1,1,209,0,0.407381," ","integrate(x^5*(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{3} x^{6} - 3 \, b d^{2} x^{4} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) + 6 \, b d x^{2} {\rm Li}_2\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) - 6 \, b d x^{2} {\rm Li}_2\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right) + 3 \, b c^{2} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right) + 3 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \log\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right) + 1\right) - 6 \, b {\rm polylog}\left(3, \cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) + 6 \, b {\rm polylog}\left(3, -\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right)}{6 \, d^{3}}"," ",0,"1/6*(a*d^3*x^6 - 3*b*d^2*x^4*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) + 6*b*d*x^2*dilog(cosh(d*x^2 + c) + sinh(d*x^2 + c)) - 6*b*d*x^2*dilog(-cosh(d*x^2 + c) - sinh(d*x^2 + c)) + 3*b*c^2*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1) + 3*(b*d^2*x^4 - b*c^2)*log(-cosh(d*x^2 + c) - sinh(d*x^2 + c) + 1) - 6*b*polylog(3, cosh(d*x^2 + c) + sinh(d*x^2 + c)) + 6*b*polylog(3, -cosh(d*x^2 + c) - sinh(d*x^2 + c)))/d^3","C",0
2,0,0,0,0.413002," ","integrate(x^4*(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{4} \operatorname{csch}\left(d x^{2} + c\right) + a x^{4}, x\right)"," ",0,"integral(b*x^4*csch(d*x^2 + c) + a*x^4, x)","F",0
3,1,144,0,0.441330," ","integrate(x^3*(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{4} - 2 \, b d x^{2} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) - 2 \, b c \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right) + 2 \, b {\rm Li}_2\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) - 2 \, b {\rm Li}_2\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right) + 2 \, {\left(b d x^{2} + b c\right)} \log\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right) + 1\right)}{4 \, d^{2}}"," ",0,"1/4*(a*d^2*x^4 - 2*b*d*x^2*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) - 2*b*c*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1) + 2*b*dilog(cosh(d*x^2 + c) + sinh(d*x^2 + c)) - 2*b*dilog(-cosh(d*x^2 + c) - sinh(d*x^2 + c)) + 2*(b*d*x^2 + b*c)*log(-cosh(d*x^2 + c) - sinh(d*x^2 + c) + 1))/d^2","B",0
4,0,0,0,0.435834," ","integrate(x^2*(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \operatorname{csch}\left(d x^{2} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*csch(d*x^2 + c) + a*x^2, x)","F",0
5,1,55,0,0.446107," ","integrate(x*(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d x^{2} - b \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) + b \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right)}{2 \, d}"," ",0,"1/2*(a*d*x^2 - b*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) + b*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1))/d","B",0
6,0,0,0,0.431675," ","integrate((a+b*csch(d*x^2+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d x^{2} + c\right) + a}{x}, x\right)"," ",0,"integral((b*csch(d*x^2 + c) + a)/x, x)","F",0
7,0,0,0,0.426927," ","integrate((a+b*csch(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csch(d*x^2 + c) + a)/x^2, x)","F",0
8,1,1031,0,0.500969," ","integrate(x^5*(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} d^{3} x^{6} + 6 \, b^{2} c^{2} - {\left(a^{2} d^{3} x^{6} - 6 \, b^{2} d^{2} x^{4} + 6 \, b^{2} c^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} d^{3} x^{6} - 6 \, b^{2} d^{2} x^{4} + 6 \, b^{2} c^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a^{2} d^{3} x^{6} - 6 \, b^{2} d^{2} x^{4} + 6 \, b^{2} c^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} + 6 \, {\left(2 \, a b d x^{2} - {\left(2 \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(2 \, a b d x^{2} + b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} + b^{2}\right)} {\rm Li}_2\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) - 6 \, {\left(2 \, a b d x^{2} - {\left(2 \, a b d x^{2} - b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a b d x^{2} - b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(2 \, a b d x^{2} - b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - b^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right) - 6 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2} - {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a b d^{2} x^{4} - b^{2} d x^{2}\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) + 6 \, {\left(a b c^{2} - b^{2} c - {\left(a b c^{2} - b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a b c^{2} - b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a b c^{2} - b^{2} c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right) + 6 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c - {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a b d^{2} x^{4} + b^{2} d x^{2} - a b c^{2} + b^{2} c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right) + 1\right) + 12 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} {\rm polylog}\left(3, \cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) - 12 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} {\rm polylog}\left(3, -\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right)}{6 \, {\left(d^{3} \cosh\left(d x^{2} + c\right)^{2} + 2 \, d^{3} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + d^{3} \sinh\left(d x^{2} + c\right)^{2} - d^{3}\right)}}"," ",0,"-1/6*(a^2*d^3*x^6 + 6*b^2*c^2 - (a^2*d^3*x^6 - 6*b^2*d^2*x^4 + 6*b^2*c^2)*cosh(d*x^2 + c)^2 - 2*(a^2*d^3*x^6 - 6*b^2*d^2*x^4 + 6*b^2*c^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a^2*d^3*x^6 - 6*b^2*d^2*x^4 + 6*b^2*c^2)*sinh(d*x^2 + c)^2 + 6*(2*a*b*d*x^2 - (2*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)^2 - 2*(2*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (2*a*b*d*x^2 + b^2)*sinh(d*x^2 + c)^2 + b^2)*dilog(cosh(d*x^2 + c) + sinh(d*x^2 + c)) - 6*(2*a*b*d*x^2 - (2*a*b*d*x^2 - b^2)*cosh(d*x^2 + c)^2 - 2*(2*a*b*d*x^2 - b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (2*a*b*d*x^2 - b^2)*sinh(d*x^2 + c)^2 - b^2)*dilog(-cosh(d*x^2 + c) - sinh(d*x^2 + c)) - 6*(a*b*d^2*x^4 - b^2*d*x^2 - (a*b*d^2*x^4 - b^2*d*x^2)*cosh(d*x^2 + c)^2 - 2*(a*b*d^2*x^4 - b^2*d*x^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a*b*d^2*x^4 - b^2*d*x^2)*sinh(d*x^2 + c)^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) + 6*(a*b*c^2 - b^2*c - (a*b*c^2 - b^2*c)*cosh(d*x^2 + c)^2 - 2*(a*b*c^2 - b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a*b*c^2 - b^2*c)*sinh(d*x^2 + c)^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1) + 6*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c - (a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*cosh(d*x^2 + c)^2 - 2*(a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a*b*d^2*x^4 + b^2*d*x^2 - a*b*c^2 + b^2*c)*sinh(d*x^2 + c)^2)*log(-cosh(d*x^2 + c) - sinh(d*x^2 + c) + 1) + 12*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*polylog(3, cosh(d*x^2 + c) + sinh(d*x^2 + c)) - 12*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*polylog(3, -cosh(d*x^2 + c) - sinh(d*x^2 + c)))/(d^3*cosh(d*x^2 + c)^2 + 2*d^3*cosh(d*x^2 + c)*sinh(d*x^2 + c) + d^3*sinh(d*x^2 + c)^2 - d^3)","C",0
9,0,0,0,0.447140," ","integrate(x^4*(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{4} \operatorname{csch}\left(d x^{2} + c\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*csch(d*x^2 + c)^2 + 2*a*b*x^4*csch(d*x^2 + c) + a^2*x^4, x)","F",0
10,1,683,0,0.431002," ","integrate(x^3*(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} d^{2} x^{4} - 4 \, b^{2} c - {\left(a^{2} d^{2} x^{4} - 4 \, b^{2} d x^{2} - 4 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} d^{2} x^{4} - 4 \, b^{2} d x^{2} - 4 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a^{2} d^{2} x^{4} - 4 \, b^{2} d x^{2} - 4 \, b^{2} c\right)} \sinh\left(d x^{2} + c\right)^{2} - 4 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} {\rm Li}_2\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right) + 4 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} {\rm Li}_2\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right)\right) - 2 \, {\left(2 \, a b d x^{2} - {\left(2 \, a b d x^{2} - b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a b d x^{2} - b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(2 \, a b d x^{2} - b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - b^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) - 2 \, {\left(2 \, a b c - {\left(2 \, a b c - b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a b c - b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(2 \, a b c - b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - b^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right) + 4 \, {\left(a b d x^{2} + a b c - {\left(a b d x^{2} + a b c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a b d x^{2} + a b c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - {\left(a b d x^{2} + a b c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(-\cosh\left(d x^{2} + c\right) - \sinh\left(d x^{2} + c\right) + 1\right)}{4 \, {\left(d^{2} \cosh\left(d x^{2} + c\right)^{2} + 2 \, d^{2} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + d^{2} \sinh\left(d x^{2} + c\right)^{2} - d^{2}\right)}}"," ",0,"-1/4*(a^2*d^2*x^4 - 4*b^2*c - (a^2*d^2*x^4 - 4*b^2*d*x^2 - 4*b^2*c)*cosh(d*x^2 + c)^2 - 2*(a^2*d^2*x^4 - 4*b^2*d*x^2 - 4*b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a^2*d^2*x^4 - 4*b^2*d*x^2 - 4*b^2*c)*sinh(d*x^2 + c)^2 - 4*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*dilog(cosh(d*x^2 + c) + sinh(d*x^2 + c)) + 4*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*dilog(-cosh(d*x^2 + c) - sinh(d*x^2 + c)) - 2*(2*a*b*d*x^2 - (2*a*b*d*x^2 - b^2)*cosh(d*x^2 + c)^2 - 2*(2*a*b*d*x^2 - b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (2*a*b*d*x^2 - b^2)*sinh(d*x^2 + c)^2 - b^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) - 2*(2*a*b*c - (2*a*b*c - b^2)*cosh(d*x^2 + c)^2 - 2*(2*a*b*c - b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (2*a*b*c - b^2)*sinh(d*x^2 + c)^2 - b^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1) + 4*(a*b*d*x^2 + a*b*c - (a*b*d*x^2 + a*b*c)*cosh(d*x^2 + c)^2 - 2*(a*b*d*x^2 + a*b*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - (a*b*d*x^2 + a*b*c)*sinh(d*x^2 + c)^2)*log(-cosh(d*x^2 + c) - sinh(d*x^2 + c) + 1))/(d^2*cosh(d*x^2 + c)^2 + 2*d^2*cosh(d*x^2 + c)*sinh(d*x^2 + c) + d^2*sinh(d*x^2 + c)^2 - d^2)","B",0
11,0,0,0,0.397907," ","integrate(x^2*(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \operatorname{csch}\left(d x^{2} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*csch(d*x^2 + c)^2 + 2*a*b*x^2*csch(d*x^2 + c) + a^2*x^2, x)","F",0
12,1,271,0,0.495653," ","integrate(x*(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{a^{2} d x^{2} \cosh\left(d x^{2} + c\right)^{2} + 2 \, a^{2} d x^{2} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a^{2} d x^{2} \sinh\left(d x^{2} + c\right)^{2} - a^{2} d x^{2} - 2 \, b^{2} - 2 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + 1\right) + 2 \, {\left(a b \cosh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + a b \sinh\left(d x^{2} + c\right)^{2} - a b\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - 1\right)}{2 \, {\left(d \cosh\left(d x^{2} + c\right)^{2} + 2 \, d \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + d \sinh\left(d x^{2} + c\right)^{2} - d\right)}}"," ",0,"1/2*(a^2*d*x^2*cosh(d*x^2 + c)^2 + 2*a^2*d*x^2*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a^2*d*x^2*sinh(d*x^2 + c)^2 - a^2*d*x^2 - 2*b^2 - 2*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + 1) + 2*(a*b*cosh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + a*b*sinh(d*x^2 + c)^2 - a*b)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - 1))/(d*cosh(d*x^2 + c)^2 + 2*d*cosh(d*x^2 + c)*sinh(d*x^2 + c) + d*sinh(d*x^2 + c)^2 - d)","B",0
13,0,0,0,0.415511," ","integrate((a+b*csch(d*x^2+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d x^{2} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*csch(d*x^2 + c)^2 + 2*a*b*csch(d*x^2 + c) + a^2)/x, x)","F",0
14,0,0,0,0.413580," ","integrate((a+b*csch(d*x^2+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d x^{2} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*csch(d*x^2 + c)^2 + 2*a*b*csch(d*x^2 + c) + a^2)/x^2, x)","F",0
15,1,2590,0,0.584214," ","integrate(x*csch(b*x^2+a)^7,x, algorithm=""fricas"")","-\frac{30 \, \cosh\left(b x^{2} + a\right)^{11} + 330 \, \cosh\left(b x^{2} + a\right) \sinh\left(b x^{2} + a\right)^{10} + 30 \, \sinh\left(b x^{2} + a\right)^{11} + 10 \, {\left(165 \, \cosh\left(b x^{2} + a\right)^{2} - 17\right)} \sinh\left(b x^{2} + a\right)^{9} - 170 \, \cosh\left(b x^{2} + a\right)^{9} + 90 \, {\left(55 \, \cosh\left(b x^{2} + a\right)^{3} - 17 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{8} + 36 \, {\left(275 \, \cosh\left(b x^{2} + a\right)^{4} - 170 \, \cosh\left(b x^{2} + a\right)^{2} + 11\right)} \sinh\left(b x^{2} + a\right)^{7} + 396 \, \cosh\left(b x^{2} + a\right)^{7} + 84 \, {\left(165 \, \cosh\left(b x^{2} + a\right)^{5} - 170 \, \cosh\left(b x^{2} + a\right)^{3} + 33 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{6} + 36 \, {\left(385 \, \cosh\left(b x^{2} + a\right)^{6} - 595 \, \cosh\left(b x^{2} + a\right)^{4} + 231 \, \cosh\left(b x^{2} + a\right)^{2} + 11\right)} \sinh\left(b x^{2} + a\right)^{5} + 396 \, \cosh\left(b x^{2} + a\right)^{5} + 180 \, {\left(55 \, \cosh\left(b x^{2} + a\right)^{7} - 119 \, \cosh\left(b x^{2} + a\right)^{5} + 77 \, \cosh\left(b x^{2} + a\right)^{3} + 11 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{4} + 10 \, {\left(495 \, \cosh\left(b x^{2} + a\right)^{8} - 1428 \, \cosh\left(b x^{2} + a\right)^{6} + 1386 \, \cosh\left(b x^{2} + a\right)^{4} + 396 \, \cosh\left(b x^{2} + a\right)^{2} - 17\right)} \sinh\left(b x^{2} + a\right)^{3} - 170 \, \cosh\left(b x^{2} + a\right)^{3} + 6 \, {\left(275 \, \cosh\left(b x^{2} + a\right)^{9} - 1020 \, \cosh\left(b x^{2} + a\right)^{7} + 1386 \, \cosh\left(b x^{2} + a\right)^{5} + 660 \, \cosh\left(b x^{2} + a\right)^{3} - 85 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{2} - 15 \, {\left(\cosh\left(b x^{2} + a\right)^{12} + 12 \, \cosh\left(b x^{2} + a\right) \sinh\left(b x^{2} + a\right)^{11} + \sinh\left(b x^{2} + a\right)^{12} + 6 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{2} - 1\right)} \sinh\left(b x^{2} + a\right)^{10} - 6 \, \cosh\left(b x^{2} + a\right)^{10} + 20 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{3} - 3 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{9} + 15 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{4} - 18 \, \cosh\left(b x^{2} + a\right)^{2} + 1\right)} \sinh\left(b x^{2} + a\right)^{8} + 15 \, \cosh\left(b x^{2} + a\right)^{8} + 24 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{5} - 30 \, \cosh\left(b x^{2} + a\right)^{3} + 5 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{7} + 4 \, {\left(231 \, \cosh\left(b x^{2} + a\right)^{6} - 315 \, \cosh\left(b x^{2} + a\right)^{4} + 105 \, \cosh\left(b x^{2} + a\right)^{2} - 5\right)} \sinh\left(b x^{2} + a\right)^{6} - 20 \, \cosh\left(b x^{2} + a\right)^{6} + 24 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{7} - 63 \, \cosh\left(b x^{2} + a\right)^{5} + 35 \, \cosh\left(b x^{2} + a\right)^{3} - 5 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{5} + 15 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{8} - 84 \, \cosh\left(b x^{2} + a\right)^{6} + 70 \, \cosh\left(b x^{2} + a\right)^{4} - 20 \, \cosh\left(b x^{2} + a\right)^{2} + 1\right)} \sinh\left(b x^{2} + a\right)^{4} + 15 \, \cosh\left(b x^{2} + a\right)^{4} + 20 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{9} - 36 \, \cosh\left(b x^{2} + a\right)^{7} + 42 \, \cosh\left(b x^{2} + a\right)^{5} - 20 \, \cosh\left(b x^{2} + a\right)^{3} + 3 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{3} + 6 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{10} - 45 \, \cosh\left(b x^{2} + a\right)^{8} + 70 \, \cosh\left(b x^{2} + a\right)^{6} - 50 \, \cosh\left(b x^{2} + a\right)^{4} + 15 \, \cosh\left(b x^{2} + a\right)^{2} - 1\right)} \sinh\left(b x^{2} + a\right)^{2} - 6 \, \cosh\left(b x^{2} + a\right)^{2} + 12 \, {\left(\cosh\left(b x^{2} + a\right)^{11} - 5 \, \cosh\left(b x^{2} + a\right)^{9} + 10 \, \cosh\left(b x^{2} + a\right)^{7} - 10 \, \cosh\left(b x^{2} + a\right)^{5} + 5 \, \cosh\left(b x^{2} + a\right)^{3} - \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right) + 1\right)} \log\left(\cosh\left(b x^{2} + a\right) + \sinh\left(b x^{2} + a\right) + 1\right) + 15 \, {\left(\cosh\left(b x^{2} + a\right)^{12} + 12 \, \cosh\left(b x^{2} + a\right) \sinh\left(b x^{2} + a\right)^{11} + \sinh\left(b x^{2} + a\right)^{12} + 6 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{2} - 1\right)} \sinh\left(b x^{2} + a\right)^{10} - 6 \, \cosh\left(b x^{2} + a\right)^{10} + 20 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{3} - 3 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{9} + 15 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{4} - 18 \, \cosh\left(b x^{2} + a\right)^{2} + 1\right)} \sinh\left(b x^{2} + a\right)^{8} + 15 \, \cosh\left(b x^{2} + a\right)^{8} + 24 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{5} - 30 \, \cosh\left(b x^{2} + a\right)^{3} + 5 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{7} + 4 \, {\left(231 \, \cosh\left(b x^{2} + a\right)^{6} - 315 \, \cosh\left(b x^{2} + a\right)^{4} + 105 \, \cosh\left(b x^{2} + a\right)^{2} - 5\right)} \sinh\left(b x^{2} + a\right)^{6} - 20 \, \cosh\left(b x^{2} + a\right)^{6} + 24 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{7} - 63 \, \cosh\left(b x^{2} + a\right)^{5} + 35 \, \cosh\left(b x^{2} + a\right)^{3} - 5 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{5} + 15 \, {\left(33 \, \cosh\left(b x^{2} + a\right)^{8} - 84 \, \cosh\left(b x^{2} + a\right)^{6} + 70 \, \cosh\left(b x^{2} + a\right)^{4} - 20 \, \cosh\left(b x^{2} + a\right)^{2} + 1\right)} \sinh\left(b x^{2} + a\right)^{4} + 15 \, \cosh\left(b x^{2} + a\right)^{4} + 20 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{9} - 36 \, \cosh\left(b x^{2} + a\right)^{7} + 42 \, \cosh\left(b x^{2} + a\right)^{5} - 20 \, \cosh\left(b x^{2} + a\right)^{3} + 3 \, \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{3} + 6 \, {\left(11 \, \cosh\left(b x^{2} + a\right)^{10} - 45 \, \cosh\left(b x^{2} + a\right)^{8} + 70 \, \cosh\left(b x^{2} + a\right)^{6} - 50 \, \cosh\left(b x^{2} + a\right)^{4} + 15 \, \cosh\left(b x^{2} + a\right)^{2} - 1\right)} \sinh\left(b x^{2} + a\right)^{2} - 6 \, \cosh\left(b x^{2} + a\right)^{2} + 12 \, {\left(\cosh\left(b x^{2} + a\right)^{11} - 5 \, \cosh\left(b x^{2} + a\right)^{9} + 10 \, \cosh\left(b x^{2} + a\right)^{7} - 10 \, \cosh\left(b x^{2} + a\right)^{5} + 5 \, \cosh\left(b x^{2} + a\right)^{3} - \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right) + 1\right)} \log\left(\cosh\left(b x^{2} + a\right) + \sinh\left(b x^{2} + a\right) - 1\right) + 6 \, {\left(55 \, \cosh\left(b x^{2} + a\right)^{10} - 255 \, \cosh\left(b x^{2} + a\right)^{8} + 462 \, \cosh\left(b x^{2} + a\right)^{6} + 330 \, \cosh\left(b x^{2} + a\right)^{4} - 85 \, \cosh\left(b x^{2} + a\right)^{2} + 5\right)} \sinh\left(b x^{2} + a\right) + 30 \, \cosh\left(b x^{2} + a\right)}{96 \, {\left(b \cosh\left(b x^{2} + a\right)^{12} + 12 \, b \cosh\left(b x^{2} + a\right) \sinh\left(b x^{2} + a\right)^{11} + b \sinh\left(b x^{2} + a\right)^{12} - 6 \, b \cosh\left(b x^{2} + a\right)^{10} + 6 \, {\left(11 \, b \cosh\left(b x^{2} + a\right)^{2} - b\right)} \sinh\left(b x^{2} + a\right)^{10} + 20 \, {\left(11 \, b \cosh\left(b x^{2} + a\right)^{3} - 3 \, b \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{9} + 15 \, b \cosh\left(b x^{2} + a\right)^{8} + 15 \, {\left(33 \, b \cosh\left(b x^{2} + a\right)^{4} - 18 \, b \cosh\left(b x^{2} + a\right)^{2} + b\right)} \sinh\left(b x^{2} + a\right)^{8} + 24 \, {\left(33 \, b \cosh\left(b x^{2} + a\right)^{5} - 30 \, b \cosh\left(b x^{2} + a\right)^{3} + 5 \, b \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{7} - 20 \, b \cosh\left(b x^{2} + a\right)^{6} + 4 \, {\left(231 \, b \cosh\left(b x^{2} + a\right)^{6} - 315 \, b \cosh\left(b x^{2} + a\right)^{4} + 105 \, b \cosh\left(b x^{2} + a\right)^{2} - 5 \, b\right)} \sinh\left(b x^{2} + a\right)^{6} + 24 \, {\left(33 \, b \cosh\left(b x^{2} + a\right)^{7} - 63 \, b \cosh\left(b x^{2} + a\right)^{5} + 35 \, b \cosh\left(b x^{2} + a\right)^{3} - 5 \, b \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{5} + 15 \, b \cosh\left(b x^{2} + a\right)^{4} + 15 \, {\left(33 \, b \cosh\left(b x^{2} + a\right)^{8} - 84 \, b \cosh\left(b x^{2} + a\right)^{6} + 70 \, b \cosh\left(b x^{2} + a\right)^{4} - 20 \, b \cosh\left(b x^{2} + a\right)^{2} + b\right)} \sinh\left(b x^{2} + a\right)^{4} + 20 \, {\left(11 \, b \cosh\left(b x^{2} + a\right)^{9} - 36 \, b \cosh\left(b x^{2} + a\right)^{7} + 42 \, b \cosh\left(b x^{2} + a\right)^{5} - 20 \, b \cosh\left(b x^{2} + a\right)^{3} + 3 \, b \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right)^{3} - 6 \, b \cosh\left(b x^{2} + a\right)^{2} + 6 \, {\left(11 \, b \cosh\left(b x^{2} + a\right)^{10} - 45 \, b \cosh\left(b x^{2} + a\right)^{8} + 70 \, b \cosh\left(b x^{2} + a\right)^{6} - 50 \, b \cosh\left(b x^{2} + a\right)^{4} + 15 \, b \cosh\left(b x^{2} + a\right)^{2} - b\right)} \sinh\left(b x^{2} + a\right)^{2} + 12 \, {\left(b \cosh\left(b x^{2} + a\right)^{11} - 5 \, b \cosh\left(b x^{2} + a\right)^{9} + 10 \, b \cosh\left(b x^{2} + a\right)^{7} - 10 \, b \cosh\left(b x^{2} + a\right)^{5} + 5 \, b \cosh\left(b x^{2} + a\right)^{3} - b \cosh\left(b x^{2} + a\right)\right)} \sinh\left(b x^{2} + a\right) + b\right)}}"," ",0,"-1/96*(30*cosh(b*x^2 + a)^11 + 330*cosh(b*x^2 + a)*sinh(b*x^2 + a)^10 + 30*sinh(b*x^2 + a)^11 + 10*(165*cosh(b*x^2 + a)^2 - 17)*sinh(b*x^2 + a)^9 - 170*cosh(b*x^2 + a)^9 + 90*(55*cosh(b*x^2 + a)^3 - 17*cosh(b*x^2 + a))*sinh(b*x^2 + a)^8 + 36*(275*cosh(b*x^2 + a)^4 - 170*cosh(b*x^2 + a)^2 + 11)*sinh(b*x^2 + a)^7 + 396*cosh(b*x^2 + a)^7 + 84*(165*cosh(b*x^2 + a)^5 - 170*cosh(b*x^2 + a)^3 + 33*cosh(b*x^2 + a))*sinh(b*x^2 + a)^6 + 36*(385*cosh(b*x^2 + a)^6 - 595*cosh(b*x^2 + a)^4 + 231*cosh(b*x^2 + a)^2 + 11)*sinh(b*x^2 + a)^5 + 396*cosh(b*x^2 + a)^5 + 180*(55*cosh(b*x^2 + a)^7 - 119*cosh(b*x^2 + a)^5 + 77*cosh(b*x^2 + a)^3 + 11*cosh(b*x^2 + a))*sinh(b*x^2 + a)^4 + 10*(495*cosh(b*x^2 + a)^8 - 1428*cosh(b*x^2 + a)^6 + 1386*cosh(b*x^2 + a)^4 + 396*cosh(b*x^2 + a)^2 - 17)*sinh(b*x^2 + a)^3 - 170*cosh(b*x^2 + a)^3 + 6*(275*cosh(b*x^2 + a)^9 - 1020*cosh(b*x^2 + a)^7 + 1386*cosh(b*x^2 + a)^5 + 660*cosh(b*x^2 + a)^3 - 85*cosh(b*x^2 + a))*sinh(b*x^2 + a)^2 - 15*(cosh(b*x^2 + a)^12 + 12*cosh(b*x^2 + a)*sinh(b*x^2 + a)^11 + sinh(b*x^2 + a)^12 + 6*(11*cosh(b*x^2 + a)^2 - 1)*sinh(b*x^2 + a)^10 - 6*cosh(b*x^2 + a)^10 + 20*(11*cosh(b*x^2 + a)^3 - 3*cosh(b*x^2 + a))*sinh(b*x^2 + a)^9 + 15*(33*cosh(b*x^2 + a)^4 - 18*cosh(b*x^2 + a)^2 + 1)*sinh(b*x^2 + a)^8 + 15*cosh(b*x^2 + a)^8 + 24*(33*cosh(b*x^2 + a)^5 - 30*cosh(b*x^2 + a)^3 + 5*cosh(b*x^2 + a))*sinh(b*x^2 + a)^7 + 4*(231*cosh(b*x^2 + a)^6 - 315*cosh(b*x^2 + a)^4 + 105*cosh(b*x^2 + a)^2 - 5)*sinh(b*x^2 + a)^6 - 20*cosh(b*x^2 + a)^6 + 24*(33*cosh(b*x^2 + a)^7 - 63*cosh(b*x^2 + a)^5 + 35*cosh(b*x^2 + a)^3 - 5*cosh(b*x^2 + a))*sinh(b*x^2 + a)^5 + 15*(33*cosh(b*x^2 + a)^8 - 84*cosh(b*x^2 + a)^6 + 70*cosh(b*x^2 + a)^4 - 20*cosh(b*x^2 + a)^2 + 1)*sinh(b*x^2 + a)^4 + 15*cosh(b*x^2 + a)^4 + 20*(11*cosh(b*x^2 + a)^9 - 36*cosh(b*x^2 + a)^7 + 42*cosh(b*x^2 + a)^5 - 20*cosh(b*x^2 + a)^3 + 3*cosh(b*x^2 + a))*sinh(b*x^2 + a)^3 + 6*(11*cosh(b*x^2 + a)^10 - 45*cosh(b*x^2 + a)^8 + 70*cosh(b*x^2 + a)^6 - 50*cosh(b*x^2 + a)^4 + 15*cosh(b*x^2 + a)^2 - 1)*sinh(b*x^2 + a)^2 - 6*cosh(b*x^2 + a)^2 + 12*(cosh(b*x^2 + a)^11 - 5*cosh(b*x^2 + a)^9 + 10*cosh(b*x^2 + a)^7 - 10*cosh(b*x^2 + a)^5 + 5*cosh(b*x^2 + a)^3 - cosh(b*x^2 + a))*sinh(b*x^2 + a) + 1)*log(cosh(b*x^2 + a) + sinh(b*x^2 + a) + 1) + 15*(cosh(b*x^2 + a)^12 + 12*cosh(b*x^2 + a)*sinh(b*x^2 + a)^11 + sinh(b*x^2 + a)^12 + 6*(11*cosh(b*x^2 + a)^2 - 1)*sinh(b*x^2 + a)^10 - 6*cosh(b*x^2 + a)^10 + 20*(11*cosh(b*x^2 + a)^3 - 3*cosh(b*x^2 + a))*sinh(b*x^2 + a)^9 + 15*(33*cosh(b*x^2 + a)^4 - 18*cosh(b*x^2 + a)^2 + 1)*sinh(b*x^2 + a)^8 + 15*cosh(b*x^2 + a)^8 + 24*(33*cosh(b*x^2 + a)^5 - 30*cosh(b*x^2 + a)^3 + 5*cosh(b*x^2 + a))*sinh(b*x^2 + a)^7 + 4*(231*cosh(b*x^2 + a)^6 - 315*cosh(b*x^2 + a)^4 + 105*cosh(b*x^2 + a)^2 - 5)*sinh(b*x^2 + a)^6 - 20*cosh(b*x^2 + a)^6 + 24*(33*cosh(b*x^2 + a)^7 - 63*cosh(b*x^2 + a)^5 + 35*cosh(b*x^2 + a)^3 - 5*cosh(b*x^2 + a))*sinh(b*x^2 + a)^5 + 15*(33*cosh(b*x^2 + a)^8 - 84*cosh(b*x^2 + a)^6 + 70*cosh(b*x^2 + a)^4 - 20*cosh(b*x^2 + a)^2 + 1)*sinh(b*x^2 + a)^4 + 15*cosh(b*x^2 + a)^4 + 20*(11*cosh(b*x^2 + a)^9 - 36*cosh(b*x^2 + a)^7 + 42*cosh(b*x^2 + a)^5 - 20*cosh(b*x^2 + a)^3 + 3*cosh(b*x^2 + a))*sinh(b*x^2 + a)^3 + 6*(11*cosh(b*x^2 + a)^10 - 45*cosh(b*x^2 + a)^8 + 70*cosh(b*x^2 + a)^6 - 50*cosh(b*x^2 + a)^4 + 15*cosh(b*x^2 + a)^2 - 1)*sinh(b*x^2 + a)^2 - 6*cosh(b*x^2 + a)^2 + 12*(cosh(b*x^2 + a)^11 - 5*cosh(b*x^2 + a)^9 + 10*cosh(b*x^2 + a)^7 - 10*cosh(b*x^2 + a)^5 + 5*cosh(b*x^2 + a)^3 - cosh(b*x^2 + a))*sinh(b*x^2 + a) + 1)*log(cosh(b*x^2 + a) + sinh(b*x^2 + a) - 1) + 6*(55*cosh(b*x^2 + a)^10 - 255*cosh(b*x^2 + a)^8 + 462*cosh(b*x^2 + a)^6 + 330*cosh(b*x^2 + a)^4 - 85*cosh(b*x^2 + a)^2 + 5)*sinh(b*x^2 + a) + 30*cosh(b*x^2 + a))/(b*cosh(b*x^2 + a)^12 + 12*b*cosh(b*x^2 + a)*sinh(b*x^2 + a)^11 + b*sinh(b*x^2 + a)^12 - 6*b*cosh(b*x^2 + a)^10 + 6*(11*b*cosh(b*x^2 + a)^2 - b)*sinh(b*x^2 + a)^10 + 20*(11*b*cosh(b*x^2 + a)^3 - 3*b*cosh(b*x^2 + a))*sinh(b*x^2 + a)^9 + 15*b*cosh(b*x^2 + a)^8 + 15*(33*b*cosh(b*x^2 + a)^4 - 18*b*cosh(b*x^2 + a)^2 + b)*sinh(b*x^2 + a)^8 + 24*(33*b*cosh(b*x^2 + a)^5 - 30*b*cosh(b*x^2 + a)^3 + 5*b*cosh(b*x^2 + a))*sinh(b*x^2 + a)^7 - 20*b*cosh(b*x^2 + a)^6 + 4*(231*b*cosh(b*x^2 + a)^6 - 315*b*cosh(b*x^2 + a)^4 + 105*b*cosh(b*x^2 + a)^2 - 5*b)*sinh(b*x^2 + a)^6 + 24*(33*b*cosh(b*x^2 + a)^7 - 63*b*cosh(b*x^2 + a)^5 + 35*b*cosh(b*x^2 + a)^3 - 5*b*cosh(b*x^2 + a))*sinh(b*x^2 + a)^5 + 15*b*cosh(b*x^2 + a)^4 + 15*(33*b*cosh(b*x^2 + a)^8 - 84*b*cosh(b*x^2 + a)^6 + 70*b*cosh(b*x^2 + a)^4 - 20*b*cosh(b*x^2 + a)^2 + b)*sinh(b*x^2 + a)^4 + 20*(11*b*cosh(b*x^2 + a)^9 - 36*b*cosh(b*x^2 + a)^7 + 42*b*cosh(b*x^2 + a)^5 - 20*b*cosh(b*x^2 + a)^3 + 3*b*cosh(b*x^2 + a))*sinh(b*x^2 + a)^3 - 6*b*cosh(b*x^2 + a)^2 + 6*(11*b*cosh(b*x^2 + a)^10 - 45*b*cosh(b*x^2 + a)^8 + 70*b*cosh(b*x^2 + a)^6 - 50*b*cosh(b*x^2 + a)^4 + 15*b*cosh(b*x^2 + a)^2 - b)*sinh(b*x^2 + a)^2 + 12*(b*cosh(b*x^2 + a)^11 - 5*b*cosh(b*x^2 + a)^9 + 10*b*cosh(b*x^2 + a)^7 - 10*b*cosh(b*x^2 + a)^5 + 5*b*cosh(b*x^2 + a)^3 - b*cosh(b*x^2 + a))*sinh(b*x^2 + a) + b)","B",0
16,1,686,0,0.432705," ","integrate(x^5/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{3} x^{6} - 6 \, a b d x^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 6 \, a b d x^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 3 \, a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 3 \, a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 6 \, a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}}{a}\right) - 6 \, a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}}{a}\right) - 3 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) + 3 \, {\left(a b d^{2} x^{4} - a b c^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right)}{6 \, {\left(a^{3} + a b^{2}\right)} d^{3}}"," ",0,"1/6*((a^2 + b^2)*d^3*x^6 - 6*a*b*d*x^2*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 6*a*b*d*x^2*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 3*a*b*c^2*sqrt((a^2 + b^2)/a^2)*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 3*a*b*c^2*sqrt((a^2 + b^2)/a^2)*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 6*a*b*sqrt((a^2 + b^2)/a^2)*polylog(3, (b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))/a) - 6*a*b*sqrt((a^2 + b^2)/a^2)*polylog(3, (b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))/a) - 3*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) + 3*(a*b*d^2*x^4 - a*b*c^2)*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a))/((a^3 + a*b^2)*d^3)","C",0
17,0,0,0,0.394235," ","integrate(x^4/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b \operatorname{csch}\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^4/(b*csch(d*x^2 + c) + a), x)","F",0
18,1,505,0,0.533587," ","integrate(x^3/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{2} x^{4} - 2 \, a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 2 \, a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 2 \, a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) - 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) + 2 \, {\left(a b d x^{2} + a b c\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right)}{4 \, {\left(a^{3} + a b^{2}\right)} d^{2}}"," ",0,"1/4*((a^2 + b^2)*d^2*x^4 - 2*a*b*c*sqrt((a^2 + b^2)/a^2)*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 2*a*b*c*sqrt((a^2 + b^2)/a^2)*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 2*a*b*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 2*a*b*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) - 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) + 2*(a*b*d*x^2 + a*b*c)*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a))/((a^3 + a*b^2)*d^2)","B",0
19,0,0,0,0.386263," ","integrate(x^2/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \operatorname{csch}\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*csch(d*x^2 + c) + a), x)","F",0
20,1,213,0,0.440248," ","integrate(x/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d x^{2} + \sqrt{a^{2} + b^{2}} b \log\left(\frac{a^{2} \cosh\left(d x^{2} + c\right)^{2} + a^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) + a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(d x^{2} + c\right) + a b\right)} \sinh\left(d x^{2} + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right) + b\right)}}{a \cosh\left(d x^{2} + c\right)^{2} + a \sinh\left(d x^{2} + c\right)^{2} + 2 \, b \cosh\left(d x^{2} + c\right) + 2 \, {\left(a \cosh\left(d x^{2} + c\right) + b\right)} \sinh\left(d x^{2} + c\right) - a}\right)}{2 \, {\left(a^{3} + a b^{2}\right)} d}"," ",0,"1/2*((a^2 + b^2)*d*x^2 + sqrt(a^2 + b^2)*b*log((a^2*cosh(d*x^2 + c)^2 + a^2*sinh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c) + a^2 + 2*b^2 + 2*(a^2*cosh(d*x^2 + c) + a*b)*sinh(d*x^2 + c) + 2*sqrt(a^2 + b^2)*(a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c) + b))/(a*cosh(d*x^2 + c)^2 + a*sinh(d*x^2 + c)^2 + 2*b*cosh(d*x^2 + c) + 2*(a*cosh(d*x^2 + c) + b)*sinh(d*x^2 + c) - a)))/((a^3 + a*b^2)*d)","B",0
21,0,0,0,0.592008," ","integrate(1/x/(a+b*csch(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{csch}\left(d x^{2} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*csch(d*x^2 + c) + a*x), x)","F",0
22,0,0,0,0.469501," ","integrate((a+b*csch(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csch(d*x^2 + c) + a)/x^2, x)","F",0
23,1,3756,0,0.546926," ","integrate(x^5/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} x^{6} + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} x^{6} - 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} x^{6} - 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} + 6 \, {\left(2 \, a^{4} b + a^{2} b^{3} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}}{a}\right) - 6 \, {\left(2 \, a^{4} b + a^{2} b^{3} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm polylog}\left(3, \frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}}{a}\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} x^{6} - 3 \, {\left(a^{2} b^{3} + b^{5}\right)} d^{2} x^{4} + 6 \, {\left(a^{2} b^{3} + b^{5}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right) + 6 \, {\left(a^{3} b^{2} + a b^{4} - {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(a^{3} b^{2} + a b^{4}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2}\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 6 \, {\left(a^{3} b^{2} + a b^{4} - {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(a^{3} b^{2} + a b^{4}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2}\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 3 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \sinh\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \sinh\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 3 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \sinh\left(d x^{2} + c\right)^{2} + 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \sinh\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 3 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c - 4 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \cosh\left(d x^{2} + c\right) - 4 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(a^{2} b^{3} + b^{5}\right)} c + {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) + 3 \, {\left(2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c - 4 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \cosh\left(d x^{2} + c\right) - 4 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d x^{2} + {\left(a^{2} b^{3} + b^{5}\right)} c + {\left({\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c^{2} + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d^{2} x^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} x^{6} - 3 \, {\left(a^{2} b^{3} + b^{5}\right)} d^{2} x^{4} + 6 \, {\left(a^{2} b^{3} + b^{5}\right)} c^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} x^{6} - 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)}{6 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} \cosh\left(d x^{2} + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{3} \cosh\left(d x^{2} + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3} \cosh\left(d x^{2} + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{3}\right)} \sinh\left(d x^{2} + c\right)\right)}}"," ",0,"-1/6*((a^5 + 2*a^3*b^2 + a*b^4)*d^3*x^6 + 6*(a^3*b^2 + a*b^4)*c^2 - ((a^5 + 2*a^3*b^2 + a*b^4)*d^3*x^6 - 6*(a^3*b^2 + a*b^4)*d^2*x^4 + 6*(a^3*b^2 + a*b^4)*c^2)*cosh(d*x^2 + c)^2 - ((a^5 + 2*a^3*b^2 + a*b^4)*d^3*x^6 - 6*(a^3*b^2 + a*b^4)*d^2*x^4 + 6*(a^3*b^2 + a*b^4)*c^2)*sinh(d*x^2 + c)^2 + 6*(2*a^4*b + a^2*b^3 - (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c)^2 - (2*a^4*b + a^2*b^3)*sinh(d*x^2 + c)^2 - 2*(2*a^3*b^2 + a*b^4)*cosh(d*x^2 + c) - 2*(2*a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*polylog(3, (b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))/a) - 6*(2*a^4*b + a^2*b^3 - (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c)^2 - (2*a^4*b + a^2*b^3)*sinh(d*x^2 + c)^2 - 2*(2*a^3*b^2 + a*b^4)*cosh(d*x^2 + c) - 2*(2*a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*polylog(3, (b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))/a) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^3*x^6 - 3*(a^2*b^3 + b^5)*d^2*x^4 + 6*(a^2*b^3 + b^5)*c^2)*cosh(d*x^2 + c) + 6*(a^3*b^2 + a*b^4 - (a^3*b^2 + a*b^4)*cosh(d*x^2 + c)^2 - (a^3*b^2 + a*b^4)*sinh(d*x^2 + c)^2 - 2*(a^2*b^3 + b^5)*cosh(d*x^2 + c) - 2*(a^2*b^3 + b^5 + (a^3*b^2 + a*b^4)*cosh(d*x^2 + c))*sinh(d*x^2 + c) + ((2*a^4*b + a^2*b^3)*d*x^2*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*d*x^2*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*d*x^2*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*d*x^2 + 2*((2*a^4*b + a^2*b^3)*d*x^2*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*d*x^2)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 6*(a^3*b^2 + a*b^4 - (a^3*b^2 + a*b^4)*cosh(d*x^2 + c)^2 - (a^3*b^2 + a*b^4)*sinh(d*x^2 + c)^2 - 2*(a^2*b^3 + b^5)*cosh(d*x^2 + c) - 2*(a^2*b^3 + b^5 + (a^3*b^2 + a*b^4)*cosh(d*x^2 + c))*sinh(d*x^2 + c) - ((2*a^4*b + a^2*b^3)*d*x^2*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*d*x^2*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*d*x^2*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*d*x^2 + 2*((2*a^4*b + a^2*b^3)*d*x^2*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*d*x^2)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 3*(2*(a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c)^2 + 2*(a^3*b^2 + a*b^4)*c*sinh(d*x^2 + c)^2 + 4*(a^2*b^3 + b^5)*c*cosh(d*x^2 + c) - 2*(a^3*b^2 + a*b^4)*c + 4*((a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c) + (a^2*b^3 + b^5)*c)*sinh(d*x^2 + c) - ((2*a^4*b + a^2*b^3)*c^2*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c^2*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*c^2*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*c^2 + 2*((2*a^4*b + a^2*b^3)*c^2*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*c^2)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 3*(2*(a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c)^2 + 2*(a^3*b^2 + a*b^4)*c*sinh(d*x^2 + c)^2 + 4*(a^2*b^3 + b^5)*c*cosh(d*x^2 + c) - 2*(a^3*b^2 + a*b^4)*c + 4*((a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c) + (a^2*b^3 + b^5)*c)*sinh(d*x^2 + c) + ((2*a^4*b + a^2*b^3)*c^2*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c^2*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*c^2*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*c^2 + 2*((2*a^4*b + a^2*b^3)*c^2*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*c^2)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 3*(2*(a^3*b^2 + a*b^4)*d*x^2 - 2*((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c)^2 - 2*((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*sinh(d*x^2 + c)^2 + 2*(a^3*b^2 + a*b^4)*c - 4*((a^2*b^3 + b^5)*d*x^2 + (a^2*b^3 + b^5)*c)*cosh(d*x^2 + c) - 4*((a^2*b^3 + b^5)*d*x^2 + (a^2*b^3 + b^5)*c + ((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c))*sinh(d*x^2 + c) - ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2 - ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*cosh(d*x^2 + c)^2 - ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*sinh(d*x^2 + c)^2 - 2*((2*a^3*b^2 + a*b^4)*d^2*x^4 - (2*a^3*b^2 + a*b^4)*c^2)*cosh(d*x^2 + c) - 2*((2*a^3*b^2 + a*b^4)*d^2*x^4 - (2*a^3*b^2 + a*b^4)*c^2 + ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) + 3*(2*(a^3*b^2 + a*b^4)*d*x^2 - 2*((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c)^2 - 2*((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*sinh(d*x^2 + c)^2 + 2*(a^3*b^2 + a*b^4)*c - 4*((a^2*b^3 + b^5)*d*x^2 + (a^2*b^3 + b^5)*c)*cosh(d*x^2 + c) - 4*((a^2*b^3 + b^5)*d*x^2 + (a^2*b^3 + b^5)*c + ((a^3*b^2 + a*b^4)*d*x^2 + (a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c))*sinh(d*x^2 + c) + ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2 - ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*cosh(d*x^2 + c)^2 - ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*sinh(d*x^2 + c)^2 - 2*((2*a^3*b^2 + a*b^4)*d^2*x^4 - (2*a^3*b^2 + a*b^4)*c^2)*cosh(d*x^2 + c) - 2*((2*a^3*b^2 + a*b^4)*d^2*x^4 - (2*a^3*b^2 + a*b^4)*c^2 + ((2*a^4*b + a^2*b^3)*d^2*x^4 - (2*a^4*b + a^2*b^3)*c^2)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^3*x^6 - 3*(a^2*b^3 + b^5)*d^2*x^4 + 6*(a^2*b^3 + b^5)*c^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^3*x^6 - 6*(a^3*b^2 + a*b^4)*d^2*x^4 + 6*(a^3*b^2 + a*b^4)*c^2)*cosh(d*x^2 + c))*sinh(d*x^2 + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d^3*cosh(d*x^2 + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^3*sinh(d*x^2 + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d^3*cosh(d*x^2 + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^3 + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d^3*cosh(d*x^2 + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d^3)*sinh(d*x^2 + c))","C",0
24,0,0,0,0.464228," ","integrate(x^4/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^4/(b^2*csch(d*x^2 + c)^2 + 2*a*b*csch(d*x^2 + c) + a^2), x)","F",0
25,1,2383,0,0.480551," ","integrate(x^3/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{4} b + a^{2} b^{3} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) + 2 \, {\left(2 \, a^{4} b + a^{2} b^{3} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} {\rm Li}_2\left(\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a} + 1\right) - 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \sinh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) + {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \sinh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d x^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \log\left(-\frac{b \cosh\left(d x^{2} + c\right) + b \sinh\left(d x^{2} + c\right) - {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - a}{a}\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} x^{4} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d x^{2} - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \cosh\left(d x^{2} + c\right) + 2 \, {\left(a^{3} b^{2} + a b^{4} - {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(a^{3} b^{2} + a b^{4}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 2 \, {\left(a^{3} b^{2} + a b^{4} - {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(a^{3} b^{2} + a b^{4}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \cosh\left(d x^{2} + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \cosh\left(d x^{2} + c\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \cosh\left(d x^{2} + c\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \log\left(2 \, a \cosh\left(d x^{2} + c\right) + 2 \, a \sinh\left(d x^{2} + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} x^{4} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d x^{2} - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} x^{4} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d x^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)}{4 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2} \cosh\left(d x^{2} + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x^{2} + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2}\right)} \sinh\left(d x^{2} + c\right)\right)}}"," ",0,"-1/4*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*x^4 - ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*x^4 - 4*(a^3*b^2 + a*b^4)*d*x^2 - 4*(a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c)^2 - ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*x^4 - 4*(a^3*b^2 + a*b^4)*d*x^2 - 4*(a^3*b^2 + a*b^4)*c)*sinh(d*x^2 + c)^2 - 2*(2*a^4*b + a^2*b^3 - (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c)^2 - (2*a^4*b + a^2*b^3)*sinh(d*x^2 + c)^2 - 2*(2*a^3*b^2 + a*b^4)*cosh(d*x^2 + c) - 2*(2*a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) + 2*(2*a^4*b + a^2*b^3 - (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c)^2 - (2*a^4*b + a^2*b^3)*sinh(d*x^2 + c)^2 - 2*(2*a^3*b^2 + a*b^4)*cosh(d*x^2 + c) - 2*(2*a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*dilog((b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a + 1) - 2*((2*a^4*b + a^2*b^3)*d*x^2 - ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*cosh(d*x^2 + c)^2 - ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*sinh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c - 2*((2*a^3*b^2 + a*b^4)*d*x^2 + (2*a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c) - 2*((2*a^3*b^2 + a*b^4)*d*x^2 + (2*a^3*b^2 + a*b^4)*c + ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) + (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) + 2*((2*a^4*b + a^2*b^3)*d*x^2 - ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*cosh(d*x^2 + c)^2 - ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*sinh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c - 2*((2*a^3*b^2 + a*b^4)*d*x^2 + (2*a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c) - 2*((2*a^3*b^2 + a*b^4)*d*x^2 + (2*a^3*b^2 + a*b^4)*c + ((2*a^4*b + a^2*b^3)*d*x^2 + (2*a^4*b + a^2*b^3)*c)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2)*log(-(b*cosh(d*x^2 + c) + b*sinh(d*x^2 + c) - (a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2) - a)/a) - 4*(a^3*b^2 + a*b^4)*c - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*x^4 - 2*(a^2*b^3 + b^5)*d*x^2 - 4*(a^2*b^3 + b^5)*c)*cosh(d*x^2 + c) + 2*(a^3*b^2 + a*b^4 - (a^3*b^2 + a*b^4)*cosh(d*x^2 + c)^2 - (a^3*b^2 + a*b^4)*sinh(d*x^2 + c)^2 - 2*(a^2*b^3 + b^5)*cosh(d*x^2 + c) - 2*(a^2*b^3 + b^5 + (a^3*b^2 + a*b^4)*cosh(d*x^2 + c))*sinh(d*x^2 + c) + ((2*a^4*b + a^2*b^3)*c*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*c + 2*((2*a^4*b + a^2*b^3)*c*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*c)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 2*(a^3*b^2 + a*b^4 - (a^3*b^2 + a*b^4)*cosh(d*x^2 + c)^2 - (a^3*b^2 + a*b^4)*sinh(d*x^2 + c)^2 - 2*(a^2*b^3 + b^5)*cosh(d*x^2 + c) - 2*(a^2*b^3 + b^5 + (a^3*b^2 + a*b^4)*cosh(d*x^2 + c))*sinh(d*x^2 + c) - ((2*a^4*b + a^2*b^3)*c*cosh(d*x^2 + c)^2 + (2*a^4*b + a^2*b^3)*c*sinh(d*x^2 + c)^2 + 2*(2*a^3*b^2 + a*b^4)*c*cosh(d*x^2 + c) - (2*a^4*b + a^2*b^3)*c + 2*((2*a^4*b + a^2*b^3)*c*cosh(d*x^2 + c) + (2*a^3*b^2 + a*b^4)*c)*sinh(d*x^2 + c))*sqrt((a^2 + b^2)/a^2))*log(2*a*cosh(d*x^2 + c) + 2*a*sinh(d*x^2 + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*x^4 - 2*(a^2*b^3 + b^5)*d*x^2 - 4*(a^2*b^3 + b^5)*c + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*x^4 - 4*(a^3*b^2 + a*b^4)*d*x^2 - 4*(a^3*b^2 + a*b^4)*c)*cosh(d*x^2 + c))*sinh(d*x^2 + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x^2 + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*sinh(d*x^2 + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d^2*cosh(d*x^2 + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2 + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x^2 + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d^2)*sinh(d*x^2 + c))","B",0
26,0,0,0,0.415511," ","integrate(x^2/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*csch(d*x^2 + c)^2 + 2*a*b*csch(d*x^2 + c) + a^2), x)","F",0
27,1,711,0,0.450660," ","integrate(x/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \cosh\left(d x^{2} + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \sinh\left(d x^{2} + c\right)^{2} - 2 \, a^{3} b^{2} - 2 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} - {\left(2 \, a^{3} b + a b^{3} - {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x^{2} + c\right)^{2} - {\left(2 \, a^{3} b + a b^{3}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x^{2} + c\right) - 2 \, {\left(2 \, a^{2} b^{2} + b^{4} + {\left(2 \, a^{3} b + a b^{3}\right)} \cosh\left(d x^{2} + c\right)\right)} \sinh\left(d x^{2} + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{a^{2} \cosh\left(d x^{2} + c\right)^{2} + a^{2} \sinh\left(d x^{2} + c\right)^{2} + 2 \, a b \cosh\left(d x^{2} + c\right) + a^{2} + 2 \, b^{2} + 2 \, {\left(a^{2} \cosh\left(d x^{2} + c\right) + a b\right)} \sinh\left(d x^{2} + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right) + b\right)}}{a \cosh\left(d x^{2} + c\right)^{2} + a \sinh\left(d x^{2} + c\right)^{2} + 2 \, b \cosh\left(d x^{2} + c\right) + 2 \, {\left(a \cosh\left(d x^{2} + c\right) + b\right)} \sinh\left(d x^{2} + c\right) - a}\right) + 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d x^{2}\right)} \cosh\left(d x^{2} + c\right) + 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d x^{2} \cosh\left(d x^{2} + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d x^{2}\right)} \sinh\left(d x^{2} + c\right)}{2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x^{2} + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d x^{2} + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x^{2} + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x^{2} + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x^{2} + c\right)\right)}}"," ",0,"1/2*((a^5 + 2*a^3*b^2 + a*b^4)*d*x^2*cosh(d*x^2 + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d*x^2*sinh(d*x^2 + c)^2 - 2*a^3*b^2 - 2*a*b^4 - (a^5 + 2*a^3*b^2 + a*b^4)*d*x^2 - (2*a^3*b + a*b^3 - (2*a^3*b + a*b^3)*cosh(d*x^2 + c)^2 - (2*a^3*b + a*b^3)*sinh(d*x^2 + c)^2 - 2*(2*a^2*b^2 + b^4)*cosh(d*x^2 + c) - 2*(2*a^2*b^2 + b^4 + (2*a^3*b + a*b^3)*cosh(d*x^2 + c))*sinh(d*x^2 + c))*sqrt(a^2 + b^2)*log((a^2*cosh(d*x^2 + c)^2 + a^2*sinh(d*x^2 + c)^2 + 2*a*b*cosh(d*x^2 + c) + a^2 + 2*b^2 + 2*(a^2*cosh(d*x^2 + c) + a*b)*sinh(d*x^2 + c) + 2*sqrt(a^2 + b^2)*(a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c) + b))/(a*cosh(d*x^2 + c)^2 + a*sinh(d*x^2 + c)^2 + 2*b*cosh(d*x^2 + c) + 2*(a*cosh(d*x^2 + c) + b)*sinh(d*x^2 + c) - a)) + 2*(a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*d*x^2)*cosh(d*x^2 + c) + 2*(a^2*b^3 + b^5 + (a^5 + 2*a^3*b^2 + a*b^4)*d*x^2*cosh(d*x^2 + c) + (a^4*b + 2*a^2*b^3 + b^5)*d*x^2)*sinh(d*x^2 + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x^2 + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d*sinh(d*x^2 + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cosh(d*x^2 + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x^2 + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d)*sinh(d*x^2 + c))","B",0
28,0,0,0,0.407828," ","integrate(1/x/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b x \operatorname{csch}\left(d x^{2} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*csch(d*x^2 + c)^2 + 2*a*b*x*csch(d*x^2 + c) + a^2*x), x)","F",0
29,0,0,0,0.407564," ","integrate(1/x^2/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \operatorname{csch}\left(d x^{2} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*csch(d*x^2 + c)^2 + 2*a*b*x^2*csch(d*x^2 + c) + a^2*x^2), x)","F",0
30,0,0,0,0.390472," ","integrate(1/x^3/(a+b*csch(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \operatorname{csch}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{3} \operatorname{csch}\left(d x^{2} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*csch(d*x^2 + c)^2 + 2*a*b*x^3*csch(d*x^2 + c) + a^2*x^3), x)","F",0
31,0,0,0,0.438754," ","integrate(x^3*(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right) + a x^{3}, x\right)"," ",0,"integral(b*x^3*csch(d*sqrt(x) + c) + a*x^3, x)","F",0
32,0,0,0,0.426183," ","integrate(x^2*(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*csch(d*sqrt(x) + c) + a*x^2, x)","F",0
33,0,0,0,0.425191," ","integrate(x*(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x \operatorname{csch}\left(d \sqrt{x} + c\right) + a x, x\right)"," ",0,"integral(b*x*csch(d*sqrt(x) + c) + a*x, x)","F",0
34,0,0,0,0.429379," ","integrate((a+b*csch(c+d*x^(1/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}{x}, x\right)"," ",0,"integral((b*csch(d*sqrt(x) + c) + a)/x, x)","F",0
35,0,0,0,0.428417," ","integrate((a+b*csch(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csch(d*sqrt(x) + c) + a)/x^2, x)","F",0
36,0,0,0,0.439711," ","integrate(x^3*(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{3}, x\right)"," ",0,"integral(b^2*x^3*csch(d*sqrt(x) + c)^2 + 2*a*b*x^3*csch(d*sqrt(x) + c) + a^2*x^3, x)","F",0
37,0,0,0,0.426678," ","integrate(x^2*(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*csch(d*sqrt(x) + c)^2 + 2*a*b*x^2*csch(d*sqrt(x) + c) + a^2*x^2, x)","F",0
38,0,0,0,0.416662," ","integrate(x*(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*csch(d*sqrt(x) + c)^2 + 2*a*b*x*csch(d*sqrt(x) + c) + a^2*x, x)","F",0
39,0,0,0,0.408915," ","integrate((a+b*csch(c+d*x^(1/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2)/x, x)","F",0
40,0,0,0,0.409326," ","integrate((a+b*csch(c+d*x^(1/2)))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2)/x^2, x)","F",0
41,0,0,0,0.420965," ","integrate(x^3/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^3/(b*csch(d*sqrt(x) + c) + a), x)","F",0
42,0,0,0,0.423146," ","integrate(x^2/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*csch(d*sqrt(x) + c) + a), x)","F",0
43,0,0,0,0.408189," ","integrate(x/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x/(b*csch(d*sqrt(x) + c) + a), x)","F",0
44,0,0,0,0.424404," ","integrate(1/x/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{csch}\left(d \sqrt{x} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*csch(d*sqrt(x) + c) + a*x), x)","F",0
45,0,0,0,0.429586," ","integrate((a+b*csch(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*csch(d*sqrt(x) + c) + a)/x^2, x)","F",0
46,0,0,0,0.437158," ","integrate(x^3/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^3/(b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2), x)","F",0
47,0,0,0,0.432357," ","integrate(x^2/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2), x)","F",0
48,0,0,0,0.449391," ","integrate(x/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2), x)","F",0
49,0,0,0,0.448475," ","integrate(1/x/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*csch(d*sqrt(x) + c)^2 + 2*a*b*x*csch(d*sqrt(x) + c) + a^2*x), x)","F",0
50,0,0,0,0.432849," ","integrate(1/x^2/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*csch(d*sqrt(x) + c)^2 + 2*a*b*x^2*csch(d*sqrt(x) + c) + a^2*x^2), x)","F",0
51,0,0,0,0.421118," ","integrate(x^(3/2)*(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{\frac{3}{2}} \operatorname{csch}\left(d \sqrt{x} + c\right) + a x^{\frac{3}{2}}, x\right)"," ",0,"integral(b*x^(3/2)*csch(d*sqrt(x) + c) + a*x^(3/2), x)","F",0
52,0,0,0,0.474372," ","integrate((a+b*csch(c+d*x^(1/2)))*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a \sqrt{x}, x\right)"," ",0,"integral(b*sqrt(x)*csch(d*sqrt(x) + c) + a*sqrt(x), x)","F",0
53,1,55,0,0.460672," ","integrate((a+b*csch(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a d \sqrt{x} - b \log\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right) + 1\right) + b \log\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right) - 1\right)\right)}}{d}"," ",0,"2*(a*d*sqrt(x) - b*log(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c) + 1) + b*log(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c) - 1))/d","B",0
54,0,0,0,0.397518," ","integrate((a+b*csch(c+d*x^(1/2)))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b*sqrt(x)*csch(d*sqrt(x) + c) + a*sqrt(x))/x^2, x)","F",0
55,0,0,0,0.428869," ","integrate((a+b*csch(c+d*x^(1/2)))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b*sqrt(x)*csch(d*sqrt(x) + c) + a*sqrt(x))/x^3, x)","F",0
56,0,0,0,0.406887," ","integrate(x^(3/2)*(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{\frac{3}{2}} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{\frac{3}{2}} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{\frac{3}{2}}, x\right)"," ",0,"integral(b^2*x^(3/2)*csch(d*sqrt(x) + c)^2 + 2*a*b*x^(3/2)*csch(d*sqrt(x) + c) + a^2*x^(3/2), x)","F",0
57,0,0,0,0.427931," ","integrate((a+b*csch(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}, x\right)"," ",0,"integral(b^2*sqrt(x)*csch(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csch(d*sqrt(x) + c) + a^2*sqrt(x), x)","F",0
58,1,271,0,0.444985," ","integrate((a+b*csch(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d \sqrt{x} \cosh\left(d \sqrt{x} + c\right)^{2} + 2 \, a^{2} d \sqrt{x} \cosh\left(d \sqrt{x} + c\right) \sinh\left(d \sqrt{x} + c\right) + a^{2} d \sqrt{x} \sinh\left(d \sqrt{x} + c\right)^{2} - a^{2} d \sqrt{x} - 2 \, b^{2} - 2 \, {\left(a b \cosh\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \cosh\left(d \sqrt{x} + c\right) \sinh\left(d \sqrt{x} + c\right) + a b \sinh\left(d \sqrt{x} + c\right)^{2} - a b\right)} \log\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right) + 1\right) + 2 \, {\left(a b \cosh\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \cosh\left(d \sqrt{x} + c\right) \sinh\left(d \sqrt{x} + c\right) + a b \sinh\left(d \sqrt{x} + c\right)^{2} - a b\right)} \log\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right) - 1\right)\right)}}{d \cosh\left(d \sqrt{x} + c\right)^{2} + 2 \, d \cosh\left(d \sqrt{x} + c\right) \sinh\left(d \sqrt{x} + c\right) + d \sinh\left(d \sqrt{x} + c\right)^{2} - d}"," ",0,"2*(a^2*d*sqrt(x)*cosh(d*sqrt(x) + c)^2 + 2*a^2*d*sqrt(x)*cosh(d*sqrt(x) + c)*sinh(d*sqrt(x) + c) + a^2*d*sqrt(x)*sinh(d*sqrt(x) + c)^2 - a^2*d*sqrt(x) - 2*b^2 - 2*(a*b*cosh(d*sqrt(x) + c)^2 + 2*a*b*cosh(d*sqrt(x) + c)*sinh(d*sqrt(x) + c) + a*b*sinh(d*sqrt(x) + c)^2 - a*b)*log(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c) + 1) + 2*(a*b*cosh(d*sqrt(x) + c)^2 + 2*a*b*cosh(d*sqrt(x) + c)*sinh(d*sqrt(x) + c) + a*b*sinh(d*sqrt(x) + c)^2 - a*b)*log(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c) - 1))/(d*cosh(d*sqrt(x) + c)^2 + 2*d*cosh(d*sqrt(x) + c)*sinh(d*sqrt(x) + c) + d*sinh(d*sqrt(x) + c)^2 - d)","B",0
59,0,0,0,0.436656," ","integrate((a+b*csch(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b^2*sqrt(x)*csch(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csch(d*sqrt(x) + c) + a^2*sqrt(x))/x^2, x)","F",0
60,0,0,0,0.452701," ","integrate((a+b*csch(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b^2*sqrt(x)*csch(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*csch(d*sqrt(x) + c) + a^2*sqrt(x))/x^3, x)","F",0
61,0,0,0,0.422110," ","integrate(x^(3/2)/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^(3/2)/(b*csch(d*sqrt(x) + c) + a), x)","F",0
62,0,0,0,0.408231," ","integrate(x^(1/2)/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b \operatorname{csch}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(sqrt(x)/(b*csch(d*sqrt(x) + c) + a), x)","F",0
63,1,123,0,0.444578," ","integrate(1/(a+b*csch(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{2} + b^{2}\right)} d \sqrt{x} + \sqrt{a^{2} + b^{2}} b \log\left(\frac{a b + {\left(a^{2} + b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \cosh\left(d \sqrt{x} + c\right) - {\left(b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \sinh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} + b^{2}} a}{a \sinh\left(d \sqrt{x} + c\right) + b}\right)\right)}}{{\left(a^{3} + a b^{2}\right)} d}"," ",0,"2*((a^2 + b^2)*d*sqrt(x) + sqrt(a^2 + b^2)*b*log((a*b + (a^2 + b^2 + sqrt(a^2 + b^2)*b)*cosh(d*sqrt(x) + c) - (b^2 + sqrt(a^2 + b^2)*b)*sinh(d*sqrt(x) + c) + sqrt(a^2 + b^2)*a)/(a*sinh(d*sqrt(x) + c) + b)))/((a^3 + a*b^2)*d)","B",0
64,0,0,0,0.431425," ","integrate(1/x^(3/2)/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^2*csch(d*sqrt(x) + c) + a*x^2), x)","F",0
65,0,0,0,0.432808," ","integrate(1/x^(5/2)/(a+b*csch(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right) + a x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^3*csch(d*sqrt(x) + c) + a*x^3), x)","F",0
66,0,0,0,0.422359," ","integrate(x^(3/2)/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^(3/2)/(b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2), x)","F",0
67,0,0,0,0.432273," ","integrate(x^(1/2)/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*csch(d*sqrt(x) + c)^2 + 2*a*b*csch(d*sqrt(x) + c) + a^2), x)","F",0
68,1,670,0,0.482551," ","integrate(1/(a+b*csch(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a^{3} b^{2} + 2 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} \cosh\left(d \sqrt{x} + c\right)^{2} - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} \sinh\left(d \sqrt{x} + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sqrt{x}\right)} \cosh\left(d \sqrt{x} + c\right) - {\left({\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left(d \sqrt{x} + c\right)^{2} + {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \sinh\left(d \sqrt{x} + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \cosh\left(d \sqrt{x} + c\right) + 2 \, {\left({\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left(d \sqrt{x} + c\right) + {\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}\right)} \sinh\left(d \sqrt{x} + c\right) - {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}}\right)} \log\left(\frac{a b + {\left(a^{2} + b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \cosh\left(d \sqrt{x} + c\right) - {\left(b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \sinh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} + b^{2}} a}{a \sinh\left(d \sqrt{x} + c\right) + b}\right) - 2 \, {\left(a^{2} b^{3} + b^{5} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{x} \cosh\left(d \sqrt{x} + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sqrt{x}\right)} \sinh\left(d \sqrt{x} + c\right)\right)}}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d \sqrt{x} + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d \sqrt{x} + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d \sqrt{x} + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d \sqrt{x} + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d \sqrt{x} + c\right)}"," ",0,"-2*(2*a^3*b^2 + 2*a*b^4 - (a^5 + 2*a^3*b^2 + a*b^4)*d*sqrt(x)*cosh(d*sqrt(x) + c)^2 - (a^5 + 2*a^3*b^2 + a*b^4)*d*sqrt(x)*sinh(d*sqrt(x) + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d*sqrt(x) - 2*(a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*d*sqrt(x))*cosh(d*sqrt(x) + c) - ((2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh(d*sqrt(x) + c)^2 + (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*sinh(d*sqrt(x) + c)^2 + 2*(2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*cosh(d*sqrt(x) + c) + 2*((2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh(d*sqrt(x) + c) + (2*a^2*b^2 + b^4)*sqrt(a^2 + b^2))*sinh(d*sqrt(x) + c) - (2*a^3*b + a*b^3)*sqrt(a^2 + b^2))*log((a*b + (a^2 + b^2 + sqrt(a^2 + b^2)*b)*cosh(d*sqrt(x) + c) - (b^2 + sqrt(a^2 + b^2)*b)*sinh(d*sqrt(x) + c) + sqrt(a^2 + b^2)*a)/(a*sinh(d*sqrt(x) + c) + b)) - 2*(a^2*b^3 + b^5 + (a^5 + 2*a^3*b^2 + a*b^4)*d*sqrt(x)*cosh(d*sqrt(x) + c) + (a^4*b + 2*a^2*b^3 + b^5)*d*sqrt(x))*sinh(d*sqrt(x) + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*sqrt(x) + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d*sinh(d*sqrt(x) + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*cosh(d*sqrt(x) + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*sqrt(x) + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d)*sinh(d*sqrt(x) + c))","B",0
69,0,0,0,0.449640," ","integrate(1/x^(3/2)/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^2*csch(d*sqrt(x) + c)^2 + 2*a*b*x^2*csch(d*sqrt(x) + c) + a^2*x^2), x)","F",0
70,0,0,0,0.446014," ","integrate(1/x^(5/2)/(a+b*csch(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \operatorname{csch}\left(d \sqrt{x} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^3*csch(d*sqrt(x) + c)^2 + 2*a*b*x^3*csch(d*sqrt(x) + c) + a^2*x^3), x)","F",0
71,0,0,0,0.430126," ","integrate((e*x)^m*(a+b*csch(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \operatorname{csch}\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*csch(d*x^n + c) + a)^p, x)","F",0
72,1,180,0,0.420014," ","integrate((e*x)^(-1+n)*(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{a d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) - {\left(b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + {\left(b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + {\left(a d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{d n}"," ",0,"(a*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + a*d*cosh(n*log(x))*sinh((n - 1)*log(e)) - (b*cosh((n - 1)*log(e)) + b*sinh((n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (b*cosh((n - 1)*log(e)) + b*sinh((n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + (a*d*cosh((n - 1)*log(e)) + a*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))/(d*n)","B",0
73,1,555,0,0.435195," ","integrate((e*x)^(-1+2*n)*(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{a d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + a d^{2} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + 2 \, {\left(b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 2 \, {\left(b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 2 \, {\left(b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) - 2 \, {\left(b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + b c \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + 2 \, {\left(b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d \cosh\left(n \log\left(x\right)\right) + b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + 2 \, {\left(a d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{2 \, d^{2} n}"," ",0,"1/2*(a*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 + a*d^2*cosh(n*log(x))^2*sinh((2*n - 1)*log(e)) + (a*d^2*cosh((2*n - 1)*log(e)) + a*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + 2*(b*cosh((2*n - 1)*log(e)) + b*sinh((2*n - 1)*log(e)))*dilog(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 2*(b*cosh((2*n - 1)*log(e)) + b*sinh((2*n - 1)*log(e)))*dilog(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 2*(b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + b*d*cosh(n*log(x))*sinh((2*n - 1)*log(e)) + (b*d*cosh((2*n - 1)*log(e)) + b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) - 2*(b*c*cosh((2*n - 1)*log(e)) + b*c*sinh((2*n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + 2*(b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + b*c*cosh((2*n - 1)*log(e)) + (b*d*cosh(n*log(x)) + b*c)*sinh((2*n - 1)*log(e)) + (b*d*cosh((2*n - 1)*log(e)) + b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + 2*(a*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*d^2*cosh(n*log(x))*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))/(d^2*n)","B",0
74,1,951,0,0.468826," ","integrate((e*x)^(-1+3*n)*(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{a d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} + a d^{3} \cosh\left(n \log\left(x\right)\right)^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} + 3 \, {\left(a d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a d^{3} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + 6 \, {\left(b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 6 \, {\left(b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 3 \, {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + 2 \, {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + 3 \, {\left(b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b c^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + 3 \, {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - b c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) - 6 \, {\left(b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + 6 \, {\left(b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, -\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + 3 \, {\left(a d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + a d^{3} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{3 \, d^{3} n}"," ",0,"1/3*(a*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 + a*d^3*cosh(n*log(x))^3*sinh((3*n - 1)*log(e)) + (a*d^3*cosh((3*n - 1)*log(e)) + a*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 + 3*(a*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a*d^3*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + 6*(b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b*d*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (b*d*cosh((3*n - 1)*log(e)) + b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 6*(b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b*d*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (b*d*cosh((3*n - 1)*log(e)) + b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 3*(b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + b*d^2*cosh(n*log(x))^2*sinh((3*n - 1)*log(e)) + (b*d^2*cosh((3*n - 1)*log(e)) + b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + 2*(b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b*d^2*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + 3*(b*c^2*cosh((3*n - 1)*log(e)) + b*c^2*sinh((3*n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + 3*(b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - b*c^2*cosh((3*n - 1)*log(e)) + (b*d^2*cosh((3*n - 1)*log(e)) + b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (b*d^2*cosh(n*log(x))^2 - b*c^2)*sinh((3*n - 1)*log(e)) + 2*(b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b*d^2*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) - 6*(b*cosh((3*n - 1)*log(e)) + b*sinh((3*n - 1)*log(e)))*polylog(3, cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + 6*(b*cosh((3*n - 1)*log(e)) + b*sinh((3*n - 1)*log(e)))*polylog(3, -cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + 3*(a*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + a*d^3*cosh(n*log(x))^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))/(d^3*n)","C",0
75,1,854,0,0.439981," ","integrate((e*x)^(-1+n)*(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","-\frac{a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a^{2} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a^{2} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, b^{2} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) - 2 \, {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a^{2} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a^{2} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a^{2} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a^{2} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left({\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) - 2 \, {\left({\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + {\left(a^{2} d \cosh\left(n \log\left(x\right)\right) + 2 \, b^{2}\right)} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + a^{2} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{d n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, d n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + d n \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - d n}"," ",0,"-(a^2*d*cosh((n - 1)*log(e))*cosh(n*log(x)) - (a^2*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + a^2*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + (a^2*d*cosh((n - 1)*log(e)) + a^2*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*b^2*cosh((n - 1)*log(e)) - 2*(a^2*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + a^2*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + (a^2*d*cosh((n - 1)*log(e)) + a^2*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^2*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + a^2*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + (a^2*d*cosh((n - 1)*log(e)) + a^2*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*((a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((n - 1)*log(e)) + 2*(a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) - 2*((a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((n - 1)*log(e)) + 2*(a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((n - 1)*log(e)) + a*b*sinh((n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + (a^2*d*cosh(n*log(x)) + 2*b^2)*sinh((n - 1)*log(e)) + (a^2*d*cosh((n - 1)*log(e)) + a^2*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))/(d*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*d*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + d*n*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - d*n)","B",0
76,1,2678,0,0.503829," ","integrate((e*x)^(-1+2*n)*(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","-\frac{a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 4 \, b^{2} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left({\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + 4 \, {\left({\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 2 \, {\left(2 \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(2 \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - b^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 2 \, {\left(2 \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(2 \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + 2 \, {\left({\left({\left(2 \, a b c - b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b c - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left({\left(2 \, a b c - b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b c - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(2 \, a b c - b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b c - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left(2 \, a b c - b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left(2 \, a b c - b^{2}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + 4 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left(n \log\left(x\right)\right) + a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left(n \log\left(x\right)\right) + a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left(n \log\left(x\right)\right) + a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a b d \cosh\left(n \log\left(x\right)\right) + a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + {\left(a^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a^{2} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a^{2} d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{2 \, {\left(d^{2} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, d^{2} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + d^{2} n \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - d^{2} n\right)}}"," ",0,"-1/2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*c*cosh((2*n - 1)*log(e)) - (a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*b^2*c*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh((2*n - 1)*log(e)) + a^2*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^2*cosh(n*log(x))^2 - 4*b^2*d*cosh(n*log(x)) - 4*b^2*c)*sinh((2*n - 1)*log(e)) + 2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh(n*log(x)) - 2*b^2*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*b^2*c*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh((2*n - 1)*log(e)) + a^2*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^2*cosh(n*log(x))^2 - 4*b^2*d*cosh(n*log(x)) - 4*b^2*c)*sinh((2*n - 1)*log(e)) + 2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh(n*log(x)) - 2*b^2*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*b^2*c*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh((2*n - 1)*log(e)) + a^2*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^2*cosh(n*log(x))^2 - 4*b^2*d*cosh(n*log(x)) - 4*b^2*c)*sinh((2*n - 1)*log(e)) + 2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d*cosh((2*n - 1)*log(e)) + (a^2*d^2*cosh(n*log(x)) - 2*b^2*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a^2*d^2*cosh((2*n - 1)*log(e)) + a^2*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 - 4*((a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((2*n - 1)*log(e)) + 2*(a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((2*n - 1)*log(e)))*dilog(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + 4*((a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((2*n - 1)*log(e)) + 2*(a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((2*n - 1)*log(e)) + a*b*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((2*n - 1)*log(e)))*dilog(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 2*(2*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - (2*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((2*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((2*n - 1)*log(e)) + 2*(a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - b^2*cosh((2*n - 1)*log(e)) - 2*(2*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((2*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((2*n - 1)*log(e)) + 2*(a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (2*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((2*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((2*n - 1)*log(e)) + 2*(a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((2*n - 1)*log(e)) + 2*(a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + 2*(((2*a*b*c - b^2)*cosh((2*n - 1)*log(e)) + (2*a*b*c - b^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*((2*a*b*c - b^2)*cosh((2*n - 1)*log(e)) + (2*a*b*c - b^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((2*a*b*c - b^2)*cosh((2*n - 1)*log(e)) + (2*a*b*c - b^2)*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - (2*a*b*c - b^2)*cosh((2*n - 1)*log(e)) - (2*a*b*c - b^2)*sinh((2*n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + 4*(a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*cosh((2*n - 1)*log(e)) - (a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*cosh((2*n - 1)*log(e)) + (a*b*d*cosh(n*log(x)) + a*b*c)*sinh((2*n - 1)*log(e)) + (a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*(a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*cosh((2*n - 1)*log(e)) + (a*b*d*cosh(n*log(x)) + a*b*c)*sinh((2*n - 1)*log(e)) + (a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*cosh((2*n - 1)*log(e)) + (a*b*d*cosh(n*log(x)) + a*b*c)*sinh((2*n - 1)*log(e)) + (a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a*b*d*cosh(n*log(x)) + a*b*c)*sinh((2*n - 1)*log(e)) + (a*b*d*cosh((2*n - 1)*log(e)) + a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (a^2*d^2*cosh(n*log(x))^2 - 4*b^2*c)*sinh((2*n - 1)*log(e)) + 2*(a^2*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a^2*d^2*cosh(n*log(x))*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))/(d^2*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*d^2*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + d^2*n*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - d^2*n)","B",0
77,1,4967,0,0.522617," ","integrate((e*x)^(-1+3*n)*(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","-\frac{a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} + 6 \, b^{2} c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} - {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a^{2} d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right) - 2 \, b^{2} d^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{3} - 6 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 \, b^{2} c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, b^{2} d^{2} \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a^{2} d^{3} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + 6 \, {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) + b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 2 \, {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) + b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) + b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) + b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 6 \, {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 2 \, {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(2 \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(2 \, a b d \cosh\left(n \log\left(x\right)\right) - b^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 6 \, {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - b^{2} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) - 6 \, {\left({\left({\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b c^{2} - b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left({\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b c^{2} - b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b c^{2} - b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - {\left(a b c^{2} - b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 1\right) + 6 \, {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - {\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} + b^{2} d \cosh\left(n \log\left(x\right)\right) + b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) + b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - {\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} + b^{2} d \cosh\left(n \log\left(x\right)\right) + b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) + b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - {\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} + b^{2} d \cosh\left(n \log\left(x\right)\right) + b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) + b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - {\left(a b c^{2} - b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} + b^{2} d \cosh\left(n \log\left(x\right)\right) + b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a b d^{2} \cosh\left(n \log\left(x\right)\right) + b^{2} d\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 1\right) + 12 \, {\left({\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) - 12 \, {\left({\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, -\cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{3} + 6 \, b^{2} c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 \, {\left(a^{2} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + a^{2} d^{3} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{3 \, {\left(d^{3} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, d^{3} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + d^{3} n \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - d^{3} n\right)}}"," ",0,"-1/3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 + 6*b^2*c^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh((3*n - 1)*log(e)) + a^2*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 - (a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 - 6*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + 6*b^2*c^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh((3*n - 1)*log(e)) + a^2*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh(n*log(x)) - 2*b^2*d^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^3*cosh(n*log(x))^3 - 6*b^2*d^2*cosh(n*log(x))^2 + 6*b^2*c^2)*sinh((3*n - 1)*log(e)) + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a^2*d^3*cosh(n*log(x))^2 - 4*b^2*d^2*cosh(n*log(x)))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 - 6*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + 6*b^2*c^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh((3*n - 1)*log(e)) + a^2*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh(n*log(x)) - 2*b^2*d^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^3*cosh(n*log(x))^3 - 6*b^2*d^2*cosh(n*log(x))^2 + 6*b^2*c^2)*sinh((3*n - 1)*log(e)) + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a^2*d^3*cosh(n*log(x))^2 - 4*b^2*d^2*cosh(n*log(x)))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 - 6*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + 6*b^2*c^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh((3*n - 1)*log(e)) + a^2*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 2*b^2*d^2*cosh((3*n - 1)*log(e)) + (a^2*d^3*cosh(n*log(x)) - 2*b^2*d^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a^2*d^3*cosh(n*log(x))^3 - 6*b^2*d^2*cosh(n*log(x))^2 + 6*b^2*c^2)*sinh((3*n - 1)*log(e)) + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 4*b^2*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a^2*d^3*cosh(n*log(x))^2 - 4*b^2*d^2*cosh(n*log(x)))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a^2*d^3*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + 6*(2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - (2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + b^2*cosh((3*n - 1)*log(e)) - 2*(2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (2*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 6*(2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - (2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - b^2*cosh((3*n - 1)*log(e)) - 2*(2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (2*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*cosh((3*n - 1)*log(e)) + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (2*a*b*d*cosh(n*log(x)) - b^2)*sinh((3*n - 1)*log(e)) + 2*(a*b*d*cosh((3*n - 1)*log(e)) + a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 6*(a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - (a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*cosh(n*log(x))^2 - b^2*d*cosh(n*log(x)))*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) - b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*(a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*cosh(n*log(x))^2 - b^2*d*cosh(n*log(x)))*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) - b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*cosh(n*log(x))^2 - b^2*d*cosh(n*log(x)))*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) - b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*cosh(n*log(x))^2 - b^2*d*cosh(n*log(x)))*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) - b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) - 6*(((a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*c^2 - b^2*c)*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*((a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*c^2 - b^2*c)*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*c^2 - b^2*c)*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - (a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) - (a*b*c^2 - b^2*c)*sinh((3*n - 1)*log(e)))*log(cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 1) + 6*(a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - (a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 - (a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*d^2*cosh(n*log(x))^2 - a*b*c^2 + b^2*d*cosh(n*log(x)) + b^2*c)*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) + b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*(a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 - (a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*d^2*cosh(n*log(x))^2 - a*b*c^2 + b^2*d*cosh(n*log(x)) + b^2*c)*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) + b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 - (a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*d^2*cosh(n*log(x))^2 - a*b*c^2 + b^2*d*cosh(n*log(x)) + b^2*c)*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) + b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a*b*d^2*cosh((3*n - 1)*log(e)) + a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 - (a*b*c^2 - b^2*c)*cosh((3*n - 1)*log(e)) + (a*b*d^2*cosh(n*log(x))^2 - a*b*c^2 + b^2*d*cosh(n*log(x)) + b^2*c)*sinh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + b^2*d*cosh((3*n - 1)*log(e)) + (2*a*b*d^2*cosh(n*log(x)) + b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(-cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + 12*((a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((3*n - 1)*log(e)) + 2*(a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((3*n - 1)*log(e)))*polylog(3, cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 12*((a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*cosh((3*n - 1)*log(e)) + 2*(a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*b*cosh((3*n - 1)*log(e)) + a*b*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - a*b*sinh((3*n - 1)*log(e)))*polylog(3, -cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (a^2*d^3*cosh(n*log(x))^3 + 6*b^2*c^2)*sinh((3*n - 1)*log(e)) + 3*(a^2*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + a^2*d^3*cosh(n*log(x))^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))/(d^3*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*d^3*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + d^3*n*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - d^3*n)","C",0
78,1,248,0,0.425504," ","integrate((e*x)^(-1+n)/(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} + b^{2}\right)} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(\sqrt{a^{2} + b^{2}} b \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + \sqrt{a^{2} + b^{2}} b \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \log\left(\frac{a b + {\left(a^{2} + b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sqrt{a^{2} + b^{2}} a}{a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + b}\right) + {\left({\left(a^{2} + b^{2}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} + b^{2}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{{\left(a^{3} + a b^{2}\right)} d n}"," ",0,"((a^2 + b^2)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + (a^2 + b^2)*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + (sqrt(a^2 + b^2)*b*cosh((n - 1)*log(e)) + sqrt(a^2 + b^2)*b*sinh((n - 1)*log(e)))*log((a*b + (a^2 + b^2 + sqrt(a^2 + b^2)*b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (b^2 + sqrt(a^2 + b^2)*b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 + b^2)*a)/(a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + b)) + ((a^2 + b^2)*d*cosh((n - 1)*log(e)) + (a^2 + b^2)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))/((a^3 + a*b^2)*d*n)","B",0
79,1,1183,0,0.490679," ","integrate((e*x)^(-1+2*n)/(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} + b^{2}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} + b^{2}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left(a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a} + 1\right) + 2 \, {\left(a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a} + 1\right) - 2 \, {\left(a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) + 2 \, {\left(a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a}\right) + 2 \, {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + a b c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a}\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} + b^{2}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{2 \, {\left(a^{3} + a b^{2}\right)} d^{2} n}"," ",0,"1/2*((a^2 + b^2)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 + (a^2 + b^2)*d^2*cosh(n*log(x))^2*sinh((2*n - 1)*log(e)) + ((a^2 + b^2)*d^2*cosh((2*n - 1)*log(e)) + (a^2 + b^2)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 - 2*(a*b*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*dilog(((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a + 1) + 2*(a*b*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*dilog(-((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a + 1) - 2*(a*b*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*c*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) + 2*(a*b*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*c*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 2*(a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + a*b*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a) + 2*(a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + a*b*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + a*b*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + a*b*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a) + 2*((a^2 + b^2)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (a^2 + b^2)*d^2*cosh(n*log(x))*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))/((a^3 + a*b^2)*d^2*n)","B",0
80,1,1850,0,0.487717," ","integrate((e*x)^(-1+3*n)/(a+b*csch(c+d*x^n)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{3} + {\left(a^{2} + b^{2}\right)} d^{3} \cosh\left(n \log\left(x\right)\right)^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} + b^{2}\right)} d^{3} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{3} + 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} + b^{2}\right)} d^{3} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - 6 \, {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a} + 1\right) + 6 \, {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} {\rm Li}_2\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a} + 1\right) + 3 \, {\left(a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 3 \, {\left(a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 3 \, {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a}\right) + 3 \, {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right)^{2} - a b c^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left(a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + a b d^{2} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a}\right) + 6 \, {\left(a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, \frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)}{a}\right) - 6 \, {\left(a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + a b \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, -\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)}{a}\right) + 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + {\left(a^{2} + b^{2}\right)} d^{3} \cosh\left(n \log\left(x\right)\right)^{2} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{3 \, {\left(a^{3} + a b^{2}\right)} d^{3} n}"," ",0,"1/3*((a^2 + b^2)*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^3 + (a^2 + b^2)*d^3*cosh(n*log(x))^3*sinh((3*n - 1)*log(e)) + ((a^2 + b^2)*d^3*cosh((3*n - 1)*log(e)) + (a^2 + b^2)*d^3*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^3 + 3*((a^2 + b^2)*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (a^2 + b^2)*d^3*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 - 6*(a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a*b*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*d*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a + 1) + 6*(a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a*b*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (a*b*d*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*d*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(-((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a + 1) + 3*(a*b*c^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*c^2*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 3*(a*b*c^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*c^2*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 3*(a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - a*b*c^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + (a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*d^2*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))^2 - a*b*c^2*sqrt((a^2 + b^2)/a^2))*sinh((3*n - 1)*log(e)) + 2*(a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(-((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a) + 3*(a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - a*b*c^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + (a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*d^2*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))^2 - a*b*c^2*sqrt((a^2 + b^2)/a^2))*sinh((3*n - 1)*log(e)) + 2*(a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + a*b*d^2*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a) + 6*(a*b*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*polylog(3, ((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))/a) - 6*(a*b*sqrt((a^2 + b^2)/a^2)*cosh((3*n - 1)*log(e)) + a*b*sqrt((a^2 + b^2)/a^2)*sinh((3*n - 1)*log(e)))*polylog(3, -((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))/a) + 3*((a^2 + b^2)*d^3*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + (a^2 + b^2)*d^3*cosh(n*log(x))^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))/((a^3 + a*b^2)*d^3*n)","C",0
81,1,1729,0,0.464859," ","integrate((e*x)^(-1+n)/(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) - {\left({\left({\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) - {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, {\left({\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b + a b^{3}\right)} \sqrt{a^{2} + b^{2}} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} \log\left(\frac{a b + {\left(a^{2} + b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(b^{2} + \sqrt{a^{2} + b^{2}} b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + \sqrt{a^{2} + b^{2}} a}{a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + b}\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(2 \, a^{3} b^{2} + 2 \, a b^{4} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right)\right)} \sinh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left({\left(n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d n\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)}"," ",0,"-((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) - ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*((a^4*b + 2*a^2*b^3 + b^5)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + (a^2*b^3 + b^5)*cosh((n - 1)*log(e)) + (a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*d*cosh(n*log(x)))*sinh((n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d*cosh((n - 1)*log(e)) + (a^4*b + 2*a^2*b^3 + b^5)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*(a^3*b^2 + a*b^4)*cosh((n - 1)*log(e)) - (((2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) + (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) + (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) - (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)) + 2*((2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) + (2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*((2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) + (2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)) + ((2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*cosh((n - 1)*log(e)) + (2*a^3*b + a*b^3)*sqrt(a^2 + b^2)*sinh((n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*log((a*b + (a^2 + b^2 + sqrt(a^2 + b^2)*b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (b^2 + sqrt(a^2 + b^2)*b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 + b^2)*a)/(a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + b)) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e))*cosh(n*log(x)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(n*log(x))*sinh((n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^2*b^3 + b^5)*cosh((n - 1)*log(e)) + (a^2*b^3 + b^5 + (a^4*b + 2*a^2*b^3 + b^5)*d*cosh(n*log(x)))*sinh((n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d*cosh((n - 1)*log(e)) + (a^4*b + 2*a^2*b^3 + b^5)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (2*a^3*b^2 + 2*a*b^4 + (a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(n*log(x)))*sinh((n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh((n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d*n*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*n + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d*n)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))","B",0
82,1,8453,0,0.616194," ","integrate((e*x)^(-1+2*n)/(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} b^{3} + b^{5}\right)} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, {\left({\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} {\rm Li}_2\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a} + 1\right) - 2 \, {\left({\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)} {\rm Li}_2\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a} + 1\right) - 2 \, {\left({\left({\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left({\left(a^{2} b^{3} + b^{5} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left({\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a^{2} b^{3} + b^{5} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{3} b^{2} + a b^{4} - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left({\left({\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left({\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left({\left(a^{2} b^{3} + b^{5} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left({\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a^{2} b^{3} + b^{5} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{2} b^{3} + b^{5} + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{3} b^{2} + a b^{4} + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \log\left(2 \, a \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + 2 \, a \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 2 \, a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + 2 \, b\right) - 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(-\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} + b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - a}{a}\right) + 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - 2 \, {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left(n \log\left(x\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} c \sqrt{\frac{a^{2} + b^{2}}{a^{2}}}\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 \, a^{4} b + a^{2} b^{3}\right)} d \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{{\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} - b\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + a}{a}\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)^{2} + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left(n \log\left(x\right)\right) - 4 \, {\left(a^{2} b^{3} + b^{5}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) - {\left(a^{2} b^{3} + b^{5}\right)} d\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 4 \, {\left(a^{3} b^{2} + a b^{4}\right)} c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} \sinh\left(n \log\left(x\right)\right)}{2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n + 2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} n \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d^{2} n\right)} \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right)}}"," ",0,"-1/2*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c)*sinh((2*n - 1)*log(e)) + 2*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 4*(a^3*b^2 + a*b^4)*c*cosh((2*n - 1)*log(e)) - ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c)*sinh((2*n - 1)*log(e)) + 2*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 2*(a^2*b^3 + b^5)*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*(a^2*b^3 + b^5)*c*cosh((2*n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e)) + (a^4*b + 2*a^2*b^3 + b^5)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(n*log(x))^2 - 2*(a^2*b^3 + b^5)*d*cosh(n*log(x)) - 4*(a^2*b^3 + b^5)*c)*sinh((2*n - 1)*log(e)) + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - (a^2*b^3 + b^5)*d*cosh((2*n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(n*log(x)) - (a^2*b^3 + b^5)*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*(((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) - (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)) + 2*((2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*((2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*dilog(((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a + 1) - 2*(((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) - (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)) + 2*((2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*((2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))*dilog(-((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a + 1) - 2*(((a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*((a^2*b^3 + b^5 - (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^2*b^3 + b^5 - (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + 2*(((a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^2*b^3 + b^5 - (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^2*b^3 + b^5 - (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^3*b^2 + a*b^4 - (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 2*(((a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*((a^2*b^3 + b^5 + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^2*b^3 + b^5 + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + 2*(((a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^2*b^3 + b^5 + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*cosh((2*n - 1)*log(e)) + (a^2*b^3 + b^5 + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^3*b^2 + a*b^4 + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)))*log(2*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 2*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 2*a*sqrt((a^2 + b^2)/a^2) + 2*b) - 2*((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) - ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 2*((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-((a*sqrt((a^2 + b^2)/a^2) + b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) + b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - a)/a) + 2*((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) - ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 2*((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - 2*((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^3*b^2 + a*b^4)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^3*b^2 + a*b^4)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh(n*log(x)) + (2*a^4*b + a^2*b^3)*c*sqrt((a^2 + b^2)/a^2))*sinh((2*n - 1)*log(e)) + ((2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*cosh((2*n - 1)*log(e)) + (2*a^4*b + a^2*b^3)*d*sqrt((a^2 + b^2)/a^2)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(((a*sqrt((a^2 + b^2)/a^2) - b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a*sqrt((a^2 + b^2)/a^2) - b)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + a)/a) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 2*(a^2*b^3 + b^5)*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*(a^2*b^3 + b^5)*c*cosh((2*n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e)) + (a^4*b + 2*a^2*b^3 + b^5)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e)) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh((2*n - 1)*log(e)))*sinh(n*log(x))^2 + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*d*cosh(n*log(x)) - 4*(a^3*b^2 + a*b^4)*c)*sinh((2*n - 1)*log(e)) + 2*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d*cosh((2*n - 1)*log(e)) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x)) - 2*(a^3*b^2 + a*b^4)*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(n*log(x))^2 - 2*(a^2*b^3 + b^5)*d*cosh(n*log(x)) - 4*(a^2*b^3 + b^5)*c)*sinh((2*n - 1)*log(e)) + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - (a^2*b^3 + b^5)*d*cosh((2*n - 1)*log(e)) + ((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(n*log(x)) - (a^2*b^3 + b^5)*d)*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + ((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x))^2 - 4*(a^3*b^2 + a*b^4)*c)*sinh((2*n - 1)*log(e)) + 2*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(n*log(x))*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*n*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*d^2*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*n + 2*((a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*n*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)*d^2*n)*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c))","B",0
83,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*csch(c+d*x^n))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
