}"," ",0,"1/48*(3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - 3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 12*a^2*x^2 + 2*(3*a^5*x^5 + 2*a^3*x^3 - 8*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 16)/(a^2*x^6)","A",0
75,1,78,0,0.764463," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^6,x, algorithm=""fricas"")","\frac{21 \, a^{2} x^{2} + 2 \, {\left(8 \, a^{7} x^{7} + 4 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - 15 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 30}{105 \, a^{2} x^{7}}"," ",0,"1/105*(21*a^2*x^2 + 2*(8*a^7*x^7 + 4*a^5*x^5 + 3*a^3*x^3 - 15*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 30)/(a^2*x^7)","A",0
76,1,65,0,1.971007," ","integrate(x^4/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""fricas"")","\frac{15 \, a^{3} x^{4} - 4 \, {\left(3 \, a^{4} x^{5} - a^{2} x^{3} - 2 \, x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{60 \, a^{4}}"," ",0,"1/60*(15*a^3*x^4 - 4*(3*a^4*x^5 - a^2*x^3 - 2*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)))/a^4","A",0
77,1,95,0,0.782344," ","integrate(x^3/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} - 3 \, {\left(2 \, a^{4} x^{4} - a^{2} x^{2}\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 3 \, \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{24 \, a^{4}}"," ",0,"1/24*(8*a^3*x^3 - 3*(2*a^4*x^4 - a^2*x^2)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 3*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^4","A",0
78,1,54,0,0.537106," ","integrate(x^2/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""fricas"")","\frac{3 \, a x^{2} - 2 \, {\left(a^{2} x^{3} - x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{6 \, a^{2}}"," ",0,"1/6*(3*a*x^2 - 2*(a^2*x^3 - x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)))/a^2","A",0
79,1,79,0,0.852314," ","integrate(x/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""fricas"")","-\frac{a^{2} x^{2} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 2 \, a x - \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right)}{2 \, a^{2}}"," ",0,"-1/2*(a^2*x^2*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 2*a*x - arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))))/a^2","A",0
80,1,115,0,0.530209," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) + \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) - 2 \, \log\left(x\right)}{2 \, a}"," ",0,"-1/2*(2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) + log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) - 2*log(x))/a","A",0
81,1,76,0,1.700407," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x, algorithm=""fricas"")","\frac{a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - a x \arctan\left(\sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}\right) - 1}{a x}"," ",0,"(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - a*x*arctan(sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))) - 1)/(a*x)","A",0
82,1,128,0,0.514241," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{2} x^{2} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) - 2 \, a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 2}{4 \, a x^{2}}"," ",0,"-1/4*(a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^2*x^2*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) - 2*a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 2)/(a*x^2)","A",0
83,1,52,0,0.785151," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} x^{3} - a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1}{3 \, a x^{3}}"," ",0,"-1/3*((a^3*x^3 - a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1)/(a*x^3)","A",0
84,1,138,0,0.628701," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x, algorithm=""fricas"")","-\frac{a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - a^{4} x^{4} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, {\left(a^{3} x^{3} - 2 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 4}{16 \, a x^{4}}"," ",0,"-1/16*(a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - a^4*x^4*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*(a^3*x^3 - 2*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 4)/(a*x^4)","A",0
85,1,60,0,0.743281," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{5} x^{5} + a^{3} x^{3} - 3 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 3}{15 \, a x^{5}}"," ",0,"-1/15*((2*a^5*x^5 + a^3*x^3 - 3*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 3)/(a*x^5)","A",0
86,1,148,0,0.830971," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x, algorithm=""fricas"")","-\frac{3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 1\right) - 3 \, a^{6} x^{6} \log\left(a x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} - 1\right) + 2 \, {\left(3 \, a^{5} x^{5} + 2 \, a^{3} x^{3} - 8 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 16}{96 \, a x^{6}}"," ",0,"-1/96*(3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 1) - 3*a^6*x^6*log(a*x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) - 1) + 2*(3*a^5*x^5 + 2*a^3*x^3 - 8*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 16)/(a*x^6)","A",0
87,1,69,0,0.805304," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{7} x^{7} + 4 \, a^{5} x^{5} + 3 \, a^{3} x^{3} - 15 \, a x\right)} \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}} + 15}{105 \, a x^{7}}"," ",0,"-1/105*((8*a^7*x^7 + 4*a^5*x^5 + 3*a^3*x^3 - 15*a*x)*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x)) + 15)/(a*x^7)","A",0
88,0,0,0,1.415264," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*(d*x)^m/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(d x\right)^{m} c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + \left(d x\right)^{m}}{c^{3} x^{3} - c x}, x\right)"," ",0,"integral(-((d*x)^m*c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + (d*x)^m)/(c^3*x^3 - c*x), x)","F",0
89,1,69,0,1.263573," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^4/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{3 \, c^{2} x^{2} + 2 \, {\left(c^{3} x^{3} + 2 \, c x\right)} \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + 3 \, \log\left(c^{2} x^{2} - 1\right)}{6 \, c^{5}}"," ",0,"-1/6*(3*c^2*x^2 + 2*(c^3*x^3 + 2*c*x)*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + 3*log(c^2*x^2 - 1))/c^5","A",0
90,1,91,0,1.566521," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^3/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{c^{2} x^{2} \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + 2 \, c x + \arctan\left(\sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}}\right) - \log\left(c x + 1\right) + \log\left(c x - 1\right)}{2 \, c^{4}}"," ",0,"-1/2*(c^2*x^2*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + 2*c*x + arctan(sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x))) - log(c*x + 1) + log(c*x - 1))/c^4","B",0
91,1,49,0,0.495551," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x^2/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{2 \, c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + \log\left(c^{2} x^{2} - 1\right)}{2 \, c^{3}}"," ",0,"-1/2*(2*c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + log(c^2*x^2 - 1))/c^3","A",0
92,1,53,0,0.824792," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(\sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}}\right) - \log\left(c x + 1\right) + \log\left(c x - 1\right)}{2 \, c^{2}}"," ",0,"-1/2*(2*arctan(sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x))) - log(c*x + 1) + log(c*x - 1))/c^2","B",0
93,1,92,0,1.913863," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{\log\left(c^{2} x^{2} - 1\right) + \log\left(c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + 1\right) - \log\left(c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} - 1\right) - 2 \, \log\left(x\right)}{2 \, c}"," ",0,"-1/2*(log(c^2*x^2 - 1) + log(c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + 1) - log(c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) - 1) - 2*log(x))/c","B",0
94,1,62,0,0.915790," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{2 \, c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} - c x \log\left(c x + 1\right) + c x \log\left(c x - 1\right) + 2}{2 \, c x}"," ",0,"-1/2*(2*c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) - c*x*log(c*x + 1) + c*x*log(c*x - 1) + 2)/(c*x)","A",0
95,1,156,0,0.854367," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x^2/(-c^2*x^2+1),x, algorithm=""fricas"")","-\frac{2 \, c^{2} x^{2} \log\left(c^{2} x^{2} - 1\right) + c^{2} x^{2} \log\left(c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + 1\right) - c^{2} x^{2} \log\left(c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} - 1\right) - 4 \, c^{2} x^{2} \log\left(x\right) + 2 \, c x \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} + 2}{4 \, c x^{2}}"," ",0,"-1/4*(2*c^2*x^2*log(c^2*x^2 - 1) + c^2*x^2*log(c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + 1) - c^2*x^2*log(c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) - 1) - 4*c^2*x^2*log(x) + 2*c*x*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) + 2)/(c*x^2)","B",0
96,1,89,0,0.863332," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x^3/(-c^2*x^2+1),x, algorithm=""fricas"")","\frac{3 \, c^{3} x^{3} \log\left(c x + 1\right) - 3 \, c^{3} x^{3} \log\left(c x - 1\right) - 6 \, c^{2} x^{2} - 2 \, {\left(2 \, c^{3} x^{3} + c x\right)} \sqrt{\frac{c x + 1}{c x}} \sqrt{-\frac{c x - 1}{c x}} - 2}{6 \, c x^{3}}"," ",0,"1/6*(3*c^3*x^3*log(c*x + 1) - 3*c^3*x^3*log(c*x - 1) - 6*c^2*x^2 - 2*(2*c^3*x^3 + c*x)*sqrt((c*x + 1)/(c*x))*sqrt(-(c*x - 1)/(c*x)) - 2)/(c*x^3)","A",0
97,1,35,0,0.629021," ","integrate(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, algorithm=""fricas"")","-\frac{x \sqrt{\frac{a x + 1}{a x}} \sqrt{-\frac{a x - 1}{a x}}}{a}"," ",0,"-x*sqrt((a*x + 1)/(a*x))*sqrt(-(a*x - 1)/(a*x))/a","A",0
98,0,0,0,0.885189," ","integrate(arcsech(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arsech}\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arcsech(b*x + a)/(b*d*x + a*d), x)","F",0
99,1,283,0,1.754152," ","integrate(x^3*arcsech(b*x^4+a),x, algorithm=""fricas"")","\frac{2 \, b x^{4} \log\left(\frac{{\left(b x^{4} + a\right)} \sqrt{-\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} + 1}{b x^{4} + a}\right) + a \log\left(\frac{{\left(b x^{4} + a\right)} \sqrt{-\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} + 1}{x^{4}}\right) - a \log\left(\frac{{\left(b x^{4} + a\right)} \sqrt{-\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}} - 1}{x^{4}}\right) - 2 \, \arctan\left(\frac{{\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2}\right)} \sqrt{-\frac{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2}}}}{b^{2} x^{8} + 2 \, a b x^{4} + a^{2} - 1}\right)}{8 \, b}"," ",0,"1/8*(2*b*x^4*log(((b*x^4 + a)*sqrt(-(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 1)/(b*x^4 + a)) + a*log(((b*x^4 + a)*sqrt(-(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) + 1)/x^4) - a*log(((b*x^4 + a)*sqrt(-(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)/(b^2*x^8 + 2*a*b*x^4 + a^2)) - 1)/x^4) - 2*arctan((b^2*x^8 + 2*a*b*x^4 + a^2)*sqrt(-(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)/(b^2*x^8 + 2*a*b*x^4 + a^2))/(b^2*x^8 + 2*a*b*x^4 + a^2 - 1)))/b","B",0
100,1,385,0,0.915347," ","integrate(x^(-1+n)*arcsech(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, {\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{\sqrt{-\frac{2 \, a b + {\left(a^{2} + b^{2} - 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} - 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} + 1}{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a}\right) + a \log\left(\frac{\sqrt{-\frac{2 \, a b + {\left(a^{2} + b^{2} - 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} - 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} + 1}{\cosh\left(n \log\left(x\right)\right) + \sinh\left(n \log\left(x\right)\right)}\right) - a \log\left(\frac{\sqrt{-\frac{2 \, a b + {\left(a^{2} + b^{2} - 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} - 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}} - 1}{\cosh\left(n \log\left(x\right)\right) + \sinh\left(n \log\left(x\right)\right)}\right) - 2 \, \arctan\left(\frac{{\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a\right)} \sqrt{-\frac{2 \, a b + {\left(a^{2} + b^{2} - 1\right)} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} - b^{2} - 1\right)} \sinh\left(n \log\left(x\right)\right)}{\cosh\left(n \log\left(x\right)\right) - \sinh\left(n \log\left(x\right)\right)}}}{b^{2} \cosh\left(n \log\left(x\right)\right)^{2} + b^{2} \sinh\left(n \log\left(x\right)\right)^{2} + 2 \, a b \cosh\left(n \log\left(x\right)\right) + a^{2} + 2 \, {\left(b^{2} \cosh\left(n \log\left(x\right)\right) + a b\right)} \sinh\left(n \log\left(x\right)\right) - 1}\right)}{2 \, b n}"," ",0,"1/2*(2*(b*cosh(n*log(x)) + b*sinh(n*log(x)))*log((sqrt(-(2*a*b + (a^2 + b^2 - 1)*cosh(n*log(x)) - (a^2 - b^2 - 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) + 1)/(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a)) + a*log((sqrt(-(2*a*b + (a^2 + b^2 - 1)*cosh(n*log(x)) - (a^2 - b^2 - 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) + 1)/(cosh(n*log(x)) + sinh(n*log(x)))) - a*log((sqrt(-(2*a*b + (a^2 + b^2 - 1)*cosh(n*log(x)) - (a^2 - b^2 - 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x)))) - 1)/(cosh(n*log(x)) + sinh(n*log(x)))) - 2*arctan((b*cosh(n*log(x)) + b*sinh(n*log(x)) + a)*sqrt(-(2*a*b + (a^2 + b^2 - 1)*cosh(n*log(x)) - (a^2 - b^2 - 1)*sinh(n*log(x)))/(cosh(n*log(x)) - sinh(n*log(x))))/(b^2*cosh(n*log(x))^2 + b^2*sinh(n*log(x))^2 + 2*a*b*cosh(n*log(x)) + a^2 + 2*(b^2*cosh(n*log(x)) + a*b)*sinh(n*log(x)) - 1)))/(b*n)","B",0
