1,0,0,0,0.000000," ","integrate(x^3*arcsech(b*x+a),x, algorithm=""maxima"")","\frac{2 \, b^{4} x^{4} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) - 2 \, b^{4} x^{4} \log\left(b x + a\right) - b^{2} x^{2} + 6 \, a b x - {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right) - 2 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(b x + a\right) - {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(-b x - a + 1\right)}{8 \, b^{4}} + \int \frac{b^{2} x^{5} + a b x^{4}}{4 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/8*(2*b^4*x^4*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) - 2*b^4*x^4*log(b*x + a) - b^2*x^2 + 6*a*b*x - (a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1) - 2*(b^4*x^4 - a^4)*log(b*x + a) - (a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(-b*x - a + 1))/b^4 + integrate(1/4*(b^2*x^5 + a*b*x^4)/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1)) - 1), x)","F",0
2,0,0,0,0.000000," ","integrate(x^2*arcsech(b*x+a),x, algorithm=""maxima"")","\frac{2 \, b^{3} x^{3} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) - 2 \, b^{3} x^{3} \log\left(b x + a\right) - 2 \, b x + {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(b x + a\right) + {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(-b x - a + 1\right)}{6 \, b^{3}} + \int \frac{b^{2} x^{4} + a b x^{3}}{3 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/6*(2*b^3*x^3*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) - 2*b^3*x^3*log(b*x + a) - 2*b*x + (a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1) - 2*(b^3*x^3 + a^3)*log(b*x + a) + (a^3 - 3*a^2 + 3*a - 1)*log(-b*x - a + 1))/b^3 + integrate(1/3*(b^2*x^4 + a*b*x^3)/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1)) - 1), x)","F",0
3,0,0,0,0.000000," ","integrate(x*arcsech(b*x+a),x, algorithm=""maxima"")","\frac{2 \, b^{2} x^{2} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) - 2 \, b^{2} x^{2} \log\left(b x + a\right) - {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(b x + a\right) - {\left(a^{2} - 2 \, a + 1\right)} \log\left(-b x - a + 1\right)}{4 \, b^{2}} + \int \frac{b^{2} x^{3} + a b x^{2}}{2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)} - 1\right)}}\,{d x}"," ",0,"1/4*(2*b^2*x^2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) - 2*b^2*x^2*log(b*x + a) - (a^2 + 2*a + 1)*log(b*x + a + 1) - 2*(b^2*x^2 - a^2)*log(b*x + a) - (a^2 - 2*a + 1)*log(-b*x - a + 1))/b^2 + integrate(1/2*(b^2*x^3 + a*b*x^2)/(b^2*x^2 + 2*a*b*x + a^2 + (b^2*x^2 + 2*a*b*x + a^2 - 1)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1)) - 1), x)","F",0
4,1,31,0,0.302999," ","integrate(arcsech(b*x+a),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \operatorname{arsech}\left(b x + a\right) - \arctan\left(\sqrt{\frac{1}{{\left(b x + a\right)}^{2}} - 1}\right)}{b}"," ",0,"((b*x + a)*arcsech(b*x + a) - arctan(sqrt(1/(b*x + a)^2 - 1)))/b","A",0
5,0,0,0,0.000000," ","integrate(arcsech(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arcsech(b*x + a)/x, x)","F",0
6,0,0,0,0.000000," ","integrate(arcsech(b*x+a)/x^2,x, algorithm=""maxima"")","\frac{b \log\left(x\right)}{a^{3} - a} - \frac{{\left(a^{2} b - a b\right)} x \log\left(b x + a + 1\right) + {\left(a^{2} b + a b\right)} x \log\left(-b x - a + 1\right) + 2 \, {\left(a^{3} - a\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) - 2 \, {\left(a^{3} + {\left(a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) - 2 \, {\left(a^{3} - a\right)} \log\left(b x + a\right)}{2 \, {\left(a^{3} - a\right)} x} - \int \frac{b^{2} x + a b}{b^{2} x^{3} + 2 \, a b x^{2} + {\left(a^{2} - 1\right)} x + {\left(b^{2} x^{3} + 2 \, a b x^{2} + {\left(a^{2} - 1\right)} x\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)}}\,{d x}"," ",0,"b*log(x)/(a^3 - a) - 1/2*((a^2*b - a*b)*x*log(b*x + a + 1) + (a^2*b + a*b)*x*log(-b*x - a + 1) + 2*(a^3 - a)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) - 2*(a^3 + (a^2*b - b)*x - a)*log(b*x + a) - 2*(a^3 - a)*log(b*x + a))/((a^3 - a)*x) - integrate((b^2*x + a*b)/(b^2*x^3 + 2*a*b*x^2 + (a^2 - 1)*x + (b^2*x^3 + 2*a*b*x^2 + (a^2 - 1)*x)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1))), x)","F",0
7,0,0,0,0.000000," ","integrate(arcsech(b*x+a)/x^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, a^{2} b^{2} - b^{2}\right)} \log\left(x\right)}{2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)}} + \frac{{\left(a^{4} b^{2} - 2 \, a^{3} b^{2} + a^{2} b^{2}\right)} x^{2} \log\left(b x + a + 1\right) + {\left(a^{4} b^{2} + 2 \, a^{3} b^{2} + a^{2} b^{2}\right)} x^{2} \log\left(-b x - a + 1\right) - 2 \, {\left(a^{3} b - a b\right)} x - 2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) + 2 \, {\left(a^{6} - 2 \, a^{4} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{2} + b^{2}\right)} x^{2} + a^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} \log\left(b x + a\right)}{4 \, {\left(a^{6} - 2 \, a^{4} + a^{2}\right)} x^{2}} - \int \frac{b^{2} x + a b}{2 \, {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} - 1\right)} x^{2} + {\left(b^{2} x^{4} + 2 \, a b x^{3} + {\left(a^{2} - 1\right)} x^{2}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)}\right)}}\,{d x}"," ",0,"-1/2*(3*a^2*b^2 - b^2)*log(x)/(a^6 - 2*a^4 + a^2) + 1/4*((a^4*b^2 - 2*a^3*b^2 + a^2*b^2)*x^2*log(b*x + a + 1) + (a^4*b^2 + 2*a^3*b^2 + a^2*b^2)*x^2*log(-b*x - a + 1) - 2*(a^3*b - a*b)*x - 2*(a^6 - 2*a^4 + a^2)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) + 2*(a^6 - 2*a^4 - (a^4*b^2 - 2*a^2*b^2 + b^2)*x^2 + a^2)*log(b*x + a) + 2*(a^6 - 2*a^4 + a^2)*log(b*x + a))/((a^6 - 2*a^4 + a^2)*x^2) - integrate(1/2*(b^2*x + a*b)/(b^2*x^4 + 2*a*b*x^3 + (a^2 - 1)*x^2 + (b^2*x^4 + 2*a*b*x^3 + (a^2 - 1)*x^2)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1))), x)","F",0
8,0,0,0,0.000000," ","integrate(arcsech(b*x+a)/x^4,x, algorithm=""maxima"")","\frac{{\left(6 \, a^{4} b^{3} - 3 \, a^{2} b^{3} + b^{3}\right)} \log\left(x\right)}{3 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)}} - \frac{{\left(a^{6} b^{3} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{3} - a^{3} b^{3}\right)} x^{3} \log\left(b x + a + 1\right) + {\left(a^{6} b^{3} + 3 \, a^{5} b^{3} + 3 \, a^{4} b^{3} + a^{3} b^{3}\right)} x^{3} \log\left(-b x - a + 1\right) - 2 \, {\left(3 \, a^{5} b^{2} - 4 \, a^{3} b^{2} + a b^{2}\right)} x^{2} + {\left(a^{6} b - 2 \, a^{4} b + a^{2} b\right)} x + 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) - 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} + {\left(a^{6} b^{3} - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{3} - b^{3}\right)} x^{3} - a^{3}\right)} \log\left(b x + a\right) - 2 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(a^{9} - 3 \, a^{7} + 3 \, a^{5} - a^{3}\right)} x^{3}} - \int \frac{b^{2} x + a b}{3 \, {\left(b^{2} x^{5} + 2 \, a b x^{4} + {\left(a^{2} - 1\right)} x^{3} + {\left(b^{2} x^{5} + 2 \, a b x^{4} + {\left(a^{2} - 1\right)} x^{3}\right)} e^{\left(\frac{1}{2} \, \log\left(b x + a + 1\right) + \frac{1}{2} \, \log\left(-b x - a + 1\right)\right)}\right)}}\,{d x}"," ",0,"1/3*(6*a^4*b^3 - 3*a^2*b^3 + b^3)*log(x)/(a^9 - 3*a^7 + 3*a^5 - a^3) - 1/6*((a^6*b^3 - 3*a^5*b^3 + 3*a^4*b^3 - a^3*b^3)*x^3*log(b*x + a + 1) + (a^6*b^3 + 3*a^5*b^3 + 3*a^4*b^3 + a^3*b^3)*x^3*log(-b*x - a + 1) - 2*(3*a^5*b^2 - 4*a^3*b^2 + a*b^2)*x^2 + (a^6*b - 2*a^4*b + a^2*b)*x + 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a) - 2*(a^9 - 3*a^7 + 3*a^5 + (a^6*b^3 - 3*a^4*b^3 + 3*a^2*b^3 - b^3)*x^3 - a^3)*log(b*x + a) - 2*(a^9 - 3*a^7 + 3*a^5 - a^3)*log(b*x + a))/((a^9 - 3*a^7 + 3*a^5 - a^3)*x^3) - integrate(1/3*(b^2*x + a*b)/(b^2*x^5 + 2*a*b*x^4 + (a^2 - 1)*x^3 + (b^2*x^5 + 2*a*b*x^4 + (a^2 - 1)*x^3)*e^(1/2*log(b*x + a + 1) + 1/2*log(-b*x - a + 1))), x)","F",0
9,0,0,0,0.000000," ","integrate(x^2*arcsech(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - \int -\frac{2 \, {\left(6 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \log\left(b x + a\right)^{2} - {\left(b^{3} x^{5} + 2 \, a b^{2} x^{4} + {\left(a^{2} b - b\right)} x^{3} + 6 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \log\left(b x + a\right) + {\left(3 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) + {\left(2 \, b^{3} x^{5} + 4 \, a b^{2} x^{4} + {\left(2 \, a^{2} b - b\right)} x^{3} + 3 \, {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)\right)}}{3 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} + {\left(3 \, a^{2} b - b\right)} x - a\right)}}\,{d x}"," ",0,"1/3*x^3*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - integrate(-2/3*(6*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + 6*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*log(b*x + a)^2 - (b^3*x^5 + 2*a*b^2*x^4 + (a^2*b - b)*x^3 + 6*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*log(b*x + a) + (3*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*sqrt(b*x + a + 1)*log(b*x + a) + (2*b^3*x^5 + 4*a*b^2*x^4 + (2*a^2*b - b)*x^3 + 3*(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) + (3*a^2*b - b)*x - a), x)","F",0
10,0,0,0,0.000000," ","integrate(x*arcsech(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - \int -\frac{4 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + 4 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + {\left(a^{2} b - b\right)} x^{2} + 4 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right) + {\left(2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) + {\left(2 \, b^{3} x^{4} + 4 \, a b^{2} x^{3} + {\left(2 \, a^{2} b - b\right)} x^{2} + 2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} + {\left(3 \, a^{2} b - b\right)} x - a}\,{d x}"," ",0,"1/2*x^2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - integrate(-(4*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + 4*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a)^2 - (b^3*x^4 + 2*a*b^2*x^3 + (a^2*b - b)*x^2 + 4*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a) + (2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*sqrt(b*x + a + 1)*log(b*x + a) + (2*b^3*x^4 + 4*a*b^2*x^3 + (2*a^2*b - b)*x^2 + 2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) + (3*a^2*b - b)*x - a), x)","F",0
11,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^2,x, algorithm=""maxima"")","x \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - \int -\frac{2 \, {\left(2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2} - {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) + {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) + {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)\right)}}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} + {\left(3 \, a^{2} b - b\right)} x - a}\,{d x}"," ",0,"x*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - integrate(-2*(2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2 - (b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) + ((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) + (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) + (3*a^2*b - b)*x - a), x)","F",0
12,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arcsech(b*x + a)^2/x, x)","F",0
13,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^2/x^2,x, algorithm=""maxima"")","-\frac{\log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2}}{x} - \int -\frac{2 \, {\left(2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x - 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) - {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) - {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x - {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)\right)}}{b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2} + {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}\,{d x}"," ",0,"-log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2/x - integrate(-2*(2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2 + (b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x - 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) - ((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) - (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x - (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2 + (b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x)","F",0
14,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^2/x^3,x, algorithm=""maxima"")","-\frac{\log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2}}{2 \, x^{2}} - \int -\frac{4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + 4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x - 4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) - {\left(2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) - {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x - 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} b - b\right)} x^{4} + {\left(a^{3} - a\right)} x^{3} + {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} b - b\right)} x^{4} + {\left(a^{3} - a\right)} x^{3}\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}\,{d x}"," ",0,"-1/2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2/x^2 - integrate(-(4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + 4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2 + (b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x - 4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) - (2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) - (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x - 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^6 + 3*a*b^2*x^5 + (3*a^2*b - b)*x^4 + (a^3 - a)*x^3 + (b^3*x^6 + 3*a*b^2*x^5 + (3*a^2*b - b)*x^4 + (a^3 - a)*x^3)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x)","F",0
15,0,0,0,0.000000," ","integrate(x*arcsech(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{3} - \int \frac{16 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{3} + 16 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)^{3} + 3 \, {\left(b^{3} x^{4} + 2 \, a b^{2} x^{3} + {\left(a^{2} b - b\right)} x^{2} + 4 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right) + {\left(2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) + {\left(2 \, b^{3} x^{4} + 4 \, a b^{2} x^{3} + {\left(2 \, a^{2} b - b\right)} x^{2} + 2 \, {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - 24 \, {\left({\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{4} + 3 \, a b^{2} x^{3} + {\left(3 \, a^{2} b - b\right)} x^{2} + {\left(a^{3} - a\right)} x\right)} \log\left(b x + a\right)^{2}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} + {\left(3 \, a^{2} b - b\right)} x - a\right)}}\,{d x}"," ",0,"1/2*x^2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^3 - integrate(1/2*(16*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^3 + 16*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a)^3 + 3*(b^3*x^4 + 2*a*b^2*x^3 + (a^2*b - b)*x^2 + 4*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a) + (2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*sqrt(b*x + a + 1)*log(b*x + a) + (2*b^3*x^4 + 4*a*b^2*x^3 + (2*a^2*b - b)*x^2 + 2*(b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - 24*((b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + (b^3*x^4 + 3*a*b^2*x^3 + (3*a^2*b - b)*x^2 + (a^3 - a)*x)*log(b*x + a)^2)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) + (3*a^2*b - b)*x - a), x)","F",0
16,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^3,x, algorithm=""maxima"")","x \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{3} - \int \frac{8 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{3} + 8 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{3} + 3 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) + {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) + {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - 12 \, {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} + {\left(3 \, a^{2} b - b\right)} x - a}\,{d x}"," ",0,"x*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^3 - integrate((8*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^3 + 8*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^3 + 3*(b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) + ((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) + (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - 12*((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) + (3*a^2*b - b)*x - a), x)","F",0
17,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(b x + a\right)^{3}}{x}\,{d x}"," ",0,"integrate(arcsech(b*x + a)^3/x, x)","F",0
18,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^3/x^2,x, algorithm=""maxima"")","-\frac{\log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{3}}{x} - \int \frac{8 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{3} + 8 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{3} - 3 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x - 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) - {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) - {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x - {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - 12 \, {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2} + {\left(b^{3} x^{5} + 3 \, a b^{2} x^{4} + {\left(3 \, a^{2} b - b\right)} x^{3} + {\left(a^{3} - a\right)} x^{2}\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1}}\,{d x}"," ",0,"-log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^3/x - integrate((8*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^3 + 8*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^3 - 3*(b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x - 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) - ((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) - (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x - (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - 12*((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2 + (b^3*x^5 + 3*a*b^2*x^4 + (3*a^2*b - b)*x^3 + (a^3 - a)*x^2)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x)","F",0
19,0,0,0,0.000000," ","integrate(arcsech(b*x+a)^3/x^3,x, algorithm=""maxima"")","-\frac{\log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{3}}{2 \, x^{2}} - \int \frac{16 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{3} + 16 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{3} - 3 \, {\left(b^{3} x^{3} + 2 \, a b^{2} x^{2} + {\left(a^{2} b - b\right)} x - 4 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right) - {\left(2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \log\left(b x + a\right) - {\left(2 \, b^{3} x^{3} + 4 \, a b^{2} x^{2} + {\left(2 \, a^{2} b - b\right)} x - 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)\right)} \sqrt{b x + a + 1}\right)} \sqrt{-b x - a + 1}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)^{2} - 24 \, {\left({\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} \log\left(b x + a\right)^{2} + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + a^{3} + {\left(3 \, a^{2} b - b\right)} x - a\right)} \log\left(b x + a\right)^{2}\right)} \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right)}{2 \, {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} b - b\right)} x^{4} + {\left(a^{3} - a\right)} x^{3} + {\left(b^{3} x^{6} + 3 \, a b^{2} x^{5} + {\left(3 \, a^{2} b - b\right)} x^{4} + {\left(a^{3} - a\right)} x^{3}\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1}\right)}}\,{d x}"," ",0,"-1/2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^3/x^2 - integrate(1/2*(16*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^3 + 16*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^3 - 3*(b^3*x^3 + 2*a*b^2*x^2 + (a^2*b - b)*x - 4*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a) - (2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*log(b*x + a) - (2*b^3*x^3 + 4*a*b^2*x^2 + (2*a^2*b - b)*x - 2*(b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a))*sqrt(b*x + a + 1))*sqrt(-b*x - a + 1))*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)^2 - 24*((b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*log(b*x + a)^2 + (b^3*x^3 + 3*a*b^2*x^2 + a^3 + (3*a^2*b - b)*x - a)*log(b*x + a)^2)*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a))/(b^3*x^6 + 3*a*b^2*x^5 + (3*a^2*b - b)*x^4 + (a^3 - a)*x^3 + (b^3*x^6 + 3*a*b^2*x^5 + (3*a^2*b - b)*x^4 + (a^3 - a)*x^3)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)), x)","F",0
20,1,58,0,0.324291," ","integrate(x^3*arcsech(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{28} \, x^{\frac{7}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{7}{2}} - \frac{3}{20} \, x^{\frac{5}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{5}{2}} + \frac{1}{4} \, x^{4} \operatorname{arsech}\left(\sqrt{x}\right) + \frac{1}{4} \, x^{\frac{3}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{3}{2}} - \frac{1}{4} \, \sqrt{x} \sqrt{\frac{1}{x} - 1}"," ",0,"1/28*x^(7/2)*(1/x - 1)^(7/2) - 3/20*x^(5/2)*(1/x - 1)^(5/2) + 1/4*x^4*arcsech(sqrt(x)) + 1/4*x^(3/2)*(1/x - 1)^(3/2) - 1/4*sqrt(x)*sqrt(1/x - 1)","A",0
21,1,46,0,0.338257," ","integrate(x^2*arcsech(x^(1/2)),x, algorithm=""maxima"")","-\frac{1}{15} \, x^{\frac{5}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{5}{2}} + \frac{1}{3} \, x^{3} \operatorname{arsech}\left(\sqrt{x}\right) + \frac{2}{9} \, x^{\frac{3}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{3}{2}} - \frac{1}{3} \, \sqrt{x} \sqrt{\frac{1}{x} - 1}"," ",0,"-1/15*x^(5/2)*(1/x - 1)^(5/2) + 1/3*x^3*arcsech(sqrt(x)) + 2/9*x^(3/2)*(1/x - 1)^(3/2) - 1/3*sqrt(x)*sqrt(1/x - 1)","A",0
22,1,34,0,0.376068," ","integrate(x*arcsech(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{6} \, x^{\frac{3}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{3}{2}} + \frac{1}{2} \, x^{2} \operatorname{arsech}\left(\sqrt{x}\right) - \frac{1}{2} \, \sqrt{x} \sqrt{\frac{1}{x} - 1}"," ",0,"1/6*x^(3/2)*(1/x - 1)^(3/2) + 1/2*x^2*arcsech(sqrt(x)) - 1/2*sqrt(x)*sqrt(1/x - 1)","A",0
23,1,19,0,0.387998," ","integrate(arcsech(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arsech}\left(\sqrt{x}\right) - \sqrt{x} \sqrt{\frac{1}{x} - 1}"," ",0,"x*arcsech(sqrt(x)) - sqrt(x)*sqrt(1/x - 1)","A",0
24,0,0,0,0.000000," ","integrate(arcsech(x^(1/2))/x,x, algorithm=""maxima"")","-\frac{1}{4} \, \log\left(x\right)^{2} + \log\left(x\right) \log\left(\sqrt{\sqrt{x} + 1} \sqrt{-\sqrt{x} + 1} + 1\right) - \log\left(\sqrt{x} + 1\right) \log\left(\sqrt{x}\right) - \log\left(\sqrt{x}\right) \log\left(-\sqrt{x} + 1\right) - {\rm Li}_2\left(-\sqrt{x}\right) - {\rm Li}_2\left(\sqrt{x}\right) + \int \frac{\log\left(x\right)}{2 \, {\left({\left(x - 1\right)} e^{\left(\frac{1}{2} \, \log\left(\sqrt{x} + 1\right) + \frac{1}{2} \, \log\left(-\sqrt{x} + 1\right)\right)} + x - 1\right)}}\,{d x}"," ",0,"-1/4*log(x)^2 + log(x)*log(sqrt(sqrt(x) + 1)*sqrt(-sqrt(x) + 1) + 1) - log(sqrt(x) + 1)*log(sqrt(x)) - log(sqrt(x))*log(-sqrt(x) + 1) - dilog(-sqrt(x)) - dilog(sqrt(x)) + integrate(1/2*log(x)/((x - 1)*e^(1/2*log(sqrt(x) + 1) + 1/2*log(-sqrt(x) + 1)) + x - 1), x)","F",0
25,1,65,0,0.300268," ","integrate(arcsech(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\sqrt{x} \sqrt{\frac{1}{x} - 1}}{2 \, {\left(x {\left(\frac{1}{x} - 1\right)} - 1\right)}} - \frac{\operatorname{arsech}\left(\sqrt{x}\right)}{x} + \frac{1}{4} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} + 1\right) - \frac{1}{4} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} - 1\right)"," ",0,"-1/2*sqrt(x)*sqrt(1/x - 1)/(x*(1/x - 1) - 1) - arcsech(sqrt(x))/x + 1/4*log(sqrt(x)*sqrt(1/x - 1) + 1) - 1/4*log(sqrt(x)*sqrt(1/x - 1) - 1)","A",0
26,1,92,0,0.342233," ","integrate(arcsech(x^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{3 \, x^{\frac{3}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{3}{2}} - 5 \, \sqrt{x} \sqrt{\frac{1}{x} - 1}}{16 \, {\left(x^{2} {\left(\frac{1}{x} - 1\right)}^{2} - 2 \, x {\left(\frac{1}{x} - 1\right)} + 1\right)}} - \frac{\operatorname{arsech}\left(\sqrt{x}\right)}{2 \, x^{2}} + \frac{3}{32} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} + 1\right) - \frac{3}{32} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} - 1\right)"," ",0,"-1/16*(3*x^(3/2)*(1/x - 1)^(3/2) - 5*sqrt(x)*sqrt(1/x - 1))/(x^2*(1/x - 1)^2 - 2*x*(1/x - 1) + 1) - 1/2*arcsech(sqrt(x))/x^2 + 3/32*log(sqrt(x)*sqrt(1/x - 1) + 1) - 3/32*log(sqrt(x)*sqrt(1/x - 1) - 1)","A",0
27,1,116,0,0.315148," ","integrate(arcsech(x^(1/2))/x^4,x, algorithm=""maxima"")","-\frac{15 \, x^{\frac{5}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{5}{2}} - 40 \, x^{\frac{3}{2}} {\left(\frac{1}{x} - 1\right)}^{\frac{3}{2}} + 33 \, \sqrt{x} \sqrt{\frac{1}{x} - 1}}{144 \, {\left(x^{3} {\left(\frac{1}{x} - 1\right)}^{3} - 3 \, x^{2} {\left(\frac{1}{x} - 1\right)}^{2} + 3 \, x {\left(\frac{1}{x} - 1\right)} - 1\right)}} - \frac{\operatorname{arsech}\left(\sqrt{x}\right)}{3 \, x^{3}} + \frac{5}{96} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} + 1\right) - \frac{5}{96} \, \log\left(\sqrt{x} \sqrt{\frac{1}{x} - 1} - 1\right)"," ",0,"-1/144*(15*x^(5/2)*(1/x - 1)^(5/2) - 40*x^(3/2)*(1/x - 1)^(3/2) + 33*sqrt(x)*sqrt(1/x - 1))/(x^3*(1/x - 1)^3 - 3*x^2*(1/x - 1)^2 + 3*x*(1/x - 1) - 1) - 1/3*arcsech(sqrt(x))/x^3 + 5/96*log(sqrt(x)*sqrt(1/x - 1) + 1) - 5/96*log(sqrt(x)*sqrt(1/x - 1) - 1)","A",0
28,1,16,0,0.317630," ","integrate(arcsech(1/x),x, algorithm=""maxima"")","x \operatorname{arsech}\left(\frac{1}{x}\right) - \sqrt{x^{2} - 1}"," ",0,"x*arcsech(1/x) - sqrt(x^2 - 1)","A",0
29,0,0,0,0.000000," ","integrate(arcsech(a*x^n)/x,x, algorithm=""maxima"")","a^{2} n \int \frac{x^{2 \, n} \log\left(x\right)}{a^{2} x x^{2 \, n} + {\left(a^{2} x x^{2 \, n} - x\right)} \sqrt{a x^{n} + 1} \sqrt{-a x^{n} + 1} - x}\,{d x} + n \int \frac{\log\left(x\right)}{2 \, {\left(a x x^{n} + x\right)}}\,{d x} - n \int \frac{\log\left(x\right)}{2 \, {\left(a x x^{n} - x\right)}}\,{d x} + \log\left(\sqrt{a x^{n} + 1} \sqrt{-a x^{n} + 1} + 1\right) \log\left(x\right) - \log\left(a\right) \log\left(x\right) - \log\left(x\right) \log\left(x^{n}\right)"," ",0,"a^2*n*integrate(x^(2*n)*log(x)/(a^2*x*x^(2*n) + (a^2*x*x^(2*n) - x)*sqrt(a*x^n + 1)*sqrt(-a*x^n + 1) - x), x) + n*integrate(1/2*log(x)/(a*x*x^n + x), x) - n*integrate(1/2*log(x)/(a*x*x^n - x), x) + log(sqrt(a*x^n + 1)*sqrt(-a*x^n + 1) + 1)*log(x) - log(a)*log(x) - log(x)*log(x^n)","F",0
30,0,0,0,0.000000," ","integrate(arcsech(a*x^5)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arsech}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arcsech(a*x^5)/x, x)","F",0
31,0,0,0,0.000000," ","integrate(arcsech(c*exp(b*x+a)),x, algorithm=""maxima"")","b c^{2} \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} e^{\left(2 \, b x + 2 \, a\right)} + {\left(c^{2} e^{\left(2 \, b x + 2 \, a\right)} - 1\right)} e^{\left(\frac{1}{2} \, \log\left(c e^{\left(b x + a\right)} + 1\right) + \frac{1}{2} \, \log\left(-c e^{\left(b x + a\right)} + 1\right)\right)} - 1}\,{d x} - \frac{1}{2} \, b x^{2} - {\left(a + \log\left(c\right)\right)} x + x \log\left(\sqrt{c e^{\left(b x + a\right)} + 1} \sqrt{-c e^{\left(b x + a\right)} + 1} + 1\right) - \frac{b x \log\left(c e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-c e^{\left(b x + a\right)}\right)}{2 \, b} - \frac{b x \log\left(-c e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(c e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"b*c^2*integrate(x*e^(2*b*x + 2*a)/(c^2*e^(2*b*x + 2*a) + (c^2*e^(2*b*x + 2*a) - 1)*e^(1/2*log(c*e^(b*x + a) + 1) + 1/2*log(-c*e^(b*x + a) + 1)) - 1), x) - 1/2*b*x^2 - (a + log(c))*x + x*log(sqrt(c*e^(b*x + a) + 1)*sqrt(-c*e^(b*x + a) + 1) + 1) - 1/2*(b*x*log(c*e^(b*x + a) + 1) + dilog(-c*e^(b*x + a)))/b - 1/2*(b*x*log(-c*e^(b*x + a) + 1) + dilog(c*e^(b*x + a)))/b","F",0
32,1,47,0,0.379190," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^4,x, algorithm=""maxima"")","\frac{x^{4}}{4 \, a} + \frac{{\left(3 \, a^{4} x^{4} - a^{2} x^{2} - 2\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{15 \, a^{5}}"," ",0,"1/4*x^4/a + 1/15*(3*a^4*x^4 - a^2*x^2 - 2)*sqrt(a*x + 1)*sqrt(-a*x + 1)/a^5","A",0
33,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^3,x, algorithm=""maxima"")","\frac{x^{3}}{3 \, a} + \frac{-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{2}} + \frac{\arcsin\left(a x\right)}{8 \, a^{3}}}{a}"," ",0,"1/3*x^3/a + integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)*x^2, x)/a","F",0
34,1,38,0,0.401410," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^2,x, algorithm=""maxima"")","\frac{x^{2}}{2 \, a} + \frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, a^{3}}"," ",0,"1/2*x^2/a + 1/3*(a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1)/a^3","A",0
35,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x,x, algorithm=""maxima"")","\frac{x}{a} + \frac{\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} x + \frac{\arcsin\left(a x\right)}{2 \, a}}{a}"," ",0,"x/a + integrate(sqrt(a*x + 1)*sqrt(-a*x + 1), x)/a","F",0
36,0,0,0,0.000000," ","integrate(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\,{d x}"," ",0,"integrate(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x), x)","F",0
37,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x, algorithm=""maxima"")","\frac{-a \arcsin\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1}}{x}}{a} - \frac{1}{a x}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^2, x)/a - 1/(a*x)","F",0
38,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\frac{1}{2} \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{2} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{2}}}{a} - \frac{1}{2 \, a x^{2}}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^3, x)/a - 1/2/(a*x^2)","F",0
39,1,43,0,0.368178," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x, algorithm=""maxima"")","\frac{{\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, a x^{4}} - \frac{1}{3 \, a x^{3}}"," ",0,"1/3*(a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a*x^4) - 1/3/(a*x^3)","A",0
40,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x, algorithm=""maxima"")","\frac{\frac{1}{8} \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} a^{4} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{8 \, x^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{4 \, x^{4}}}{a} - \frac{1}{4 \, a x^{4}}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^5, x)/a - 1/4/(a*x^4)","F",0
41,1,51,0,0.333490," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x, algorithm=""maxima"")","\frac{{\left(2 \, a^{4} x^{5} + a^{2} x^{3} - 3 \, x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{15 \, a x^{6}} - \frac{1}{5 \, a x^{5}}"," ",0,"1/15*(2*a^4*x^5 + a^2*x^3 - 3*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a*x^6) - 1/5/(a*x^5)","A",0
42,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x, algorithm=""maxima"")","\frac{\frac{1}{16} \, a^{6} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{16} \, \sqrt{-a^{2} x^{2} + 1} a^{6} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4}}{16 \, x^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{8 \, x^{4}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{6 \, x^{6}}}{a} - \frac{1}{6 \, a x^{6}}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^7, x)/a - 1/6/(a*x^6)","F",0
43,1,60,0,0.341090," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x, algorithm=""maxima"")","\frac{{\left(8 \, a^{6} x^{7} + 4 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - 15 \, x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{105 \, a x^{8}} - \frac{1}{7 \, a x^{7}}"," ",0,"1/105*(8*a^6*x^7 + 4*a^4*x^5 + 3*a^2*x^3 - 15*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a*x^8) - 1/7/(a*x^7)","A",0
44,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^8,x, algorithm=""maxima"")","\frac{\frac{5}{128} \, a^{8} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{5}{128} \, \sqrt{-a^{2} x^{2} + 1} a^{8} - \frac{5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{6}}{128 \, x^{2}} - \frac{5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4}}{64 \, x^{4}} - \frac{5 \, {\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{48 \, x^{6}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{8 \, x^{8}}}{a} - \frac{1}{8 \, a x^{8}}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^9, x)/a - 1/8/(a*x^8)","F",0
45,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^7,x, algorithm=""maxima"")","\frac{x^{6}}{6 \, a} + \frac{-\frac{{\left(-a^{2} x^{4} + 1\right)}^{\frac{3}{2}} x^{2}}{8 \, a^{2}} + \frac{\sqrt{-a^{2} x^{4} + 1} x^{2}}{16 \, a^{2}} + \frac{\arcsin\left(a x^{2}\right)}{16 \, a^{3}}}{a}"," ",0,"1/6*x^6/a + integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)*x^5, x)/a","F",0
46,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^6,x, algorithm=""maxima"")","\frac{x^{5}}{5 \, a} + \frac{\int \sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1} x^{4}\,{d x}}{a}"," ",0,"1/5*x^5/a + integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)*x^4, x)/a","F",0
47,1,42,0,0.399525," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^5,x, algorithm=""maxima"")","\frac{x^{4}}{4 \, a} + \frac{{\left(a^{2} x^{4} - 1\right)} \sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1}}{6 \, a^{3}}"," ",0,"1/4*x^4/a + 1/6*(a^2*x^4 - 1)*sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/a^3","A",0
48,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^4,x, algorithm=""maxima"")","\frac{x^{3}}{3 \, a} + \frac{\int \sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1} x^{2}\,{d x}}{a}"," ",0,"1/3*x^3/a + integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)*x^2, x)/a","F",0
49,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^3,x, algorithm=""maxima"")","\frac{x^{2}}{2 \, a} + \frac{\frac{1}{4} \, \sqrt{-a^{2} x^{4} + 1} x^{2} + \frac{\arcsin\left(a x^{2}\right)}{4 \, a}}{a}"," ",0,"1/2*x^2/a + integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)*x, x)/a","F",0
50,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^2,x, algorithm=""maxima"")","\frac{x}{a} + \frac{\int \sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1}\,{d x}}{a}"," ",0,"x/a + integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1), x)/a","F",0
51,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x,x, algorithm=""maxima"")","\frac{\frac{1}{2} \, \sqrt{-a^{2} x^{4} + 1} - \frac{1}{2} \, \log\left(\frac{2 \, \sqrt{-a^{2} x^{4} + 1}}{x^{2}} + \frac{2}{x^{2}}\right)}{a} + \frac{\log\left(x\right)}{a}"," ",0,"integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/x, x)/a + log(x)/a","F",0
52,0,0,0,0.000000," ","integrate(1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2),x, algorithm=""maxima"")","\frac{\int \frac{\sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1}}{x^{2}}\,{d x}}{a} - \frac{1}{a x}"," ",0,"integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/x^2, x)/a - 1/(a*x)","F",0
53,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x,x, algorithm=""maxima"")","\frac{-\frac{1}{2} \, a \arcsin\left(a x^{2}\right) - \frac{\sqrt{-a^{2} x^{4} + 1}}{2 \, x^{2}}}{a} - \frac{1}{2 \, a x^{2}}"," ",0,"integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/x^3, x)/a - 1/2/(a*x^2)","F",0
54,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\int \frac{\sqrt{a x^{2} + 1} \sqrt{-a x^{2} + 1}}{x^{4}}\,{d x}}{a} - \frac{1}{3 \, a x^{3}}"," ",0,"integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/x^4, x)/a - 1/3/(a*x^3)","F",0
55,0,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))/x^3,x, algorithm=""maxima"")","\frac{\frac{1}{4} \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{4} + 1}}{x^{2}} + \frac{2}{x^{2}}\right) - \frac{1}{4} \, \sqrt{-a^{2} x^{4} + 1} a^{2} - \frac{{\left(-a^{2} x^{4} + 1\right)}^{\frac{3}{2}}}{4 \, x^{4}}}{a} - \frac{1}{4 \, a x^{4}}"," ",0,"integrate(sqrt(a*x^2 + 1)*sqrt(-a*x^2 + 1)/x^5, x)/a - 1/4/(a*x^4)","F",0
56,-2,0,0,0.000000," ","integrate((1/a/x^3+(1/a/x^3-1)^(1/2)*(1/a/x^3+1)^(1/2))*x^m,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(m-3>0)', see `assume?` for more details)Is m-3 equal to -1?","F(-2)",0
57,-2,0,0,0.000000," ","integrate((1/a/x^2+(1/a/x^2-1)^(1/2)*(1/a/x^2+1)^(1/2))*x^m,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(m-2>0)', see `assume?` for more details)Is m-2 equal to -1?","F(-2)",0
58,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))*x^m,x, algorithm=""maxima"")","\frac{\int \frac{\sqrt{a x + 1} \sqrt{-a x + 1} x^{m}}{x}\,{d x}}{a} + \frac{x^{m}}{a m}"," ",0,"integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)*x^m/x, x)/a + x^m/(a*m)","F",0
59,0,0,0,0.000000," ","integrate((x/a+(-1+x/a)^(1/2)*(1+x/a)^(1/2))*x^m,x, algorithm=""maxima"")","\frac{x^{2} x^{m}}{a {\left(m + 2\right)}} + \frac{\int \sqrt{a + x} \sqrt{-a + x} x^{m}\,{d x}}{a}"," ",0,"x^2*x^m/(a*(m + 2)) + integrate(sqrt(a + x)*sqrt(-a + x)*x^m, x)/a","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(m-p>0)', see `assume?` for more details)Is m-p equal to -1?","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(1-p>0)', see `assume?` for more details)Is 1-p equal to -1?","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(-p>0)', see `assume?` for more details)Is -p equal to -1?","F(-2)",0
63,0,0,0,0.000000," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x,x, algorithm=""maxima"")","\frac{\int \frac{\sqrt{a x^{p} + 1} \sqrt{-a x^{p} + 1}}{x x^{p}}\,{d x}}{a} - \frac{1}{a p x^{p}}"," ",0,"integrate(sqrt(a*x^p + 1)*sqrt(-a*x^p + 1)/(x*x^p), x)/a - 1/(a*p*x^p)","F",0
64,0,0,0,0.000000," ","integrate((1/a/(x^p)+(1/a/(x^p)-1)^(1/2)*(1/a/(x^p)+1)^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\int \frac{\sqrt{a x^{p} + 1} \sqrt{-a x^{p} + 1}}{x^{2} x^{p}}\,{d x}}{a} - \frac{x^{-p - 1}}{a {\left(p + 1\right)}}"," ",0,"integrate(sqrt(a*x^p + 1)*sqrt(-a*x^p + 1)/(x^2*x^p), x)/a - x^(-p - 1)/(a*(p + 1))","F",0
65,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^4,x, algorithm=""maxima"")","\frac{2 \, x^{3}}{3 \, a^{2}} + \frac{2 \, {\left(-\frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} x}{4 \, a^{2}} + \frac{\sqrt{-a^{2} x^{2} + 1} x}{8 \, a^{2}} + \frac{\arcsin\left(a x\right)}{8 \, a^{3}}\right)}}{a^{2}} - \int x^{4}\,{d x}"," ",0,"2/3*x^3/a^2 + 2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)*x^2, x)/a^2 - integrate(x^4, x)","F",0
66,1,42,0,0.414235," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, x^{4} + \frac{x^{2}}{a^{2}} + \frac{2 \, {\left(a^{2} x^{2} - 1\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, a^{4}}"," ",0,"-1/4*x^4 + x^2/a^2 + 2/3*(a^2*x^2 - 1)*sqrt(a*x + 1)*sqrt(-a*x + 1)/a^4","A",0
67,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x^2,x, algorithm=""maxima"")","\frac{2 \, x}{a^{2}} + \frac{2 \, {\left(\frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} x + \frac{\arcsin\left(a x\right)}{2 \, a}\right)}}{a^{2}} - \int x^{2}\,{d x}"," ",0,"2*x/a^2 + 2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1), x)/a^2 - integrate(x^2, x)","F",0
68,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2*x,x, algorithm=""maxima"")","\int x {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}^{2}\,{d x}"," ",0,"integrate(x*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))^2, x)","F",0
69,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2,x, algorithm=""maxima"")","-x + \frac{2 \, {\left(-a \arcsin\left(a x\right) - \frac{\sqrt{-a^{2} x^{2} + 1}}{x}\right)}}{a^{2}} + \frac{-\frac{1}{x}}{a^{2}} - \frac{1}{a^{2} x}"," ",0,"-x + 2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^2, x)/a^2 + integrate(x^(-2), x)/a^2 - 1/(a^2*x)","F",0
70,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{1}{2} \, a^{2} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{2} \, \sqrt{-a^{2} x^{2} + 1} a^{2} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{2 \, x^{2}}\right)}}{a^{2}} - \frac{1}{a^{2} x^{2}} - \int \frac{1}{x}\,{d x}"," ",0,"2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^3, x)/a^2 - 1/(a^2*x^2) - integrate(1/x, x)","F",0
71,1,46,0,0.347654," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^2,x, algorithm=""maxima"")","\frac{1}{x} + \frac{2 \, {\left(a^{2} x^{3} - x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{3 \, a^{2} x^{4}} - \frac{2}{3 \, a^{2} x^{3}}"," ",0,"1/x + 2/3*(a^2*x^3 - x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^2*x^4) - 2/3/(a^2*x^3)","A",0
72,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{1}{8} \, a^{4} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{8} \, \sqrt{-a^{2} x^{2} + 1} a^{4} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{8 \, x^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{4 \, x^{4}}\right)}}{a^{2}} - \frac{1}{2 \, a^{2} x^{4}} - \int \frac{1}{x^{3}}\,{d x}"," ",0,"2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^5, x)/a^2 - 1/2/(a^2*x^4) - integrate(x^(-3), x)","F",0
73,1,56,0,0.396856," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3 \, x^{3}} + \frac{2 \, {\left(2 \, a^{4} x^{5} + a^{2} x^{3} - 3 \, x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{15 \, a^{2} x^{6}} - \frac{2}{5 \, a^{2} x^{5}}"," ",0,"1/3/x^3 + 2/15*(2*a^4*x^5 + a^2*x^3 - 3*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^2*x^6) - 2/5/(a^2*x^5)","A",0
74,0,0,0,0.000000," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^5,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{1}{16} \, a^{6} \log\left(\frac{2 \, \sqrt{-a^{2} x^{2} + 1}}{{\left| x \right|}} + \frac{2}{{\left| x \right|}}\right) - \frac{1}{16} \, \sqrt{-a^{2} x^{2} + 1} a^{6} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{4}}{16 \, x^{2}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}} a^{2}}{8 \, x^{4}} - \frac{{\left(-a^{2} x^{2} + 1\right)}^{\frac{3}{2}}}{6 \, x^{6}}\right)}}{a^{2}} - \frac{1}{3 \, a^{2} x^{6}} - \int \frac{1}{x^{5}}\,{d x}"," ",0,"2*integrate(sqrt(a*x + 1)*sqrt(-a*x + 1)/x^7, x)/a^2 - 1/3/(a^2*x^6) - integrate(x^(-5), x)","F",0
75,1,65,0,0.396655," ","integrate((1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))^2/x^6,x, algorithm=""maxima"")","\frac{1}{5 \, x^{5}} + \frac{2 \, {\left(8 \, a^{6} x^{7} + 4 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - 15 \, x\right)} \sqrt{a x + 1} \sqrt{-a x + 1}}{105 \, a^{2} x^{8}} - \frac{2}{7 \, a^{2} x^{7}}"," ",0,"1/5/x^5 + 2/105*(8*a^6*x^7 + 4*a^4*x^5 + 3*a^2*x^3 - 15*x)*sqrt(a*x + 1)*sqrt(-a*x + 1)/(a^2*x^8) - 2/7/(a^2*x^7)","A",0
76,0,0,0,0.000000," ","integrate(x^4/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""maxima"")","\int \frac{x^{4}}{\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}}\,{d x}"," ",0,"integrate(x^4/(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)), x)","F",0
77,0,0,0,0.000000," ","integrate(x^3/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}}\,{d x}"," ",0,"integrate(x^3/(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)), x)","F",0
78,0,0,0,0.000000," ","integrate(x^2/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}}\,{d x}"," ",0,"integrate(x^2/(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)), x)","F",0
79,0,0,0,0.000000," ","integrate(x/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}}\,{d x}"," ",0,"integrate(x/(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2)),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}}\,{d x}"," ",0,"integrate(1/(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)), x)","F",0
81,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x,x, algorithm=""maxima"")","\int \frac{1}{x {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
82,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^2,x, algorithm=""maxima"")","\int \frac{1}{x^{2} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^2*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
83,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^3,x, algorithm=""maxima"")","\int \frac{1}{x^{3} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^3*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^4,x, algorithm=""maxima"")","\int \frac{1}{x^{4} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^4*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
85,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^5,x, algorithm=""maxima"")","\int \frac{1}{x^{5} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^5*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
86,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^6,x, algorithm=""maxima"")","\int \frac{1}{x^{6} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^6*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(1/a/x+(1/a/x-1)^(1/2)*(1+1/a/x)^(1/2))/x^7,x, algorithm=""maxima"")","\int \frac{1}{x^{7} {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)}}\,{d x}"," ",0,"integrate(1/(x^7*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x))), x)","F",0
88,0,0,0,0.000000," ","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=""maxima"")","-d^{m} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} x^{m}}{c^{3} x^{3} - c x}\,{d x} - d^{m} \int \frac{x^{m}}{2 \, {\left(c x + 1\right)}}\,{d x} - d^{m} \int \frac{x^{m}}{2 \, {\left(c x - 1\right)}}\,{d x} + \frac{d^{m} x^{m}}{c m}"," ",0,"-d^m*integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^m/(c^3*x^3 - c*x), x) - d^m*integrate(1/2*x^m/(c*x + 1), x) - d^m*integrate(1/2*x^m/(c*x - 1), x) + d^m*x^m/(c*m)","F",0
89,0,0,0,0.000000," ","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=""maxima"")","-\frac{\frac{1}{2} \, x^{2}}{c^{3}} - \frac{\log\left(c x + 1\right)}{2 \, c^{5}} - \frac{\log\left(c x - 1\right)}{2 \, c^{5}} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} x^{3}}{c^{3} x^{2} - c}\,{d x}"," ",0,"-integrate(x, x)/c^3 - 1/2*log(c*x + 1)/c^5 - 1/2*log(c*x - 1)/c^5 - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^3/(c^3*x^2 - c), x)","F",0
90,0,0,0,0.000000," ","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=""maxima"")","-\frac{x}{c^{3}} + \frac{\log\left(c x + 1\right)}{2 \, c^{4}} - \frac{\log\left(c x - 1\right)}{2 \, c^{4}} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} x^{2}}{c^{3} x^{2} - c}\,{d x}"," ",0,"-x/c^3 + 1/2*log(c*x + 1)/c^4 - 1/2*log(c*x - 1)/c^4 - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x^2/(c^3*x^2 - c), x)","F",0
91,0,0,0,0.000000," ","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=""maxima"")","-\frac{\log\left(c x + 1\right)}{2 \, c^{3}} - \frac{\log\left(c x - 1\right)}{2 \, c^{3}} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} x}{c^{3} x^{2} - c}\,{d x}"," ",0,"-1/2*log(c*x + 1)/c^3 - 1/2*log(c*x - 1)/c^3 - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)*x/(c^3*x^2 - c), x)","F",0
92,0,0,0,0.000000," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))*x/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{\log\left(c x + 1\right)}{2 \, c^{2}} - \frac{\log\left(c x - 1\right)}{2 \, c^{2}} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} x^{2} - c}\,{d x}"," ",0,"1/2*log(c*x + 1)/c^2 - 1/2*log(c*x - 1)/c^2 - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*x^2 - c), x)","F",0
93,0,0,0,0.000000," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{\log\left(x\right)}{c} - \frac{\log\left(c x + 1\right)}{2 \, c} - \frac{\log\left(c x - 1\right)}{2 \, c} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} x^{3} - c x}\,{d x}"," ",0,"integrate(1/x, x)/c - 1/2*log(c*x + 1)/c - 1/2*log(c*x - 1)/c - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*x^3 - c*x), x)","F",0
94,0,0,0,0.000000," ","integrate((1/c/x+(-1+1/c/x)^(1/2)*(1+1/c/x)^(1/2))/x/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{-\frac{1}{x}}{c} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} x^{4} - c x^{2}}\,{d x} + \frac{1}{2} \, \log\left(c x + 1\right) - \frac{1}{2} \, \log\left(c x - 1\right)"," ",0,"integrate(x^(-2), x)/c - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*x^4 - c*x^2), x) + 1/2*log(c*x + 1) - 1/2*log(c*x - 1)","F",0
95,0,0,0,0.000000," ","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=""maxima"")","c \int \frac{1}{x}\,{d x} - \frac{1}{2} \, c \log\left(c x + 1\right) - \frac{1}{2} \, c \log\left(c x - 1\right) + \frac{-\frac{1}{2 \, x^{2}}}{c} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} x^{5} - c x^{3}}\,{d x}"," ",0,"c*integrate(1/x, x) - 1/2*c*log(c*x + 1) - 1/2*c*log(c*x - 1) + integrate(x^(-3), x)/c - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*x^5 - c*x^3), x)","F",0
96,0,0,0,0.000000," ","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=""maxima"")","\frac{1}{2} \, c^{2} \log\left(c x + 1\right) - \frac{1}{2} \, c^{2} \log\left(c x - 1\right) + c \int \frac{1}{x^{2}}\,{d x} + \frac{-\frac{1}{3 \, x^{3}}}{c} - \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1}}{c^{3} x^{6} - c x^{4}}\,{d x}"," ",0,"1/2*c^2*log(c*x + 1) - 1/2*c^2*log(c*x - 1) + c*integrate(x^(-2), x) + integrate(x^(-4), x)/c - integrate(sqrt(c*x + 1)*sqrt(-c*x + 1)/(c^3*x^6 - c*x^4), x)","F",0
97,0,0,0,0.000000," ","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=""maxima"")","-\int \frac{{\left(a x {\left(\sqrt{\frac{1}{a x} + 1} \sqrt{\frac{1}{a x} - 1} + \frac{1}{a x}\right)} - 1\right)} x}{a^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((a*x*(sqrt(1/(a*x) + 1)*sqrt(1/(a*x) - 1) + 1/(a*x)) - 1)*x/(a^2*x^2 - 1), x)","F",0
98,0,0,0,0.000000," ","integrate(arcsech(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\frac{2 \, \log\left(\sqrt{b x + a + 1} \sqrt{-b x - a + 1} b x + \sqrt{b x + a + 1} \sqrt{-b x - a + 1} a + b x + a\right) \log\left(b x + a\right) - 3 \, \log\left(b x + a\right)^{2}}{2 \, d} - \frac{\log\left(b x + a + 1\right) \log\left(b x + a\right) + {\rm Li}_2\left(-b x - a\right)}{2 \, d} - \frac{\log\left(b x + a\right) \log\left(-b x - a + 1\right) + {\rm Li}_2\left(b x + a\right)}{2 \, d} + \int \frac{{\left(b^{2} x + a b\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + 2 \, a b d x + a^{2} d + {\left(b^{2} d x^{2} + 2 \, a b d x + a^{2} d - d\right)} \sqrt{b x + a + 1} \sqrt{-b x - a + 1} - d}\,{d x}"," ",0,"1/2*(2*log(sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*b*x + sqrt(b*x + a + 1)*sqrt(-b*x - a + 1)*a + b*x + a)*log(b*x + a) - 3*log(b*x + a)^2)/d - 1/2*(log(b*x + a + 1)*log(b*x + a) + dilog(-b*x - a))/d - 1/2*(log(b*x + a)*log(-b*x - a + 1) + dilog(b*x + a))/d + integrate((b^2*x + a*b)*log(b*x + a)/(b^2*d*x^2 + 2*a*b*d*x + a^2*d + (b^2*d*x^2 + 2*a*b*d*x + a^2*d - d)*sqrt(b*x + a + 1)*sqrt(-b*x - a + 1) - d), x)","F",0
99,1,38,0,0.363209," ","integrate(x^3*arcsech(b*x^4+a),x, algorithm=""maxima"")","\frac{{\left(b x^{4} + a\right)} \operatorname{arsech}\left(b x^{4} + a\right) - \arctan\left(\sqrt{\frac{1}{{\left(b x^{4} + a\right)}^{2}} - 1}\right)}{4 \, b}"," ",0,"1/4*((b*x^4 + a)*arcsech(b*x^4 + a) - arctan(sqrt(1/(b*x^4 + a)^2 - 1)))/b","A",0
100,1,40,0,0.380584," ","integrate(x^(-1+n)*arcsech(a+b*x^n),x, algorithm=""maxima"")","\frac{{\left(b x^{n} + a\right)} \operatorname{arsech}\left(b x^{n} + a\right) - \arctan\left(\sqrt{\frac{1}{{\left(b x^{n} + a\right)}^{2}} - 1}\right)}{b n}"," ",0,"((b*x^n + a)*arcsech(b*x^n + a) - arctan(sqrt(1/(b*x^n + a)^2 - 1)))/(b*n)","A",0
