1,0,0,0,0.000000," ","integrate(x^3*arccsch(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(-i \, a^{3} + i \, a\right)} {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right)\right)}}{2 \, b^{4}} + \frac{2 \, b^{4} x^{4} \log\left(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right) + b^{2} x^{2} - 6 \, a b x - {\left(a^{4} - 6 \, a^{2} + 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(b x + a\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)}^{\frac{3}{2}} + 1\right)}}\,{d x}"," ",0,"-1/2*(-I*a^3 + I*a)*(log(I*(b^2*x + a*b)/b + 1) - log(-I*(b^2*x + a*b)/b + 1))/b^4 + 1/8*(2*b^4*x^4*log(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1) + b^2*x^2 - 6*a*b*x - (a^4 - 6*a^2 + 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(b^4*x^4 - a^4)*log(b*x + a))/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)^(3/2) + 1), x)","F",0
2,0,0,0,0.000000," ","integrate(x^2*arccsch(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(3 i \, a^{2} - i\right)} {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right)\right)}}{6 \, b^{3}} + \frac{2 \, b^{3} x^{3} \log\left(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right) + 2 \, b x + {\left(a^{3} - 3 \, a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(b x + a\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)}^{\frac{3}{2}} + 1\right)}}\,{d x}"," ",0,"-1/6*(3*I*a^2 - I)*(log(I*(b^2*x + a*b)/b + 1) - log(-I*(b^2*x + a*b)/b + 1))/b^3 + 1/6*(2*b^3*x^3*log(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1) + 2*b*x + (a^3 - 3*a)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(b^3*x^3 + a^3)*log(b*x + a))/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)^(3/2) + 1), x)","F",0
3,0,0,0,0.000000," ","integrate(x*arccsch(b*x+a),x, algorithm=""maxima"")","\frac{i \, a {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right)\right)}}{2 \, b^{2}} + \frac{2 \, b^{2} x^{2} \log\left(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\right) - {\left(a^{2} - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(b x + a\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)}^{\frac{3}{2}} + 1\right)}}\,{d x}"," ",0,"1/2*I*a*(log(I*(b^2*x + a*b)/b + 1) - log(-I*(b^2*x + a*b)/b + 1))/b^2 + 1/4*(2*b^2*x^2*log(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1) - (a^2 - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(b^2*x^2 - a^2)*log(b*x + a))/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)^(3/2) + 1), x)","F",0
4,0,0,0,0.000000," ","integrate(arccsch(b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcsch}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arccsch(b*x + a)/x, x)","F",0
5,0,0,0,0.000000," ","integrate(arccsch(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{i \, b {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right)\right)}}{2 \, {\left(a^{2} + 1\right)}} - \frac{b \log\left(x\right)}{a^{3} + a} - \frac{a^{2} b x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\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(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\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)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"-1/2*I*b*(log(I*(b^2*x + a*b)/b + 1) - log(-I*(b^2*x + a*b)/b + 1))/(a^2 + 1) - b*log(x)/(a^3 + a) - 1/2*(a^2*b*x*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(a^3 + (a^2*b + b)*x + a)*log(b*x + a) + 2*(a^3 + a)*log(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1))/((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)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
6,0,0,0,0.000000," ","integrate(arccsch(b*x+a)/x^3,x, algorithm=""maxima"")","\frac{i \, a b^{2} {\left(\log\left(\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right) - \log\left(-\frac{i \, {\left(b^{2} x + a b\right)}}{b} + 1\right)\right)}}{2 \, {\left(a^{4} + 2 \, a^{2} + 1\right)}} + \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} - a^{2} b^{2}\right)} x^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) + 2 \, {\left(a^{3} b + a b\right)} x + 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(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\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)} \sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}\right)}}\,{d x}"," ",0,"1/2*I*a*b^2*(log(I*(b^2*x + a*b)/b + 1) - log(-I*(b^2*x + a*b)/b + 1))/(a^4 + 2*a^2 + 1) + 1/2*(3*a^2*b^2 + b^2)*log(x)/(a^6 + 2*a^4 + a^2) + 1/4*((a^4*b^2 - a^2*b^2)*x^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1) + 2*(a^3*b + a*b)*x + 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(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1))/((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)*sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1)), x)","F",0
7,0,0,0,0.000000," ","integrate((f*x+e)^3*(a+b*arccsch(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} f^{3} x^{4} + a^{2} e f^{2} x^{3} + \frac{3}{2} \, a^{2} e^{2} f x^{2} + a^{2} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcsch}\left(d x + c\right) + \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} - 1\right)\right)} a b e^{3}}{d} + \frac{1}{4} \, {\left(b^{2} f^{3} x^{4} + 4 \, b^{2} e f^{2} x^{3} + 6 \, b^{2} e^{2} f x^{2} + 4 \, b^{2} e^{3} x\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2} - \int -\frac{2 \, {\left(b^{2} d^{2} f^{3} x^{5} + b^{2} c^{2} e^{3} + b^{2} e^{3} + {\left(3 \, b^{2} d^{2} e f^{2} + 2 \, b^{2} c d f^{3}\right)} x^{4} + {\left(6 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} b^{2}\right)} x^{3} + {\left(6 \, b^{2} c d e^{2} f + 3 \, b^{2} c^{2} e f^{2} + {\left(d^{2} e^{3} + 3 \, e f^{2}\right)} b^{2}\right)} x^{2} + {\left(2 \, b^{2} c d e^{3} + 3 \, b^{2} c^{2} e^{2} f + 3 \, b^{2} e^{2} f\right)} x\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(a b d^{2} f^{3} x^{5} + {\left(3 \, a b d^{2} e f^{2} + 2 \, a b c d f^{3}\right)} x^{4} + {\left(6 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} a b\right)} x^{3} + 3 \, {\left(2 \, a b c d e^{2} f + a b c^{2} e f^{2} + a b e f^{2}\right)} x^{2} + 3 \, {\left(a b c^{2} e^{2} f + a b e^{2} f\right)} x\right)} \log\left(d x + c\right) + {\left(4 \, a b d^{2} f^{3} x^{5} + 4 \, {\left(3 \, a b d^{2} e f^{2} + 2 \, a b c d f^{3}\right)} x^{4} + 4 \, {\left(6 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} a b\right)} x^{3} + 12 \, {\left(2 \, a b c d e^{2} f + a b c^{2} e f^{2} + a b e f^{2}\right)} x^{2} + 12 \, {\left(a b c^{2} e^{2} f + a b e^{2} f\right)} x - 4 \, {\left(b^{2} d^{2} f^{3} x^{5} + b^{2} c^{2} e^{3} + b^{2} e^{3} + {\left(3 \, b^{2} d^{2} e f^{2} + 2 \, b^{2} c d f^{3}\right)} x^{4} + {\left(6 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} b^{2}\right)} x^{3} + {\left(6 \, b^{2} c d e^{2} f + 3 \, b^{2} c^{2} e f^{2} + {\left(d^{2} e^{3} + 3 \, e f^{2}\right)} b^{2}\right)} x^{2} + {\left(2 \, b^{2} c d e^{3} + 3 \, b^{2} c^{2} e^{2} f + 3 \, b^{2} e^{2} f\right)} x\right)} \log\left(d x + c\right) + {\left({\left(4 \, a b d^{2} f^{3} - b^{2} d^{2} f^{3}\right)} x^{5} + {\left(12 \, a b d^{2} e f^{2} - 4 \, b^{2} d^{2} e f^{2} + {\left(8 \, a b d f^{3} - b^{2} d f^{3}\right)} c\right)} x^{4} - 2 \, {\left(3 \, b^{2} d^{2} e^{2} f - 2 \, a b c^{2} f^{3} - 2 \, {\left(3 \, d^{2} e^{2} f + f^{3}\right)} a b - 2 \, {\left(6 \, a b d e f^{2} - b^{2} d e f^{2}\right)} c\right)} x^{3} - 2 \, {\left(2 \, b^{2} d^{2} e^{3} - 6 \, a b c^{2} e f^{2} - 6 \, a b e f^{2} - 3 \, {\left(4 \, a b d e^{2} f - b^{2} d e^{2} f\right)} c\right)} x^{2} - 4 \, {\left(b^{2} c d e^{3} - 3 \, a b c^{2} e^{2} f - 3 \, a b e^{2} f\right)} x - 4 \, {\left(b^{2} d^{2} f^{3} x^{5} + b^{2} c^{2} e^{3} + b^{2} e^{3} + {\left(3 \, b^{2} d^{2} e f^{2} + 2 \, b^{2} c d f^{3}\right)} x^{4} + {\left(6 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} b^{2}\right)} x^{3} + {\left(6 \, b^{2} c d e^{2} f + 3 \, b^{2} c^{2} e f^{2} + {\left(d^{2} e^{3} + 3 \, e f^{2}\right)} b^{2}\right)} x^{2} + {\left(2 \, b^{2} c d e^{3} + 3 \, b^{2} c^{2} e^{2} f + 3 \, b^{2} e^{2} f\right)} x\right)} \log\left(d x + c\right)\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right) + 2 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(b^{2} d^{2} f^{3} x^{5} + b^{2} c^{2} e^{3} + b^{2} e^{3} + {\left(3 \, b^{2} d^{2} e f^{2} + 2 \, b^{2} c d f^{3}\right)} x^{4} + {\left(6 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} b^{2}\right)} x^{3} + {\left(6 \, b^{2} c d e^{2} f + 3 \, b^{2} c^{2} e f^{2} + {\left(d^{2} e^{3} + 3 \, e f^{2}\right)} b^{2}\right)} x^{2} + {\left(2 \, b^{2} c d e^{3} + 3 \, b^{2} c^{2} e^{2} f + 3 \, b^{2} e^{2} f\right)} x\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{3} x^{5} + {\left(3 \, a b d^{2} e f^{2} + 2 \, a b c d f^{3}\right)} x^{4} + {\left(6 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(3 \, d^{2} e^{2} f + f^{3}\right)} a b\right)} x^{3} + 3 \, {\left(2 \, a b c d e^{2} f + a b c^{2} e f^{2} + a b e f^{2}\right)} x^{2} + 3 \, {\left(a b c^{2} e^{2} f + a b e^{2} f\right)} x\right)} \log\left(d x + c\right)\right)}}{2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 1\right)}}\,{d x}"," ",0,"1/4*a^2*f^3*x^4 + a^2*e*f^2*x^3 + 3/2*a^2*e^2*f*x^2 + a^2*e^3*x + (2*(d*x + c)*arccsch(d*x + c) + log(sqrt(1/(d*x + c)^2 + 1) + 1) - log(sqrt(1/(d*x + c)^2 + 1) - 1))*a*b*e^3/d + 1/4*(b^2*f^3*x^4 + 4*b^2*e*f^2*x^3 + 6*b^2*e^2*f*x^2 + 4*b^2*e^3*x)*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2 - integrate(-1/2*(2*(b^2*d^2*f^3*x^5 + b^2*c^2*e^3 + b^2*e^3 + (3*b^2*d^2*e*f^2 + 2*b^2*c*d*f^3)*x^4 + (6*b^2*c*d*e*f^2 + b^2*c^2*f^3 + (3*d^2*e^2*f + f^3)*b^2)*x^3 + (6*b^2*c*d*e^2*f + 3*b^2*c^2*e*f^2 + (d^2*e^3 + 3*e*f^2)*b^2)*x^2 + (2*b^2*c*d*e^3 + 3*b^2*c^2*e^2*f + 3*b^2*e^2*f)*x)*log(d*x + c)^2 - 4*(a*b*d^2*f^3*x^5 + (3*a*b*d^2*e*f^2 + 2*a*b*c*d*f^3)*x^4 + (6*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (3*d^2*e^2*f + f^3)*a*b)*x^3 + 3*(2*a*b*c*d*e^2*f + a*b*c^2*e*f^2 + a*b*e*f^2)*x^2 + 3*(a*b*c^2*e^2*f + a*b*e^2*f)*x)*log(d*x + c) + (4*a*b*d^2*f^3*x^5 + 4*(3*a*b*d^2*e*f^2 + 2*a*b*c*d*f^3)*x^4 + 4*(6*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (3*d^2*e^2*f + f^3)*a*b)*x^3 + 12*(2*a*b*c*d*e^2*f + a*b*c^2*e*f^2 + a*b*e*f^2)*x^2 + 12*(a*b*c^2*e^2*f + a*b*e^2*f)*x - 4*(b^2*d^2*f^3*x^5 + b^2*c^2*e^3 + b^2*e^3 + (3*b^2*d^2*e*f^2 + 2*b^2*c*d*f^3)*x^4 + (6*b^2*c*d*e*f^2 + b^2*c^2*f^3 + (3*d^2*e^2*f + f^3)*b^2)*x^3 + (6*b^2*c*d*e^2*f + 3*b^2*c^2*e*f^2 + (d^2*e^3 + 3*e*f^2)*b^2)*x^2 + (2*b^2*c*d*e^3 + 3*b^2*c^2*e^2*f + 3*b^2*e^2*f)*x)*log(d*x + c) + ((4*a*b*d^2*f^3 - b^2*d^2*f^3)*x^5 + (12*a*b*d^2*e*f^2 - 4*b^2*d^2*e*f^2 + (8*a*b*d*f^3 - b^2*d*f^3)*c)*x^4 - 2*(3*b^2*d^2*e^2*f - 2*a*b*c^2*f^3 - 2*(3*d^2*e^2*f + f^3)*a*b - 2*(6*a*b*d*e*f^2 - b^2*d*e*f^2)*c)*x^3 - 2*(2*b^2*d^2*e^3 - 6*a*b*c^2*e*f^2 - 6*a*b*e*f^2 - 3*(4*a*b*d*e^2*f - b^2*d*e^2*f)*c)*x^2 - 4*(b^2*c*d*e^3 - 3*a*b*c^2*e^2*f - 3*a*b*e^2*f)*x - 4*(b^2*d^2*f^3*x^5 + b^2*c^2*e^3 + b^2*e^3 + (3*b^2*d^2*e*f^2 + 2*b^2*c*d*f^3)*x^4 + (6*b^2*c*d*e*f^2 + b^2*c^2*f^3 + (3*d^2*e^2*f + f^3)*b^2)*x^3 + (6*b^2*c*d*e^2*f + 3*b^2*c^2*e*f^2 + (d^2*e^3 + 3*e*f^2)*b^2)*x^2 + (2*b^2*c*d*e^3 + 3*b^2*c^2*e^2*f + 3*b^2*e^2*f)*x)*log(d*x + c))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1) + 2*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((b^2*d^2*f^3*x^5 + b^2*c^2*e^3 + b^2*e^3 + (3*b^2*d^2*e*f^2 + 2*b^2*c*d*f^3)*x^4 + (6*b^2*c*d*e*f^2 + b^2*c^2*f^3 + (3*d^2*e^2*f + f^3)*b^2)*x^3 + (6*b^2*c*d*e^2*f + 3*b^2*c^2*e*f^2 + (d^2*e^3 + 3*e*f^2)*b^2)*x^2 + (2*b^2*c*d*e^3 + 3*b^2*c^2*e^2*f + 3*b^2*e^2*f)*x)*log(d*x + c)^2 - 2*(a*b*d^2*f^3*x^5 + (3*a*b*d^2*e*f^2 + 2*a*b*c*d*f^3)*x^4 + (6*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (3*d^2*e^2*f + f^3)*a*b)*x^3 + 3*(2*a*b*c*d*e^2*f + a*b*c^2*e*f^2 + a*b*e*f^2)*x^2 + 3*(a*b*c^2*e^2*f + a*b*e^2*f)*x)*log(d*x + c)))/(d^2*x^2 + 2*c*d*x + c^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 1), x)","F",0
8,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccsch(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} f^{2} x^{3} + a^{2} e f x^{2} + a^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcsch}\left(d x + c\right) + \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} - 1\right)\right)} a b e^{2}}{d} + \frac{1}{3} \, {\left(b^{2} f^{2} x^{3} + 3 \, b^{2} e f x^{2} + 3 \, b^{2} e^{2} x\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2} - \int -\frac{3 \, {\left(b^{2} d^{2} f^{2} x^{4} + b^{2} c^{2} e^{2} + b^{2} e^{2} + 2 \, {\left(b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + {\left(4 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(d^{2} e^{2} + f^{2}\right)} b^{2}\right)} x^{2} + 2 \, {\left(b^{2} c d e^{2} + b^{2} c^{2} e f + b^{2} e f\right)} x\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(a b d^{2} f^{2} x^{4} + 2 \, {\left(a b d^{2} e f + a b c d f^{2}\right)} x^{3} + {\left(4 \, a b c d e f + a b c^{2} f^{2} + a b f^{2}\right)} x^{2} + 2 \, {\left(a b c^{2} e f + a b e f\right)} x\right)} \log\left(d x + c\right) + 2 \, {\left(3 \, a b d^{2} f^{2} x^{4} + 6 \, {\left(a b d^{2} e f + a b c d f^{2}\right)} x^{3} + 3 \, {\left(4 \, a b c d e f + a b c^{2} f^{2} + a b f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} e f + a b e f\right)} x - 3 \, {\left(b^{2} d^{2} f^{2} x^{4} + b^{2} c^{2} e^{2} + b^{2} e^{2} + 2 \, {\left(b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + {\left(4 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(d^{2} e^{2} + f^{2}\right)} b^{2}\right)} x^{2} + 2 \, {\left(b^{2} c d e^{2} + b^{2} c^{2} e f + b^{2} e f\right)} x\right)} \log\left(d x + c\right) + {\left({\left(3 \, a b d^{2} f^{2} - b^{2} d^{2} f^{2}\right)} x^{4} + {\left(6 \, a b d^{2} e f - 3 \, b^{2} d^{2} e f + {\left(6 \, a b d f^{2} - b^{2} d f^{2}\right)} c\right)} x^{3} - 3 \, {\left(b^{2} d^{2} e^{2} - a b c^{2} f^{2} - a b f^{2} - {\left(4 \, a b d e f - b^{2} d e f\right)} c\right)} x^{2} - 3 \, {\left(b^{2} c d e^{2} - 2 \, a b c^{2} e f - 2 \, a b e f\right)} x - 3 \, {\left(b^{2} d^{2} f^{2} x^{4} + b^{2} c^{2} e^{2} + b^{2} e^{2} + 2 \, {\left(b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + {\left(4 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(d^{2} e^{2} + f^{2}\right)} b^{2}\right)} x^{2} + 2 \, {\left(b^{2} c d e^{2} + b^{2} c^{2} e f + b^{2} e f\right)} x\right)} \log\left(d x + c\right)\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right) + 3 \, \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(b^{2} d^{2} f^{2} x^{4} + b^{2} c^{2} e^{2} + b^{2} e^{2} + 2 \, {\left(b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + {\left(4 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(d^{2} e^{2} + f^{2}\right)} b^{2}\right)} x^{2} + 2 \, {\left(b^{2} c d e^{2} + b^{2} c^{2} e f + b^{2} e f\right)} x\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{2} x^{4} + 2 \, {\left(a b d^{2} e f + a b c d f^{2}\right)} x^{3} + {\left(4 \, a b c d e f + a b c^{2} f^{2} + a b f^{2}\right)} x^{2} + 2 \, {\left(a b c^{2} e f + a b e f\right)} x\right)} \log\left(d x + c\right)\right)}}{3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 1\right)}}\,{d x}"," ",0,"1/3*a^2*f^2*x^3 + a^2*e*f*x^2 + a^2*e^2*x + (2*(d*x + c)*arccsch(d*x + c) + log(sqrt(1/(d*x + c)^2 + 1) + 1) - log(sqrt(1/(d*x + c)^2 + 1) - 1))*a*b*e^2/d + 1/3*(b^2*f^2*x^3 + 3*b^2*e*f*x^2 + 3*b^2*e^2*x)*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2 - integrate(-1/3*(3*(b^2*d^2*f^2*x^4 + b^2*c^2*e^2 + b^2*e^2 + 2*(b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + (4*b^2*c*d*e*f + b^2*c^2*f^2 + (d^2*e^2 + f^2)*b^2)*x^2 + 2*(b^2*c*d*e^2 + b^2*c^2*e*f + b^2*e*f)*x)*log(d*x + c)^2 - 6*(a*b*d^2*f^2*x^4 + 2*(a*b*d^2*e*f + a*b*c*d*f^2)*x^3 + (4*a*b*c*d*e*f + a*b*c^2*f^2 + a*b*f^2)*x^2 + 2*(a*b*c^2*e*f + a*b*e*f)*x)*log(d*x + c) + 2*(3*a*b*d^2*f^2*x^4 + 6*(a*b*d^2*e*f + a*b*c*d*f^2)*x^3 + 3*(4*a*b*c*d*e*f + a*b*c^2*f^2 + a*b*f^2)*x^2 + 6*(a*b*c^2*e*f + a*b*e*f)*x - 3*(b^2*d^2*f^2*x^4 + b^2*c^2*e^2 + b^2*e^2 + 2*(b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + (4*b^2*c*d*e*f + b^2*c^2*f^2 + (d^2*e^2 + f^2)*b^2)*x^2 + 2*(b^2*c*d*e^2 + b^2*c^2*e*f + b^2*e*f)*x)*log(d*x + c) + ((3*a*b*d^2*f^2 - b^2*d^2*f^2)*x^4 + (6*a*b*d^2*e*f - 3*b^2*d^2*e*f + (6*a*b*d*f^2 - b^2*d*f^2)*c)*x^3 - 3*(b^2*d^2*e^2 - a*b*c^2*f^2 - a*b*f^2 - (4*a*b*d*e*f - b^2*d*e*f)*c)*x^2 - 3*(b^2*c*d*e^2 - 2*a*b*c^2*e*f - 2*a*b*e*f)*x - 3*(b^2*d^2*f^2*x^4 + b^2*c^2*e^2 + b^2*e^2 + 2*(b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + (4*b^2*c*d*e*f + b^2*c^2*f^2 + (d^2*e^2 + f^2)*b^2)*x^2 + 2*(b^2*c*d*e^2 + b^2*c^2*e*f + b^2*e*f)*x)*log(d*x + c))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1) + 3*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((b^2*d^2*f^2*x^4 + b^2*c^2*e^2 + b^2*e^2 + 2*(b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + (4*b^2*c*d*e*f + b^2*c^2*f^2 + (d^2*e^2 + f^2)*b^2)*x^2 + 2*(b^2*c*d*e^2 + b^2*c^2*e*f + b^2*e*f)*x)*log(d*x + c)^2 - 2*(a*b*d^2*f^2*x^4 + 2*(a*b*d^2*e*f + a*b*c*d*f^2)*x^3 + (4*a*b*c*d*e*f + a*b*c^2*f^2 + a*b*f^2)*x^2 + 2*(a*b*c^2*e*f + a*b*e*f)*x)*log(d*x + c)))/(d^2*x^2 + 2*c*d*x + c^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 1), x)","F",0
9,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccsch(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} f x^{2} + a^{2} e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcsch}\left(d x + c\right) + \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} - 1\right)\right)} a b e}{d} + \frac{1}{2} \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2} - \int -\frac{{\left(b^{2} d^{2} f x^{3} + b^{2} c^{2} e + b^{2} e + {\left(b^{2} d^{2} e + 2 \, b^{2} c d f\right)} x^{2} + {\left(2 \, b^{2} c d e + b^{2} c^{2} f + b^{2} f\right)} x\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{3} + 2 \, a b c d f x^{2} + {\left(a b c^{2} f + a b f\right)} x\right)} \log\left(d x + c\right) + {\left(2 \, a b d^{2} f x^{3} + 4 \, a b c d f x^{2} + 2 \, {\left(a b c^{2} f + a b f\right)} x - 2 \, {\left(b^{2} d^{2} f x^{3} + b^{2} c^{2} e + b^{2} e + {\left(b^{2} d^{2} e + 2 \, b^{2} c d f\right)} x^{2} + {\left(2 \, b^{2} c d e + b^{2} c^{2} f + b^{2} f\right)} x\right)} \log\left(d x + c\right) + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(2 \, a b d^{2} f - b^{2} d^{2} f\right)} x^{3} - {\left(2 \, b^{2} d^{2} e - {\left(4 \, a b d f - b^{2} d f\right)} c\right)} x^{2} - 2 \, {\left(b^{2} c d e - a b c^{2} f - a b f\right)} x - 2 \, {\left(b^{2} d^{2} f x^{3} + b^{2} c^{2} e + b^{2} e + {\left(b^{2} d^{2} e + 2 \, b^{2} c d f\right)} x^{2} + {\left(2 \, b^{2} c d e + b^{2} c^{2} f + b^{2} f\right)} x\right)} \log\left(d x + c\right)\right)}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right) + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(b^{2} d^{2} f x^{3} + b^{2} c^{2} e + b^{2} e + {\left(b^{2} d^{2} e + 2 \, b^{2} c d f\right)} x^{2} + {\left(2 \, b^{2} c d e + b^{2} c^{2} f + b^{2} f\right)} x\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{3} + 2 \, a b c d f x^{2} + {\left(a b c^{2} f + a b f\right)} x\right)} \log\left(d x + c\right)\right)}}{d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 1}\,{d x}"," ",0,"1/2*a^2*f*x^2 + a^2*e*x + (2*(d*x + c)*arccsch(d*x + c) + log(sqrt(1/(d*x + c)^2 + 1) + 1) - log(sqrt(1/(d*x + c)^2 + 1) - 1))*a*b*e/d + 1/2*(b^2*f*x^2 + 2*b^2*e*x)*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2 - integrate(-((b^2*d^2*f*x^3 + b^2*c^2*e + b^2*e + (b^2*d^2*e + 2*b^2*c*d*f)*x^2 + (2*b^2*c*d*e + b^2*c^2*f + b^2*f)*x)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^3 + 2*a*b*c*d*f*x^2 + (a*b*c^2*f + a*b*f)*x)*log(d*x + c) + (2*a*b*d^2*f*x^3 + 4*a*b*c*d*f*x^2 + 2*(a*b*c^2*f + a*b*f)*x - 2*(b^2*d^2*f*x^3 + b^2*c^2*e + b^2*e + (b^2*d^2*e + 2*b^2*c*d*f)*x^2 + (2*b^2*c*d*e + b^2*c^2*f + b^2*f)*x)*log(d*x + c) + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((2*a*b*d^2*f - b^2*d^2*f)*x^3 - (2*b^2*d^2*e - (4*a*b*d*f - b^2*d*f)*c)*x^2 - 2*(b^2*c*d*e - a*b*c^2*f - a*b*f)*x - 2*(b^2*d^2*f*x^3 + b^2*c^2*e + b^2*e + (b^2*d^2*e + 2*b^2*c*d*f)*x^2 + (2*b^2*c*d*e + b^2*c^2*f + b^2*f)*x)*log(d*x + c)))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1) + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((b^2*d^2*f*x^3 + b^2*c^2*e + b^2*e + (b^2*d^2*e + 2*b^2*c*d*f)*x^2 + (2*b^2*c*d*e + b^2*c^2*f + b^2*f)*x)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^3 + 2*a*b*c*d*f*x^2 + (a*b*c^2*f + a*b*f)*x)*log(d*x + c)))/(d^2*x^2 + 2*c*d*x + c^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 1), x)","F",0
10,0,0,0,0.000000," ","integrate((a+b*arccsch(d*x+c))^2,x, algorithm=""maxima"")","{\left(x \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2} - \int -\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} \log\left(d x + c\right)^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \log\left(d x + c\right)^{2} - 2 \, {\left({\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \log\left(d x + c\right) + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left(d^{2} x^{2} + c d x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \log\left(d x + c\right)\right)}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}^{\frac{3}{2}} + 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcsch}\left(d x + c\right) + \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} - 1\right)\right)} a b}{d}"," ",0,"(x*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2 - integrate(-((d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2)*log(d*x + c)^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)*log(d*x + c)^2 - 2*((d^2*x^2 + 2*c*d*x + c^2 + 1)*log(d*x + c) + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*(d^2*x^2 + c*d*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)*log(d*x + c)))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1))/(d^2*x^2 + 2*c*d*x + c^2 + (d^2*x^2 + 2*c*d*x + c^2 + 1)^(3/2) + 1), x))*b^2 + a^2*x + (2*(d*x + c)*arccsch(d*x + c) + log(sqrt(1/(d*x + c)^2 + 1) + 1) - log(sqrt(1/(d*x + c)^2 + 1) - 1))*a*b/d","F",0
11,0,0,0,0.000000," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} + \int \frac{b^{2} \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + \frac{1}{d x + c}\right)^{2}}{f x + e} + \frac{2 \, a b \log\left(\sqrt{\frac{1}{{\left(d x + c\right)}^{2}} + 1} + \frac{1}{d x + c}\right)}{f x + e}\,{d x}"," ",0,"a^2*log(f*x + e)/f + integrate(b^2*log(sqrt(1/(d*x + c)^2 + 1) + 1/(d*x + c))^2/(f*x + e) + 2*a*b*log(sqrt(1/(d*x + c)^2 + 1) + 1/(d*x + c))/(f*x + e), x)","F",0
12,0,0,0,0.000000," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e)^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2}}{f^{2} x + e f} - \frac{a^{2}}{f^{2} x + e f} - \int -\frac{{\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{2} + 2 \, a b c d f x + {\left(c^{2} f + f\right)} a b\right)} \log\left(d x + c\right) + 2 \, {\left(a b d^{2} f x^{2} + 2 \, a b c d f x + {\left(c^{2} f + f\right)} a b - {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right) + {\left(b^{2} c d e + {\left(c^{2} f + f\right)} a b + {\left(a b d^{2} f + b^{2} d^{2} f\right)} x^{2} + {\left(2 \, a b c d f + {\left(d^{2} e + c d f\right)} b^{2}\right)} x - {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right) + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{2} + 2 \, a b c d f x + {\left(c^{2} f + f\right)} a b\right)} \log\left(d x + c\right)\right)}}{d^{2} f^{3} x^{4} + c^{2} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + e^{2} f + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + c^{2} f^{3} + f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + c^{2} e f^{2} + e f^{2}\right)} x + {\left(d^{2} f^{3} x^{4} + c^{2} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + e^{2} f + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + c^{2} f^{3} + f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + c^{2} e f^{2} + e f^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-b^2*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2/(f^2*x + e*f) - a^2/(f^2*x + e*f) - integrate(-((b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^2 + 2*a*b*c*d*f*x + (c^2*f + f)*a*b)*log(d*x + c) + 2*(a*b*d^2*f*x^2 + 2*a*b*c*d*f*x + (c^2*f + f)*a*b - (b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c) + (b^2*c*d*e + (c^2*f + f)*a*b + (a*b*d^2*f + b^2*d^2*f)*x^2 + (2*a*b*c*d*f + (d^2*e + c*d*f)*b^2)*x - (b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1) + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^2 + 2*a*b*c*d*f*x + (c^2*f + f)*a*b)*log(d*x + c)))/(d^2*f^3*x^4 + c^2*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + e^2*f + (d^2*e^2*f + 4*c*d*e*f^2 + c^2*f^3 + f^3)*x^2 + 2*(c*d*e^2*f + c^2*e*f^2 + e*f^2)*x + (d^2*f^3*x^4 + c^2*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + e^2*f + (d^2*e^2*f + 4*c*d*e*f^2 + c^2*f^3 + f^3)*x^2 + 2*(c*d*e^2*f + c^2*e*f^2 + e*f^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
13,0,0,0,0.000000," ","integrate((a+b*arccsch(d*x+c))^2/(f*x+e)^3,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right)^{2}}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}} - \frac{a^{2}}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}} - \int -\frac{{\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{2} + 2 \, a b c d f x + {\left(c^{2} f + f\right)} a b\right)} \log\left(d x + c\right) + {\left(2 \, a b d^{2} f x^{2} + 4 \, a b c d f x + 2 \, {\left(c^{2} f + f\right)} a b - 2 \, {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right) + {\left(b^{2} c d e + 2 \, {\left(c^{2} f + f\right)} a b + {\left(2 \, a b d^{2} f + b^{2} d^{2} f\right)} x^{2} + {\left(4 \, a b c d f + {\left(d^{2} e + c d f\right)} b^{2}\right)} x - 2 \, {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\right)} \log\left(\sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} + 1\right) + \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1} {\left({\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} c d f x + {\left(c^{2} f + f\right)} b^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f x^{2} + 2 \, a b c d f x + {\left(c^{2} f + f\right)} a b\right)} \log\left(d x + c\right)\right)}}{d^{2} f^{4} x^{5} + c^{2} e^{3} f + {\left(3 \, d^{2} e f^{3} + 2 \, c d f^{4}\right)} x^{4} + e^{3} f + {\left(3 \, d^{2} e^{2} f^{2} + 6 \, c d e f^{3} + c^{2} f^{4} + f^{4}\right)} x^{3} + {\left(d^{2} e^{3} f + 6 \, c d e^{2} f^{2} + 3 \, c^{2} e f^{3} + 3 \, e f^{3}\right)} x^{2} + {\left(2 \, c d e^{3} f + 3 \, c^{2} e^{2} f^{2} + 3 \, e^{2} f^{2}\right)} x + {\left(d^{2} f^{4} x^{5} + c^{2} e^{3} f + {\left(3 \, d^{2} e f^{3} + 2 \, c d f^{4}\right)} x^{4} + e^{3} f + {\left(3 \, d^{2} e^{2} f^{2} + 6 \, c d e f^{3} + c^{2} f^{4} + f^{4}\right)} x^{3} + {\left(d^{2} e^{3} f + 6 \, c d e^{2} f^{2} + 3 \, c^{2} e f^{3} + 3 \, e f^{3}\right)} x^{2} + {\left(2 \, c d e^{3} f + 3 \, c^{2} e^{2} f^{2} + 3 \, e^{2} f^{2}\right)} x\right)} \sqrt{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}}\,{d x}"," ",0,"-1/2*b^2*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1)^2/(f^3*x^2 + 2*e*f^2*x + e^2*f) - 1/2*a^2/(f^3*x^2 + 2*e*f^2*x + e^2*f) - integrate(-((b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^2 + 2*a*b*c*d*f*x + (c^2*f + f)*a*b)*log(d*x + c) + (2*a*b*d^2*f*x^2 + 4*a*b*c*d*f*x + 2*(c^2*f + f)*a*b - 2*(b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c) + (b^2*c*d*e + 2*(c^2*f + f)*a*b + (2*a*b*d^2*f + b^2*d^2*f)*x^2 + (4*a*b*c*d*f + (d^2*e + c*d*f)*b^2)*x - 2*(b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c))*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1))*log(sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1) + 1) + sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)*((b^2*d^2*f*x^2 + 2*b^2*c*d*f*x + (c^2*f + f)*b^2)*log(d*x + c)^2 - 2*(a*b*d^2*f*x^2 + 2*a*b*c*d*f*x + (c^2*f + f)*a*b)*log(d*x + c)))/(d^2*f^4*x^5 + c^2*e^3*f + (3*d^2*e*f^3 + 2*c*d*f^4)*x^4 + e^3*f + (3*d^2*e^2*f^2 + 6*c*d*e*f^3 + c^2*f^4 + f^4)*x^3 + (d^2*e^3*f + 6*c*d*e^2*f^2 + 3*c^2*e*f^3 + 3*e*f^3)*x^2 + (2*c*d*e^3*f + 3*c^2*e^2*f^2 + 3*e^2*f^2)*x + (d^2*f^4*x^5 + c^2*e^3*f + (3*d^2*e*f^3 + 2*c*d*f^4)*x^4 + e^3*f + (3*d^2*e^2*f^2 + 6*c*d*e*f^3 + c^2*f^4 + f^4)*x^3 + (d^2*e^3*f + 6*c*d*e^2*f^2 + 3*c^2*e*f^3 + 3*e*f^3)*x^2 + (2*c*d*e^3*f + 3*c^2*e^2*f^2 + 3*e^2*f^2)*x)*sqrt(d^2*x^2 + 2*c*d*x + c^2 + 1)), x)","F",0
14,1,58,0,0.308534," ","integrate(x^3*arccsch(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{arcsch}\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*arccsch(sqrt(x)) + 1/4*x^(3/2)*(1/x + 1)^(3/2) - 1/4*sqrt(x)*sqrt(1/x + 1)","A",0
15,1,46,0,0.319296," ","integrate(x^2*arccsch(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{arcsch}\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*arccsch(sqrt(x)) - 2/9*x^(3/2)*(1/x + 1)^(3/2) + 1/3*sqrt(x)*sqrt(1/x + 1)","A",0
16,1,34,0,0.320385," ","integrate(x*arccsch(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{arcsch}\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*arccsch(sqrt(x)) - 1/2*sqrt(x)*sqrt(1/x + 1)","A",0
17,1,18,0,0.319429," ","integrate(arccsch(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arcsch}\left(\sqrt{x}\right) + \sqrt{x} \sqrt{\frac{1}{x} + 1}"," ",0,"x*arccsch(sqrt(x)) + sqrt(x)*sqrt(1/x + 1)","A",0
18,0,0,0,0.000000," ","integrate(arccsch(x^(1/2))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcsch}\left(\sqrt{x}\right)}{x}\,{d x}"," ",0,"integrate(arccsch(sqrt(x))/x, x)","F",0
19,1,65,0,0.321581," ","integrate(arccsch(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{arcsch}\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) - arccsch(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
20,1,92,0,0.319180," ","integrate(arccsch(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{arcsch}\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*arccsch(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
21,1,116,0,0.318935," ","integrate(arccsch(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{arcsch}\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*arccsch(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
22,1,16,0,0.311533," ","integrate(arccsch(1/x),x, algorithm=""maxima"")","x \operatorname{arcsch}\left(\frac{1}{x}\right) - \sqrt{x^{2} + 1}"," ",0,"x*arccsch(1/x) - sqrt(x^2 + 1)","A",0
23,0,0,0,0.000000," ","integrate(arccsch(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^{2} x^{2 \, n} + 1} + x}\,{d x} + n \int \frac{\log\left(x\right)}{a^{2} x x^{2 \, n} + x}\,{d x} - \log\left(a\right) \log\left(x\right) - \log\left(x\right) \log\left(x^{n}\right) + \log\left(x\right) \log\left(\sqrt{a^{2} x^{2 \, n} + 1} + 1\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^2*x^(2*n) + 1) + x), x) + n*integrate(log(x)/(a^2*x*x^(2*n) + x), x) - log(a)*log(x) - log(x)*log(x^n) + log(x)*log(sqrt(a^2*x^(2*n) + 1) + 1)","F",0
24,0,0,0,0.000000," ","integrate(arccsch(a*x^5)/x,x, algorithm=""maxima"")","5 \, a^{2} \int \frac{x^{9} \log\left(x\right)}{a^{2} x^{10} + {\left(a^{2} x^{10} + 1\right)}^{\frac{3}{2}} + 1}\,{d x} - \frac{1}{2} \, \log\left(a^{2} x^{10} + 1\right) \log\left(x\right) - \log\left(a\right) \log\left(x\right) - \frac{5}{2} \, \log\left(x\right)^{2} + \log\left(x\right) \log\left(\sqrt{a^{2} x^{10} + 1} + 1\right) - \frac{1}{20} \, {\rm Li}_2\left(-a^{2} x^{10}\right)"," ",0,"5*a^2*integrate(x^9*log(x)/(a^2*x^10 + (a^2*x^10 + 1)^(3/2) + 1), x) - 1/2*log(a^2*x^10 + 1)*log(x) - log(a)*log(x) - 5/2*log(x)^2 + log(x)*log(sqrt(a^2*x^10 + 1) + 1) - 1/20*dilog(-a^2*x^10)","F",0
25,0,0,0,0.000000," ","integrate(arccsch(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)}^{\frac{3}{2}} + 1}\,{d x} - \frac{1}{2} \, b x^{2} - {\left(a + \log\left(c\right)\right)} x + x \log\left(\sqrt{c^{2} e^{\left(2 \, b x + 2 \, a\right)} + 1} + 1\right) - \frac{2 \, b x \log\left(c^{2} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-c^{2} e^{\left(2 \, b x + 2 \, a\right)}\right)}{4 \, 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)^(3/2) + 1), x) - 1/2*b*x^2 - (a + log(c))*x + x*log(sqrt(c^2*e^(2*b*x + 2*a) + 1) + 1) - 1/4*(2*b*x*log(c^2*e^(2*b*x + 2*a) + 1) + dilog(-c^2*e^(2*b*x + 2*a)))/b","F",0
26,0,0,0,0.000000," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^m,x, algorithm=""maxima"")","\frac{\frac{x^{m} \Gamma\left(\frac{1}{2} \, m\right) \,_2F_1\left(\begin{matrix} -\frac{1}{2},\frac{1}{2} \, m \\ \frac{1}{2} \, m + 1 \end{matrix} ; -a^{2} x^{2} \right)}{2 \, \Gamma\left(\frac{1}{2} \, m + 1\right)}}{a} + \frac{x^{m}}{a m}"," ",0,"integrate(sqrt(a^2*x^2 + 1)*x^m/x, x)/a + x^m/(a*m)","F",0
27,1,50,0,0.326581," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^4,x, algorithm=""maxima"")","\frac{x^{4}}{4 \, a} + \frac{3 \, a^{2} x^{5} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 5 \, x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{15 \, a^{2}}"," ",0,"1/4*x^4/a + 1/15*(3*a^2*x^5*(1/(a^2*x^2) + 1)^(5/2) - 5*x^3*(1/(a^2*x^2) + 1)^(3/2))/a^2","A",0
28,1,107,0,0.317332," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^3,x, algorithm=""maxima"")","\frac{x^{3}}{3 \, a} + \frac{{\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \sqrt{\frac{1}{a^{2} x^{2}} + 1}}{8 \, {\left(a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{2} - 2 \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} + a^{4}\right)}} - \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{16 \, a^{4}} + \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{16 \, a^{4}}"," ",0,"1/3*x^3/a + 1/8*((1/(a^2*x^2) + 1)^(3/2) + sqrt(1/(a^2*x^2) + 1))/(a^4*(1/(a^2*x^2) + 1)^2 - 2*a^4*(1/(a^2*x^2) + 1) + a^4) - 1/16*log(sqrt(1/(a^2*x^2) + 1) + 1)/a^4 + 1/16*log(sqrt(1/(a^2*x^2) + 1) - 1)/a^4","A",0
29,1,25,0,0.311435," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \frac{x^{2}}{2 \, a}"," ",0,"1/3*x^3*(1/(a^2*x^2) + 1)^(3/2) + 1/2*x^2/a","A",0
30,1,78,0,0.310416," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))*x,x, algorithm=""maxima"")","\frac{x}{a} + \frac{\sqrt{\frac{1}{a^{2} x^{2}} + 1}}{2 \, {\left(a^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} - a^{2}\right)}} + \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{4 \, a^{2}} - \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{4 \, a^{2}}"," ",0,"x/a + 1/2*sqrt(1/(a^2*x^2) + 1)/(a^2*(1/(a^2*x^2) + 1) - a^2) + 1/4*log(sqrt(1/(a^2*x^2) + 1) + 1)/a^2 - 1/4*log(sqrt(1/(a^2*x^2) + 1) - 1)/a^2","A",0
31,1,64,0,0.313695," ","integrate(1/a/x+(1+1/a^2/x^2)^(1/2),x, algorithm=""maxima"")","x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - \frac{\log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{2 \, a} + \frac{\log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{2 \, a} + \frac{\log\left(x\right)}{a}"," ",0,"x*sqrt(1/(a^2*x^2) + 1) - 1/2*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1)/a + 1/2*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1)/a + log(x)/a","A",0
32,1,54,0,0.312050," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x,x, algorithm=""maxima"")","-\sqrt{\frac{1}{a^{2} x^{2}} + 1} - \frac{1}{a x} + \frac{1}{2} \, \log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)"," ",0,"-sqrt(1/(a^2*x^2) + 1) - 1/(a*x) + 1/2*log(sqrt(1/(a^2*x^2) + 1) + 1) - 1/2*log(sqrt(1/(a^2*x^2) + 1) - 1)","A",0
33,1,86,0,0.323142," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{a^{2} x \sqrt{\frac{1}{a^{2} x^{2}} + 1}}{2 \, {\left(a^{2} x^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} - 1\right)}} - \frac{1}{4} \, a \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) + \frac{1}{4} \, a \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right) - \frac{1}{2 \, a x^{2}}"," ",0,"-1/2*a^2*x*sqrt(1/(a^2*x^2) + 1)/(a^2*x^2*(1/(a^2*x^2) + 1) - 1) - 1/4*a*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1) + 1/4*a*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1) - 1/2/(a*x^2)","B",0
34,1,25,0,0.305238," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{1}{3} \, a^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - \frac{1}{3 \, a x^{3}}"," ",0,"-1/3*a^2*(1/(a^2*x^2) + 1)^(3/2) - 1/3/(a*x^3)","A",0
35,1,129,0,0.322736," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^4,x, algorithm=""maxima"")","\frac{1}{16} \, a^{3} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) - \frac{1}{16} \, a^{3} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right) - \frac{a^{6} x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + a^{4} x \sqrt{\frac{1}{a^{2} x^{2}} + 1}}{8 \, {\left(a^{4} x^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{2} - 2 \, a^{2} x^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} + 1\right)}} - \frac{1}{4 \, a x^{4}}"," ",0,"1/16*a^3*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1) - 1/16*a^3*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1) - 1/8*(a^6*x^3*(1/(a^2*x^2) + 1)^(3/2) + a^4*x*sqrt(1/(a^2*x^2) + 1))/(a^4*x^4*(1/(a^2*x^2) + 1)^2 - 2*a^2*x^2*(1/(a^2*x^2) + 1) + 1) - 1/4/(a*x^4)","B",0
36,1,41,0,0.314796," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))/x^5,x, algorithm=""maxima"")","-\frac{1}{5} \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{5}{2}} + \frac{1}{3} \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - \frac{1}{5 \, a x^{5}}"," ",0,"-1/5*a^4*(1/(a^2*x^2) + 1)^(5/2) + 1/3*a^4*(1/(a^2*x^2) + 1)^(3/2) - 1/5/(a*x^5)","A",0
37,-2,0,0,0.000000," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(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
38,0,0,0,0.000000," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^4,x, algorithm=""maxima"")","\frac{x^{3}}{3 \, a} + \frac{\frac{x^{3} \Gamma\left(\frac{3}{4}\right) \,_2F_1\left(\begin{matrix} -\frac{1}{2},\frac{3}{4} \\ \frac{7}{4} \end{matrix} ; -a^{2} x^{4} \right)}{4 \, \Gamma\left(\frac{7}{4}\right)}}{a}"," ",0,"1/3*x^3/a + integrate(sqrt(a^2*x^4 + 1)*x^2, x)/a","F",0
39,1,81,0,0.328325," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^3,x, algorithm=""maxima"")","\frac{x^{2}}{2 \, a} + \frac{\sqrt{\frac{1}{a^{2} x^{4}} + 1}}{4 \, {\left(a^{2} {\left(\frac{1}{a^{2} x^{4}} + 1\right)} - a^{2}\right)}} + \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{4}} + 1} + 1\right)}{8 \, a^{2}} - \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{4}} + 1} - 1\right)}{8 \, a^{2}}"," ",0,"1/2*x^2/a + 1/4*sqrt(1/(a^2*x^4) + 1)/(a^2*(1/(a^2*x^4) + 1) - a^2) + 1/8*log(sqrt(1/(a^2*x^4) + 1) + 1)/a^2 - 1/8*log(sqrt(1/(a^2*x^4) + 1) - 1)/a^2","A",0
40,0,0,0,0.000000," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x^2,x, algorithm=""maxima"")","\frac{x}{a} + \frac{\frac{x \Gamma\left(\frac{1}{4}\right) \,_2F_1\left(\begin{matrix} -\frac{1}{2},\frac{1}{4} \\ \frac{5}{4} \end{matrix} ; -a^{2} x^{4} \right)}{4 \, \Gamma\left(\frac{5}{4}\right)}}{a}"," ",0,"x/a + integrate(sqrt(a^2*x^4 + 1), x)/a","F",0
41,1,71,0,0.365534," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))*x,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1} - \frac{\log\left(a x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1} + 1\right)}{4 \, a} + \frac{\log\left(a x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1} - 1\right)}{4 \, a} + \frac{\log\left(x\right)}{a}"," ",0,"1/2*x^2*sqrt(1/(a^2*x^4) + 1) - 1/4*log(a*x^2*sqrt(1/(a^2*x^4) + 1) + 1)/a + 1/4*log(a*x^2*sqrt(1/(a^2*x^4) + 1) - 1)/a + log(x)/a","B",0
42,0,0,0,0.000000," ","integrate(1/a/x^2+(1+1/a^2/x^4)^(1/2),x, algorithm=""maxima"")","\frac{\frac{\Gamma\left(-\frac{1}{4}\right) \,_2F_1\left(\begin{matrix} -\frac{1}{2},-\frac{1}{4} \\ \frac{3}{4} \end{matrix} ; -a^{2} x^{4} \right)}{4 \, x \Gamma\left(\frac{3}{4}\right)}}{a} - \frac{1}{a x}"," ",0,"integrate(sqrt(a^2*x^4 + 1)/x^2, x)/a - 1/(a*x)","F",0
43,1,54,0,0.306389," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, \sqrt{\frac{1}{a^{2} x^{4}} + 1} - \frac{1}{2 \, a x^{2}} + \frac{1}{4} \, \log\left(\sqrt{\frac{1}{a^{2} x^{4}} + 1} + 1\right) - \frac{1}{4} \, \log\left(\sqrt{\frac{1}{a^{2} x^{4}} + 1} - 1\right)"," ",0,"-1/2*sqrt(1/(a^2*x^4) + 1) - 1/2/(a*x^2) + 1/4*log(sqrt(1/(a^2*x^4) + 1) + 1) - 1/4*log(sqrt(1/(a^2*x^4) + 1) - 1)","A",0
44,0,0,0,0.000000," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^2,x, algorithm=""maxima"")","\frac{\frac{\Gamma\left(-\frac{3}{4}\right) \,_2F_1\left(\begin{matrix} -\frac{3}{4},-\frac{1}{2} \\ \frac{1}{4} \end{matrix} ; -a^{2} x^{4} \right)}{4 \, x^{3} \Gamma\left(\frac{1}{4}\right)}}{a} - \frac{1}{3 \, a x^{3}}"," ",0,"integrate(sqrt(a^2*x^4 + 1)/x^4, x)/a - 1/3/(a*x^3)","F",0
45,1,92,0,0.310925," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{a^{2} x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1}}{4 \, {\left(a^{2} x^{4} {\left(\frac{1}{a^{2} x^{4}} + 1\right)} - 1\right)}} - \frac{1}{8} \, a \log\left(a x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1} + 1\right) + \frac{1}{8} \, a \log\left(a x^{2} \sqrt{\frac{1}{a^{2} x^{4}} + 1} - 1\right) - \frac{1}{4 \, a x^{4}}"," ",0,"-1/4*a^2*x^2*sqrt(1/(a^2*x^4) + 1)/(a^2*x^4*(1/(a^2*x^4) + 1) - 1) - 1/8*a*log(a*x^2*sqrt(1/(a^2*x^4) + 1) + 1) + 1/8*a*log(a*x^2*sqrt(1/(a^2*x^4) + 1) - 1) - 1/4/(a*x^4)","B",0
46,0,0,0,0.000000," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^4,x, algorithm=""maxima"")","\frac{\frac{\Gamma\left(-\frac{5}{4}\right) \,_2F_1\left(\begin{matrix} -\frac{5}{4},-\frac{1}{2} \\ -\frac{1}{4} \end{matrix} ; -a^{2} x^{4} \right)}{4 \, x^{5} \Gamma\left(-\frac{1}{4}\right)}}{a} - \frac{1}{5 \, a x^{5}}"," ",0,"integrate(sqrt(a^2*x^4 + 1)/x^6, x)/a - 1/5/(a*x^5)","F",0
47,1,25,0,0.320662," ","integrate((1/a/x^2+(1+1/a^2/x^4)^(1/2))/x^5,x, algorithm=""maxima"")","-\frac{1}{6} \, a^{2} {\left(\frac{1}{a^{2} x^{4}} + 1\right)}^{\frac{3}{2}} - \frac{1}{6 \, a x^{6}}"," ",0,"-1/6*a^2*(1/(a^2*x^4) + 1)^(3/2) - 1/6/(a*x^6)","A",0
48,-2,0,0,0.000000," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^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
49,1,117,0,0.312243," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^4,x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} + \frac{2 \, x^{3}}{3 \, a^{2}} + \frac{\frac{2 \, {\left({\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + \sqrt{\frac{1}{a^{2} x^{2}} + 1}\right)}}{a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{2} - 2 \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} + a^{4}} - \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{a^{4}} + \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{a^{4}}}{8 \, a}"," ",0,"1/5*x^5 + 2/3*x^3/a^2 + 1/8*(2*((1/(a^2*x^2) + 1)^(3/2) + sqrt(1/(a^2*x^2) + 1))/(a^4*(1/(a^2*x^2) + 1)^2 - 2*a^4*(1/(a^2*x^2) + 1) + a^4) - log(sqrt(1/(a^2*x^2) + 1) + 1)/a^4 + log(sqrt(1/(a^2*x^2) + 1) - 1)/a^4)/a","A",0
50,1,32,0,0.305496," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} + \frac{2 \, x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}}}{3 \, a} + \frac{x^{2}}{a^{2}}"," ",0,"1/4*x^4 + 2/3*x^3*(1/(a^2*x^2) + 1)^(3/2)/a + x^2/a^2","A",0
51,1,89,0,0.322476," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} + \frac{\frac{2 \, \sqrt{\frac{1}{a^{2} x^{2}} + 1}}{a^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} - a^{2}} + \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{a^{2}} - \frac{\log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{a^{2}}}{2 \, a} + \frac{2 \, x}{a^{2}}"," ",0,"1/3*x^3 + 1/2*(2*sqrt(1/(a^2*x^2) + 1)/(a^2*(1/(a^2*x^2) + 1) - a^2) + log(sqrt(1/(a^2*x^2) + 1) + 1)/a^2 - log(sqrt(1/(a^2*x^2) + 1) - 1)/a^2)/a + 2*x/a^2","A",0
52,1,75,0,0.309471," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2*x,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} + \frac{2 \, x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - \frac{\log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right)}{a} + \frac{\log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{a}}{a} + \frac{2 \, \log\left(x\right)}{a^{2}}"," ",0,"1/2*x^2 + (2*x*sqrt(1/(a^2*x^2) + 1) - log(a*x*sqrt(1/(a^2*x^2) + 1) + 1)/a + log(a*x*sqrt(1/(a^2*x^2) + 1) - 1)/a)/a + 2*log(x)/a^2","A",0
53,1,59,0,0.311759," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2,x, algorithm=""maxima"")","x - \frac{2 \, \sqrt{\frac{1}{a^{2} x^{2}} + 1} - \log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) + \log\left(\sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{a} - \frac{2}{a^{2} x}"," ",0,"x - (2*sqrt(1/(a^2*x^2) + 1) - log(sqrt(1/(a^2*x^2) + 1) + 1) + log(sqrt(1/(a^2*x^2) + 1) - 1))/a - 2/(a^2*x)","A",0
54,1,93,0,0.317523," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x,x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{2} x \sqrt{\frac{1}{a^{2} x^{2}} + 1}}{a^{2} x^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} - 1} + a \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) - a \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right)}{2 \, a} - \frac{1}{a^{2} x^{2}} + \log\left(x\right)"," ",0,"-1/2*(2*a^2*x*sqrt(1/(a^2*x^2) + 1)/(a^2*x^2*(1/(a^2*x^2) + 1) - 1) + a*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1) - a*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1))/a - 1/(a^2*x^2) + log(x)","B",0
55,1,28,0,0.306920," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^2,x, algorithm=""maxima"")","-\frac{2}{3} \, a {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - \frac{1}{x} - \frac{2}{3 \, a^{2} x^{3}}"," ",0,"-2/3*a*(1/(a^2*x^2) + 1)^(3/2) - 1/x - 2/3/(a^2*x^3)","A",0
56,1,139,0,0.311595," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^3,x, algorithm=""maxima"")","\frac{a^{3} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) - a^{3} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right) - \frac{2 \, {\left(a^{6} x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} + a^{4} x \sqrt{\frac{1}{a^{2} x^{2}} + 1}\right)}}{a^{4} x^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{2} - 2 \, a^{2} x^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} + 1}}{8 \, a} - \frac{1}{2 \, x^{2}} - \frac{1}{2 \, a^{2} x^{4}}"," ",0,"1/8*(a^3*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1) - a^3*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1) - 2*(a^6*x^3*(1/(a^2*x^2) + 1)^(3/2) + a^4*x*sqrt(1/(a^2*x^2) + 1))/(a^4*x^4*(1/(a^2*x^2) + 1)^2 - 2*a^2*x^2*(1/(a^2*x^2) + 1) + 1))/a - 1/2/x^2 - 1/2/(a^2*x^4)","B",0
57,1,52,0,0.304103," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 5 \, a^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}}\right)}}{15 \, a} - \frac{1}{3 \, x^{3}} - \frac{2}{5 \, a^{2} x^{5}}"," ",0,"-2/15*(3*a^4*(1/(a^2*x^2) + 1)^(5/2) - 5*a^4*(1/(a^2*x^2) + 1)^(3/2))/a - 1/3/x^3 - 2/5/(a^2*x^5)","A",0
58,1,180,0,0.306405," ","integrate((1/a/x+(1+1/a^2/x^2)^(1/2))^2/x^5,x, algorithm=""maxima"")","-\frac{3 \, a^{5} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} + 1\right) - 3 \, a^{5} \log\left(a x \sqrt{\frac{1}{a^{2} x^{2}} + 1} - 1\right) - \frac{2 \, {\left(3 \, a^{10} x^{5} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{5}{2}} - 8 \, a^{8} x^{3} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{\frac{3}{2}} - 3 \, a^{6} x \sqrt{\frac{1}{a^{2} x^{2}} + 1}\right)}}{a^{6} x^{6} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{3} - 3 \, a^{4} x^{4} {\left(\frac{1}{a^{2} x^{2}} + 1\right)}^{2} + 3 \, a^{2} x^{2} {\left(\frac{1}{a^{2} x^{2}} + 1\right)} - 1}}{48 \, a} - \frac{1}{4 \, x^{4}} - \frac{1}{3 \, a^{2} x^{6}}"," ",0,"-1/48*(3*a^5*log(a*x*sqrt(1/(a^2*x^2) + 1) + 1) - 3*a^5*log(a*x*sqrt(1/(a^2*x^2) + 1) - 1) - 2*(3*a^10*x^5*(1/(a^2*x^2) + 1)^(5/2) - 8*a^8*x^3*(1/(a^2*x^2) + 1)^(3/2) - 3*a^6*x*sqrt(1/(a^2*x^2) + 1))/(a^6*x^6*(1/(a^2*x^2) + 1)^3 - 3*a^4*x^4*(1/(a^2*x^2) + 1)^2 + 3*a^2*x^2*(1/(a^2*x^2) + 1) - 1))/a - 1/4/x^4 - 1/3/(a^2*x^6)","B",0
59,0,0,0,0.000000," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*(d*x)^m/(c^2*x^2+1),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m} {\left(\sqrt{\frac{1}{c^{2} x^{2}} + 1} + \frac{1}{c x}\right)}}{c^{2} x^{2} + 1}\,{d x}"," ",0,"integrate((d*x)^m*(sqrt(1/(c^2*x^2) + 1) + 1/(c*x))/(c^2*x^2 + 1), x)","F",0
60,1,162,0,0.402492," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^5/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{c^{2} x^{3} - 3 \, x}{3 \, c^{5}} - \frac{\frac{2 \, {\left(\frac{5 \, \sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} - \frac{3 \, \left(\frac{c^{2} x^{2} + 1}{x^{2}}\right)^{\frac{3}{2}}}{c^{3}}\right)}}{\frac{2 \, {\left(c^{2} x^{2} + 1\right)}}{c^{2} x^{2}} - \frac{{\left(c^{2} x^{2} + 1\right)}^{2}}{c^{4} x^{4}} - 1} - 3 \, \log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} + 1\right) + 3 \, \log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} - 1\right)}{16 \, c^{6}} + \frac{\arctan\left(c x\right)}{c^{6}}"," ",0,"1/3*(c^2*x^3 - 3*x)/c^5 - 1/16*(2*(5*sqrt((c^2*x^2 + 1)/x^2)/c - 3*((c^2*x^2 + 1)/x^2)^(3/2)/c^3)/(2*(c^2*x^2 + 1)/(c^2*x^2) - (c^2*x^2 + 1)^2/(c^4*x^4) - 1) - 3*log(sqrt((c^2*x^2 + 1)/x^2)/c + 1) + 3*log(sqrt((c^2*x^2 + 1)/x^2)/c - 1))/c^6 + arctan(c*x)/c^6","B",0
61,1,49,0,0.321995," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^4/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{x^{2}}{2 \, c^{3}} + \frac{\sqrt{c^{2} x^{2} + 1} {\left(c^{2} x^{2} - 2\right)}}{3 \, c^{5}} - \frac{\log\left(c^{2} x^{2} + 1\right)}{2 \, c^{5}}"," ",0,"1/2*x^2/c^3 + 1/3*sqrt(c^2*x^2 + 1)*(c^2*x^2 - 2)/c^5 - 1/2*log(c^2*x^2 + 1)/c^5","A",0
62,1,107,0,0.492268," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^3/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{x}{c^{3}} + \frac{\frac{2 \, \sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c {\left(\frac{c^{2} x^{2} + 1}{c^{2} x^{2}} - 1\right)}} - \log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} + 1\right) + \log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} - 1\right)}{4 \, c^{4}} - \frac{\arctan\left(c x\right)}{c^{4}}"," ",0,"x/c^3 + 1/4*(2*sqrt((c^2*x^2 + 1)/x^2)/(c*((c^2*x^2 + 1)/(c^2*x^2) - 1)) - log(sqrt((c^2*x^2 + 1)/x^2)/c + 1) + log(sqrt((c^2*x^2 + 1)/x^2)/c - 1))/c^4 - arctan(c*x)/c^4","B",0
63,1,31,0,0.403579," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x^2/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{\log\left(c^{3} x^{2} + c\right)}{2 \, c^{3}} + \frac{\sqrt{c^{2} x^{2} + 1}}{c^{3}}"," ",0,"1/2*log(c^3*x^2 + c)/c^3 + sqrt(c^2*x^2 + 1)/c^3","A",0
64,1,61,0,0.412996," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))*x/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} + 1\right) - \log\left(\frac{\sqrt{\frac{c^{2} x^{2} + 1}{x^{2}}}}{c} - 1\right)}{2 \, c^{2}} + \frac{\arctan\left(c x\right)}{c^{2}}"," ",0,"1/2*(log(sqrt((c^2*x^2 + 1)/x^2)/c + 1) - log(sqrt((c^2*x^2 + 1)/x^2)/c - 1))/c^2 + arctan(c*x)/c^2","B",0
65,0,0,0,0.000000," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/(c^2*x^2+1),x, algorithm=""maxima"")","-\frac{\log\left(c^{2} x^{2} + 1\right)}{2 \, c} + \frac{\log\left(x\right)}{c} + \int \frac{\sqrt{c^{2} x^{2} + 1}}{c^{3} x^{3} + c x}\,{d x}"," ",0,"-1/2*log(c^2*x^2 + 1)/c + log(x)/c + integrate(sqrt(c^2*x^2 + 1)/(c^3*x^3 + c*x), x)","F",0
66,1,34,0,0.426621," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x/(c^2*x^2+1),x, algorithm=""maxima"")","-\frac{\sqrt{c^{2} x^{2} + 1}}{c x} - \frac{1}{c x} - \arctan\left(c x\right)"," ",0,"-sqrt(c^2*x^2 + 1)/(c*x) - 1/(c*x) - arctan(c*x)","A",0
67,0,0,0,0.000000," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x^2/(c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, c \log\left(c^{2} x^{2} + 1\right) - c \log\left(x\right) - \frac{1}{2 \, c x^{2}} + \int \frac{\sqrt{c^{2} x^{2} + 1}}{c^{3} x^{5} + c x^{3}}\,{d x}"," ",0,"1/2*c*log(c^2*x^2 + 1) - c*log(x) - 1/2/(c*x^2) + integrate(sqrt(c^2*x^2 + 1)/(c^3*x^5 + c*x^3), x)","F",0
68,1,56,0,0.425971," ","integrate((1/c/x+(1+1/c^2/x^2)^(1/2))/x^3/(c^2*x^2+1),x, algorithm=""maxima"")","c^{2} \arctan\left(c x\right) + \frac{{\left(2 \, c^{2} x^{2} - 1\right)} \sqrt{c^{2} x^{2} + 1}}{3 \, c x^{3}} + \frac{3 \, c^{2} x^{2} - 1}{3 \, c x^{3}}"," ",0,"c^2*arctan(c*x) + 1/3*(2*c^2*x^2 - 1)*sqrt(c^2*x^2 + 1)/(c*x^3) + 1/3*(3*c^2*x^2 - 1)/(c*x^3)","A",0
69,0,0,0,0.000000," ","integrate(arccsch(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","-\frac{2 \, \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) \log\left(b x + a\right) + {\rm Li}_2\left(-b^{2} x^{2} - 2 \, a b x - a^{2}\right)}{4 \, d} - \frac{\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1} + 1\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^{2} x^{2} + 2 \, a b x + a^{2} + 1} + d}\,{d x}"," ",0,"-1/4*(2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)*log(b*x + a) + dilog(-b^2*x^2 - 2*a*b*x - a^2))/d - 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1))/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^2*x^2 + 2*a*b*x + a^2 + 1) + d), x)","F",0
70,1,57,0,0.307048," ","integrate(x^3*arccsch(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{4} + a\right)} \operatorname{arcsch}\left(b x^{4} + a\right) + \log\left(\sqrt{\frac{1}{{\left(b x^{4} + a\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(b x^{4} + a\right)}^{2}} + 1} - 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arccsch(b*x^4 + a) + log(sqrt(1/(b*x^4 + a)^2 + 1) + 1) - log(sqrt(1/(b*x^4 + a)^2 + 1) - 1))/b","A",0
71,1,60,0,0.314770," ","integrate(x^(-1+n)*arccsch(a+b*x^n),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{n} + a\right)} \operatorname{arcsch}\left(b x^{n} + a\right) + \log\left(\sqrt{\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} + 1\right) - \log\left(\sqrt{\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1} - 1\right)}{2 \, b n}"," ",0,"1/2*(2*(b*x^n + a)*arccsch(b*x^n + a) + log(sqrt(1/(b*x^n + a)^2 + 1) + 1) - log(sqrt(1/(b*x^n + a)^2 + 1) - 1))/(b*n)","A",0
