1,1,254,0,0.424327," ","integrate(x^5*(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{3} x^{6} + 6 i \, b d x^{2} {\rm Li}_2\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) - 6 i \, b d x^{2} {\rm Li}_2\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right)\right) + 3 i \, b c^{2} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + i\right) - 3 i \, b c^{2} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - i\right) + {\left(-3 i \, b d^{2} x^{4} + 3 i \, b c^{2}\right)} \log\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right) + 1\right) + {\left(3 i \, b d^{2} x^{4} - 3 i \, b c^{2}\right)} \log\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right) + 1\right) - 6 i \, b {\rm polylog}\left(3, i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) + 6 i \, b {\rm polylog}\left(3, -i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right)\right)}{6 \, d^{3}}"," ",0,"1/6*(a*d^3*x^6 + 6*I*b*d*x^2*dilog(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) - 6*I*b*d*x^2*dilog(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c)) + 3*I*b*c^2*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + I) - 3*I*b*c^2*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - I) + (-3*I*b*d^2*x^4 + 3*I*b*c^2)*log(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c) + 1) + (3*I*b*d^2*x^4 - 3*I*b*c^2)*log(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c) + 1) - 6*I*b*polylog(3, I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) + 6*I*b*polylog(3, -I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c)))/d^3","C",0
2,0,0,0,0.388961," ","integrate(x^4*(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{4} \operatorname{sech}\left(d x^{2} + c\right) + a x^{4}, x\right)"," ",0,"integral(b*x^4*sech(d*x^2 + c) + a*x^4, x)","F",0
3,1,182,0,0.424601," ","integrate(x^3*(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{4} - 2 i \, b c \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + i\right) + 2 i \, b c \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - i\right) + 2 i \, b {\rm Li}_2\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) - 2 i \, b {\rm Li}_2\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right)\right) + {\left(-2 i \, b d x^{2} - 2 i \, b c\right)} \log\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right) + 1\right) + {\left(2 i \, b d x^{2} + 2 i \, b c\right)} \log\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right) + 1\right)}{4 \, d^{2}}"," ",0,"1/4*(a*d^2*x^4 - 2*I*b*c*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + I) + 2*I*b*c*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - I) + 2*I*b*dilog(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) - 2*I*b*dilog(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c)) + (-2*I*b*d*x^2 - 2*I*b*c)*log(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c) + 1) + (2*I*b*d*x^2 + 2*I*b*c)*log(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c) + 1))/d^2","B",0
4,0,0,0,0.417733," ","integrate(x^2*(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \operatorname{sech}\left(d x^{2} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*sech(d*x^2 + c) + a*x^2, x)","F",0
5,1,33,0,0.423625," ","integrate(x*(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d x^{2} + 2 \, b \arctan\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\right)}{2 \, d}"," ",0,"1/2*(a*d*x^2 + 2*b*arctan(cosh(d*x^2 + c) + sinh(d*x^2 + c)))/d","A",0
6,0,0,0,0.417917," ","integrate((a+b*sech(d*x^2+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d x^{2} + c\right) + a}{x}, x\right)"," ",0,"integral((b*sech(d*x^2 + c) + a)/x, x)","F",0
7,0,0,0,0.481727," ","integrate((a+b*sech(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sech(d*x^2 + c) + a)/x^2, x)","F",0
8,1,1210,0,0.495138," ","integrate(x^5*(a+b*sech(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} + {\left(12 i \, a b d x^{2} - 6 \, {\left(-2 i \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 12 \, {\left(-2 i \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 6 \, {\left(-2 i \, a b d x^{2} + b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 6 \, b^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) + {\left(-12 i \, a b d x^{2} - 6 \, {\left(2 i \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 12 \, {\left(2 i \, a b d x^{2} + b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 6 \, {\left(2 i \, a b d x^{2} + b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 6 \, b^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right)\right) + {\left(6 i \, a b c^{2} + 6 \, b^{2} c + {\left(6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(12 i \, a b c^{2} + 12 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(6 i \, a b c^{2} + 6 \, 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) + i\right) + {\left(-6 i \, a b c^{2} + 6 \, b^{2} c + {\left(-6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(-12 i \, a b c^{2} + 12 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(-6 i \, a b c^{2} + 6 \, 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) - i\right) + {\left(-6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} + 6 i \, a b c^{2} - 6 \, b^{2} c + {\left(-6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} + 6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(-12 i \, a b d^{2} x^{4} - 12 \, b^{2} d x^{2} + 12 i \, a b c^{2} - 12 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(-6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} + 6 i \, a b c^{2} - 6 \, b^{2} c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right) + 1\right) + {\left(6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} - 6 i \, a b c^{2} - 6 \, b^{2} c + {\left(6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} - 6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(12 i \, a b d^{2} x^{4} - 12 \, b^{2} d x^{2} - 12 i \, a b c^{2} - 12 \, b^{2} c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(6 i \, a b d^{2} x^{4} - 6 \, b^{2} d x^{2} - 6 i \, a b c^{2} - 6 \, b^{2} c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right) + 1\right) + {\left(-12 i \, a b \cosh\left(d x^{2} + c\right)^{2} - 24 i \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 12 i \, a b \sinh\left(d x^{2} + c\right)^{2} - 12 i \, a b\right)} {\rm polylog}\left(3, i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) + {\left(12 i \, a b \cosh\left(d x^{2} + c\right)^{2} + 24 i \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + 12 i \, a b \sinh\left(d x^{2} + c\right)^{2} + 12 i \, a b\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x^{2} + c\right) - i \, \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 + (12*I*a*b*d*x^2 - 6*(-2*I*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)^2 - 12*(-2*I*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 6*(-2*I*a*b*d*x^2 + b^2)*sinh(d*x^2 + c)^2 - 6*b^2)*dilog(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) + (-12*I*a*b*d*x^2 - 6*(2*I*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)^2 - 12*(2*I*a*b*d*x^2 + b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 6*(2*I*a*b*d*x^2 + b^2)*sinh(d*x^2 + c)^2 - 6*b^2)*dilog(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c)) + (6*I*a*b*c^2 + 6*b^2*c + (6*I*a*b*c^2 + 6*b^2*c)*cosh(d*x^2 + c)^2 + (12*I*a*b*c^2 + 12*b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (6*I*a*b*c^2 + 6*b^2*c)*sinh(d*x^2 + c)^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + I) + (-6*I*a*b*c^2 + 6*b^2*c + (-6*I*a*b*c^2 + 6*b^2*c)*cosh(d*x^2 + c)^2 + (-12*I*a*b*c^2 + 12*b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (-6*I*a*b*c^2 + 6*b^2*c)*sinh(d*x^2 + c)^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - I) + (-6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 + 6*I*a*b*c^2 - 6*b^2*c + (-6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 + 6*I*a*b*c^2 - 6*b^2*c)*cosh(d*x^2 + c)^2 + (-12*I*a*b*d^2*x^4 - 12*b^2*d*x^2 + 12*I*a*b*c^2 - 12*b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (-6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 + 6*I*a*b*c^2 - 6*b^2*c)*sinh(d*x^2 + c)^2)*log(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c) + 1) + (6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 - 6*I*a*b*c^2 - 6*b^2*c + (6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 - 6*I*a*b*c^2 - 6*b^2*c)*cosh(d*x^2 + c)^2 + (12*I*a*b*d^2*x^4 - 12*b^2*d*x^2 - 12*I*a*b*c^2 - 12*b^2*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (6*I*a*b*d^2*x^4 - 6*b^2*d*x^2 - 6*I*a*b*c^2 - 6*b^2*c)*sinh(d*x^2 + c)^2)*log(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c) + 1) + (-12*I*a*b*cosh(d*x^2 + c)^2 - 24*I*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 12*I*a*b*sinh(d*x^2 + c)^2 - 12*I*a*b)*polylog(3, I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) + (12*I*a*b*cosh(d*x^2 + c)^2 + 24*I*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + 12*I*a*b*sinh(d*x^2 + c)^2 + 12*I*a*b)*polylog(3, -I*cosh(d*x^2 + c) - I*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
9,0,0,0,0.513335," ","integrate(x^4*(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{4} \operatorname{sech}\left(d x^{2} + c\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*sech(d*x^2 + c)^2 + 2*a*b*x^4*sech(d*x^2 + c) + a^2*x^4, x)","F",0
10,1,782,0,0.484385," ","integrate(x^3*(a+b*sech(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} + {\left(4 i \, a b \cosh\left(d x^{2} + c\right)^{2} + 8 i \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + 4 i \, a b \sinh\left(d x^{2} + c\right)^{2} + 4 i \, a b\right)} {\rm Li}_2\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right)\right) + {\left(-4 i \, a b \cosh\left(d x^{2} + c\right)^{2} - 8 i \, a b \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 4 i \, a b \sinh\left(d x^{2} + c\right)^{2} - 4 i \, a b\right)} {\rm Li}_2\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \sinh\left(d x^{2} + c\right)\right) + {\left(-4 i \, a b c - 2 \, {\left(2 i \, a b c + b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 4 \, {\left(2 i \, a b c + b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 2 \, {\left(2 i \, a b c + b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, b^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) + i\right) + {\left(4 i \, a b c - 2 \, {\left(-2 i \, a b c + b^{2}\right)} \cosh\left(d x^{2} + c\right)^{2} - 4 \, {\left(-2 i \, a b c + b^{2}\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) - 2 \, {\left(-2 i \, a b c + b^{2}\right)} \sinh\left(d x^{2} + c\right)^{2} - 2 \, b^{2}\right)} \log\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right) - i\right) + {\left(-4 i \, a b d x^{2} - 4 i \, a b c + {\left(-4 i \, a b d x^{2} - 4 i \, a b c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(-8 i \, a b d x^{2} - 8 i \, a b c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(-4 i \, a b d x^{2} - 4 i \, a b c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x^{2} + c\right) + i \, \sinh\left(d x^{2} + c\right) + 1\right) + {\left(4 i \, a b d x^{2} + 4 i \, a b c + {\left(4 i \, a b d x^{2} + 4 i \, a b c\right)} \cosh\left(d x^{2} + c\right)^{2} + {\left(8 i \, a b d x^{2} + 8 i \, a b c\right)} \cosh\left(d x^{2} + c\right) \sinh\left(d x^{2} + c\right) + {\left(4 i \, a b d x^{2} + 4 i \, a b c\right)} \sinh\left(d x^{2} + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x^{2} + c\right) - i \, \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*I*a*b*cosh(d*x^2 + c)^2 + 8*I*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) + 4*I*a*b*sinh(d*x^2 + c)^2 + 4*I*a*b)*dilog(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c)) + (-4*I*a*b*cosh(d*x^2 + c)^2 - 8*I*a*b*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 4*I*a*b*sinh(d*x^2 + c)^2 - 4*I*a*b)*dilog(-I*cosh(d*x^2 + c) - I*sinh(d*x^2 + c)) + (-4*I*a*b*c - 2*(2*I*a*b*c + b^2)*cosh(d*x^2 + c)^2 - 4*(2*I*a*b*c + b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 2*(2*I*a*b*c + b^2)*sinh(d*x^2 + c)^2 - 2*b^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) + I) + (4*I*a*b*c - 2*(-2*I*a*b*c + b^2)*cosh(d*x^2 + c)^2 - 4*(-2*I*a*b*c + b^2)*cosh(d*x^2 + c)*sinh(d*x^2 + c) - 2*(-2*I*a*b*c + b^2)*sinh(d*x^2 + c)^2 - 2*b^2)*log(cosh(d*x^2 + c) + sinh(d*x^2 + c) - I) + (-4*I*a*b*d*x^2 - 4*I*a*b*c + (-4*I*a*b*d*x^2 - 4*I*a*b*c)*cosh(d*x^2 + c)^2 + (-8*I*a*b*d*x^2 - 8*I*a*b*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (-4*I*a*b*d*x^2 - 4*I*a*b*c)*sinh(d*x^2 + c)^2)*log(I*cosh(d*x^2 + c) + I*sinh(d*x^2 + c) + 1) + (4*I*a*b*d*x^2 + 4*I*a*b*c + (4*I*a*b*d*x^2 + 4*I*a*b*c)*cosh(d*x^2 + c)^2 + (8*I*a*b*d*x^2 + 8*I*a*b*c)*cosh(d*x^2 + c)*sinh(d*x^2 + c) + (4*I*a*b*d*x^2 + 4*I*a*b*c)*sinh(d*x^2 + c)^2)*log(-I*cosh(d*x^2 + c) - I*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
11,0,0,0,0.470931," ","integrate(x^2*(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \operatorname{sech}\left(d x^{2} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*sech(d*x^2 + c)^2 + 2*a*b*x^2*sech(d*x^2 + c) + a^2*x^2, x)","F",0
12,1,194,0,0.507285," ","integrate(x*(a+b*sech(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} + 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)} \arctan\left(\cosh\left(d x^{2} + c\right) + \sinh\left(d x^{2} + c\right)\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 + 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)*arctan(cosh(d*x^2 + c) + sinh(d*x^2 + c)))/(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
13,0,0,0,0.726299," ","integrate((a+b*sech(d*x^2+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x^{2} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*sech(d*x^2 + c)^2 + 2*a*b*sech(d*x^2 + c) + a^2)/x, x)","F",0
14,0,0,0,0.546944," ","integrate((a+b*sech(d*x^2+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x^{2} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*sech(d*x^2 + c)^2 + 2*a*b*sech(d*x^2 + c) + a^2)/x^2, x)","F",0
15,1,1918,0,0.414880," ","integrate(x*sech(b*x^2+a)^7,x, algorithm=""fricas"")","\frac{15 \, \cosh\left(b x^{2} + a\right)^{11} + 165 \, \cosh\left(b x^{2} + a\right) \sinh\left(b x^{2} + a\right)^{10} + 15 \, \sinh\left(b x^{2} + a\right)^{11} + 5 \, {\left(165 \, \cosh\left(b x^{2} + a\right)^{2} + 17\right)} \sinh\left(b x^{2} + a\right)^{9} + 85 \, \cosh\left(b x^{2} + a\right)^{9} + 45 \, {\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} + 18 \, {\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} + 198 \, \cosh\left(b x^{2} + a\right)^{7} + 42 \, {\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} + 18 \, {\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} - 198 \, \cosh\left(b x^{2} + a\right)^{5} + 90 \, {\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} + 5 \, {\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} - 85 \, \cosh\left(b x^{2} + a\right)^{3} + 3 \, {\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)} \arctan\left(\cosh\left(b x^{2} + a\right) + \sinh\left(b x^{2} + a\right)\right) + 3 \, {\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) - 15 \, \cosh\left(b x^{2} + a\right)}{48 \, {\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,"1/48*(15*cosh(b*x^2 + a)^11 + 165*cosh(b*x^2 + a)*sinh(b*x^2 + a)^10 + 15*sinh(b*x^2 + a)^11 + 5*(165*cosh(b*x^2 + a)^2 + 17)*sinh(b*x^2 + a)^9 + 85*cosh(b*x^2 + a)^9 + 45*(55*cosh(b*x^2 + a)^3 + 17*cosh(b*x^2 + a))*sinh(b*x^2 + a)^8 + 18*(275*cosh(b*x^2 + a)^4 + 170*cosh(b*x^2 + a)^2 + 11)*sinh(b*x^2 + a)^7 + 198*cosh(b*x^2 + a)^7 + 42*(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 + 18*(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 - 198*cosh(b*x^2 + a)^5 + 90*(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 + 5*(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 - 85*cosh(b*x^2 + a)^3 + 3*(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)*arctan(cosh(b*x^2 + a) + sinh(b*x^2 + a)) + 3*(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) - 15*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
16,1,731,0,0.433938," ","integrate(x^5/(a+b*sech(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
17,0,0,0,0.407761," ","integrate(x^4/(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b \operatorname{sech}\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^4/(b*sech(d*x^2 + c) + a), x)","F",0
18,1,536,0,0.433729," ","integrate(x^3/(a+b*sech(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
19,0,0,0,0.378962," ","integrate(x^2/(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \operatorname{sech}\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sech(d*x^2 + c) + a), x)","F",0
20,1,304,0,0.446665," ","integrate(x/(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","\left[\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}, \frac{{\left(a^{2} - b^{2}\right)} d x^{2} + 2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",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), 1/2*((a^2 - b^2)*d*x^2 + 2*sqrt(a^2 - b^2)*b*arctan(-(a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c) + b)/sqrt(a^2 - b^2)))/((a^3 - a*b^2)*d)]","A",0
21,0,0,0,0.411409," ","integrate(1/x/(a+b*sech(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{sech}\left(d x^{2} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sech(d*x^2 + c) + a*x), x)","F",0
22,0,0,0,0.408295," ","integrate((a+b*sech(d*x^2+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d x^{2} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sech(d*x^2 + c) + a)/x^2, x)","F",0
23,1,3918,0,0.549383," ","integrate(x^5/(a+b*sech(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
24,0,0,0,0.416048," ","integrate(x^4/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{b^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^4/(b^2*sech(d*x^2 + c)^2 + 2*a*b*sech(d*x^2 + c) + a^2), x)","F",0
25,1,2473,0,0.471117," ","integrate(x^3/(a+b*sech(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
26,0,0,0,0.406545," ","integrate(x^2/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d x^{2} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*sech(d*x^2 + c)^2 + 2*a*b*sech(d*x^2 + c) + a^2), x)","F",0
27,1,1314,0,0.462707," ","integrate(x/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","\left[\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)}}, \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} + 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}} \arctan\left(-\frac{a \cosh\left(d x^{2} + c\right) + a \sinh\left(d x^{2} + c\right) + b}{\sqrt{a^{2} - b^{2}}}\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)}}\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)), 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*(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)*arctan(-(a*cosh(d*x^2 + c) + a*sinh(d*x^2 + c) + b)/sqrt(a^2 - b^2)) - 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
28,0,0,0,0.411101," ","integrate(1/x/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b x \operatorname{sech}\left(d x^{2} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*sech(d*x^2 + c)^2 + 2*a*b*x*sech(d*x^2 + c) + a^2*x), x)","F",0
29,0,0,0,0.423173," ","integrate(1/x^2/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{2} \operatorname{sech}\left(d x^{2} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*sech(d*x^2 + c)^2 + 2*a*b*x^2*sech(d*x^2 + c) + a^2*x^2), x)","F",0
30,0,0,0,0.419871," ","integrate(1/x^3/(a+b*sech(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{3} \operatorname{sech}\left(d x^{2} + c\right)^{2} + 2 \, a b x^{3} \operatorname{sech}\left(d x^{2} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(1/(b^2*x^3*sech(d*x^2 + c)^2 + 2*a*b*x^3*sech(d*x^2 + c) + a^2*x^3), x)","F",0
31,1,28,0,0.375615," ","integrate(sech(1/x)^2/x^2,x, algorithm=""fricas"")","\frac{2}{\cosh\left(\frac{1}{x}\right)^{2} + 2 \, \cosh\left(\frac{1}{x}\right) \sinh\left(\frac{1}{x}\right) + \sinh\left(\frac{1}{x}\right)^{2} + 1}"," ",0,"2/(cosh(1/x)^2 + 2*cosh(1/x)*sinh(1/x) + sinh(1/x)^2 + 1)","B",0
32,0,0,0,0.406791," ","integrate(x^3*(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right) + a x^{3}, x\right)"," ",0,"integral(b*x^3*sech(d*sqrt(x) + c) + a*x^3, x)","F",0
33,0,0,0,0.430858," ","integrate(x^2*(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*sech(d*sqrt(x) + c) + a*x^2, x)","F",0
34,0,0,0,0.417897," ","integrate(x*(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x \operatorname{sech}\left(d \sqrt{x} + c\right) + a x, x\right)"," ",0,"integral(b*x*sech(d*sqrt(x) + c) + a*x, x)","F",0
35,0,0,0,0.420556," ","integrate((a+b*sech(c+d*x^(1/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}{x}, x\right)"," ",0,"integral((b*sech(d*sqrt(x) + c) + a)/x, x)","F",0
36,0,0,0,0.424410," ","integrate((a+b*sech(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sech(d*sqrt(x) + c) + a)/x^2, x)","F",0
37,0,0,0,0.422398," ","integrate(x^3*(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{3}, x\right)"," ",0,"integral(b^2*x^3*sech(d*sqrt(x) + c)^2 + 2*a*b*x^3*sech(d*sqrt(x) + c) + a^2*x^3, x)","F",0
38,0,0,0,0.405835," ","integrate(x^2*(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*sech(d*sqrt(x) + c)^2 + 2*a*b*x^2*sech(d*sqrt(x) + c) + a^2*x^2, x)","F",0
39,0,0,0,0.405466," ","integrate(x*(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*sech(d*sqrt(x) + c)^2 + 2*a*b*x*sech(d*sqrt(x) + c) + a^2*x, x)","F",0
40,0,0,0,0.417334," ","integrate((a+b*sech(c+d*x^(1/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2)/x, x)","F",0
41,0,0,0,0.418242," ","integrate((a+b*sech(c+d*x^(1/2)))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2)/x^2, x)","F",0
42,0,0,0,0.459361," ","integrate(x^3/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^3/(b*sech(d*sqrt(x) + c) + a), x)","F",0
43,0,0,0,0.426812," ","integrate(x^2/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sech(d*sqrt(x) + c) + a), x)","F",0
44,0,0,0,0.460895," ","integrate(x/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x/(b*sech(d*sqrt(x) + c) + a), x)","F",0
45,0,0,0,0.447567," ","integrate(1/x/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \operatorname{sech}\left(d \sqrt{x} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sech(d*sqrt(x) + c) + a*x), x)","F",0
46,0,0,0,0.485479," ","integrate((a+b*sech(c+d*x^(1/2)))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sech(d*sqrt(x) + c) + a)/x^2, x)","F",0
47,0,0,0,0.500298," ","integrate(x^3/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^3/(b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2), x)","F",0
48,0,0,0,0.500424," ","integrate(x^2/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^2/(b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2), x)","F",0
49,0,0,0,0.500058," ","integrate(x/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x/(b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2), x)","F",0
50,0,0,0,0.471211," ","integrate(1/x/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*sech(d*sqrt(x) + c)^2 + 2*a*b*x*sech(d*sqrt(x) + c) + a^2*x), x)","F",0
51,0,0,0,0.558342," ","integrate(1/x^2/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*sech(d*sqrt(x) + c)^2 + 2*a*b*x^2*sech(d*sqrt(x) + c) + a^2*x^2), x)","F",0
52,0,0,0,0.436819," ","integrate(x^(3/2)*(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(b x^{\frac{3}{2}} \operatorname{sech}\left(d \sqrt{x} + c\right) + a x^{\frac{3}{2}}, x\right)"," ",0,"integral(b*x^(3/2)*sech(d*sqrt(x) + c) + a*x^(3/2), x)","F",0
53,0,0,0,0.417208," ","integrate((a+b*sech(c+d*x^(1/2)))*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a \sqrt{x}, x\right)"," ",0,"integral(b*sqrt(x)*sech(d*sqrt(x) + c) + a*sqrt(x), x)","F",0
54,1,33,0,0.519855," ","integrate((a+b*sech(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(a d \sqrt{x} + 2 \, b \arctan\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right)\right)\right)}}{d}"," ",0,"2*(a*d*sqrt(x) + 2*b*arctan(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c)))/d","A",0
55,0,0,0,0.549361," ","integrate((a+b*sech(c+d*x^(1/2)))/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b*sqrt(x)*sech(d*sqrt(x) + c) + a*sqrt(x))/x^2, x)","F",0
56,0,0,0,0.523968," ","integrate((a+b*sech(c+d*x^(1/2)))/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b*sqrt(x)*sech(d*sqrt(x) + c) + a*sqrt(x))/x^3, x)","F",0
57,0,0,0,0.499637," ","integrate(x^(3/2)*(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{\frac{3}{2}} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{\frac{3}{2}} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{\frac{3}{2}}, x\right)"," ",0,"integral(b^2*x^(3/2)*sech(d*sqrt(x) + c)^2 + 2*a*b*x^(3/2)*sech(d*sqrt(x) + c) + a^2*x^(3/2), x)","F",0
58,0,0,0,0.415484," ","integrate((a+b*sech(c+d*x^(1/2)))^2*x^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}, x\right)"," ",0,"integral(b^2*sqrt(x)*sech(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sech(d*sqrt(x) + c) + a^2*sqrt(x), x)","F",0
59,1,194,0,0.445299," ","integrate((a+b*sech(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} + 4 \, {\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)} \arctan\left(\cosh\left(d \sqrt{x} + c\right) + \sinh\left(d \sqrt{x} + c\right)\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 + 4*(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)*arctan(cosh(d*sqrt(x) + c) + sinh(d*sqrt(x) + c)))/(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
60,0,0,0,0.416149," ","integrate((a+b*sech(c+d*x^(1/2)))^2/x^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{2}}, x\right)"," ",0,"integral((b^2*sqrt(x)*sech(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sech(d*sqrt(x) + c) + a^2*sqrt(x))/x^2, x)","F",0
61,0,0,0,0.406626," ","integrate((a+b*sech(c+d*x^(1/2)))^2/x^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \sqrt{x} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} \sqrt{x}}{x^{3}}, x\right)"," ",0,"integral((b^2*sqrt(x)*sech(d*sqrt(x) + c)^2 + 2*a*b*sqrt(x)*sech(d*sqrt(x) + c) + a^2*sqrt(x))/x^3, x)","F",0
62,0,0,0,0.406869," ","integrate(x^(3/2)/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(x^(3/2)/(b*sech(d*sqrt(x) + c) + a), x)","F",0
63,0,0,0,0.407245," ","integrate(x^(1/2)/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b \operatorname{sech}\left(d \sqrt{x} + c\right) + a}, x\right)"," ",0,"integral(sqrt(x)/(b*sech(d*sqrt(x) + c) + a), x)","F",0
64,1,254,0,0.433875," ","integrate(1/(a+b*sech(c+d*x^(1/2)))/x^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left({\left(a^{2} - b^{2}\right)} d \sqrt{x} - \sqrt{-a^{2} + b^{2}} b \log\left(\frac{a b + {\left(b^{2} + \sqrt{-a^{2} + b^{2}} b\right)} \cosh\left(d \sqrt{x} + c\right) + {\left(a^{2} - b^{2} - \sqrt{-a^{2} + b^{2}} b\right)} \sinh\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{a \cosh\left(d \sqrt{x} + c\right) + b}\right)\right)}}{{\left(a^{3} - a b^{2}\right)} d}, \frac{2 \, {\left({\left(a^{2} - b^{2}\right)} d \sqrt{x} + 2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{\sqrt{a^{2} - b^{2}} a \cosh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} a \sinh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} b}{a^{2} - b^{2}}\right)\right)}}{{\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[2*((a^2 - b^2)*d*sqrt(x) - sqrt(-a^2 + b^2)*b*log((a*b + (b^2 + sqrt(-a^2 + b^2)*b)*cosh(d*sqrt(x) + c) + (a^2 - b^2 - sqrt(-a^2 + b^2)*b)*sinh(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/(a*cosh(d*sqrt(x) + c) + b)))/((a^3 - a*b^2)*d), 2*((a^2 - b^2)*d*sqrt(x) + 2*sqrt(a^2 - b^2)*b*arctan(-(sqrt(a^2 - b^2)*a*cosh(d*sqrt(x) + c) + sqrt(a^2 - b^2)*a*sinh(d*sqrt(x) + c) + sqrt(a^2 - b^2)*b)/(a^2 - b^2)))/((a^3 - a*b^2)*d)]","B",0
65,0,0,0,0.404412," ","integrate(1/x^(3/2)/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^2*sech(d*sqrt(x) + c) + a*x^2), x)","F",0
66,0,0,0,0.437822," ","integrate(1/x^(5/2)/(a+b*sech(c+d*x^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right) + a x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b*x^3*sech(d*sqrt(x) + c) + a*x^3), x)","F",0
67,0,0,0,0.429112," ","integrate(x^(3/2)/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{\frac{3}{2}}}{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(x^(3/2)/(b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2), x)","F",0
68,0,0,0,0.423539," ","integrate(x^(1/2)/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*sech(d*sqrt(x) + c)^2 + 2*a*b*sech(d*sqrt(x) + c) + a^2), x)","F",0
69,1,1387,0,0.480006," ","integrate(1/(a+b*sech(c+d*x^(1/2)))^2/x^(1/2),x, algorithm=""fricas"")","\left[-\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(b^{2} + \sqrt{-a^{2} + b^{2}} b\right)} \cosh\left(d \sqrt{x} + c\right) + {\left(a^{2} - b^{2} - \sqrt{-a^{2} + b^{2}} b\right)} \sinh\left(d \sqrt{x} + c\right) + \sqrt{-a^{2} + b^{2}} a}{a \cosh\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)}, -\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({\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)} \arctan\left(-\frac{\sqrt{a^{2} - b^{2}} a \cosh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} a \sinh\left(d \sqrt{x} + c\right) + \sqrt{a^{2} - b^{2}} b}{a^{2} - b^{2}}\right) + 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) + 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)}\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 + (b^2 + sqrt(-a^2 + b^2)*b)*cosh(d*sqrt(x) + c) + (a^2 - b^2 - sqrt(-a^2 + b^2)*b)*sinh(d*sqrt(x) + c) + sqrt(-a^2 + b^2)*a)/(a*cosh(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)), -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*((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))*arctan(-(sqrt(a^2 - b^2)*a*cosh(d*sqrt(x) + c) + sqrt(a^2 - b^2)*a*sinh(d*sqrt(x) + c) + sqrt(a^2 - b^2)*b)/(a^2 - b^2)) + 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^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
70,0,0,0,0.421430," ","integrate(1/x^(3/2)/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{2} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^2*sech(d*sqrt(x) + c)^2 + 2*a*b*x^2*sech(d*sqrt(x) + c) + a^2*x^2), x)","F",0
71,0,0,0,0.427177," ","integrate(1/x^(5/2)/(a+b*sech(c+d*x^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x}}{b^{2} x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right)^{2} + 2 \, a b x^{3} \operatorname{sech}\left(d \sqrt{x} + c\right) + a^{2} x^{3}}, x\right)"," ",0,"integral(sqrt(x)/(b^2*x^3*sech(d*sqrt(x) + c)^2 + 2*a*b*x^3*sech(d*sqrt(x) + c) + a^2*x^3), x)","F",0
72,0,0,0,0.444541," ","integrate((e*x)^m*(a+b*sech(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \operatorname{sech}\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sech(d*x^n + c) + a)^p, x)","F",0
73,1,122,0,0.405473," ","integrate((e*x)^(-1+n)*(a+b*sech(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) + 2 \, {\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)} \arctan\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) + {\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)) + 2*(b*cosh((n - 1)*log(e)) + b*sinh((n - 1)*log(e)))*arctan(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*d*cosh((n - 1)*log(e)) + a*d*sinh((n - 1)*log(e)))*sinh(n*log(x)))/(d*n)","B",0
74,1,658,0,0.452960," ","integrate((e*x)^(-1+2*n)*(a+b*sech(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} + {\left(2 i \, b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 i \, b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(-2 i \, b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 2 i \, b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(-2 i \, b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 2 i \, 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) + i\right) + {\left(2 i \, b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 i \, 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) - i\right) + {\left(-2 i \, b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 2 i \, b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, b d \cosh\left(n \log\left(x\right)\right) - 2 i \, b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 2 i \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \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(2 i \, b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 2 i \, b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, b d \cosh\left(n \log\left(x\right)\right) + 2 i \, b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 2 i \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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*I*b*cosh((2*n - 1)*log(e)) + 2*I*b*sinh((2*n - 1)*log(e)))*dilog(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (-2*I*b*cosh((2*n - 1)*log(e)) - 2*I*b*sinh((2*n - 1)*log(e)))*dilog(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (-2*I*b*c*cosh((2*n - 1)*log(e)) - 2*I*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) + I) + (2*I*b*c*cosh((2*n - 1)*log(e)) + 2*I*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) - I) + (-2*I*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 2*I*b*c*cosh((2*n - 1)*log(e)) + (-2*I*b*d*cosh(n*log(x)) - 2*I*b*c)*sinh((2*n - 1)*log(e)) + (-2*I*b*d*cosh((2*n - 1)*log(e)) - 2*I*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (2*I*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + 2*I*b*c*cosh((2*n - 1)*log(e)) + (2*I*b*d*cosh(n*log(x)) + 2*I*b*c)*sinh((2*n - 1)*log(e)) + (2*I*b*d*cosh((2*n - 1)*log(e)) + 2*I*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*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
75,1,1072,0,0.486439," ","integrate((e*x)^(-1+3*n)*(a+b*sech(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} + {\left(6 i \, b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 6 i \, b d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 6 i \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(-6 i \, b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 i \, b d \cosh\left(n \log\left(x\right)\right) \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 i \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(3 i \, b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 i \, 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) + i\right) + {\left(-3 i \, b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 3 i \, 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) - i\right) + {\left(-3 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} + 3 i \, b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-3 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 3 i \, 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(-3 i \, b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 3 i \, b c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 i \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \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(3 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right)^{2} - 3 i \, b c^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(3 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 3 i \, 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(3 i \, b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 3 i \, b c^{2}\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 6 i \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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(-6 i \, b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 i \, b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(6 i \, b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 6 i \, b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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*I*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + 6*I*b*d*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (6*I*b*d*cosh((3*n - 1)*log(e)) + 6*I*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (-6*I*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*I*b*d*cosh(n*log(x))*sinh((3*n - 1)*log(e)) + (-6*I*b*d*cosh((3*n - 1)*log(e)) - 6*I*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (3*I*b*c^2*cosh((3*n - 1)*log(e)) + 3*I*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) + I) + (-3*I*b*c^2*cosh((3*n - 1)*log(e)) - 3*I*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) - I) + (-3*I*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 + 3*I*b*c^2*cosh((3*n - 1)*log(e)) + (-3*I*b*d^2*cosh((3*n - 1)*log(e)) - 3*I*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (-3*I*b*d^2*cosh(n*log(x))^2 + 3*I*b*c^2)*sinh((3*n - 1)*log(e)) + (-6*I*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*I*b*d^2*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (3*I*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 3*I*b*c^2*cosh((3*n - 1)*log(e)) + (3*I*b*d^2*cosh((3*n - 1)*log(e)) + 3*I*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (3*I*b*d^2*cosh(n*log(x))^2 - 3*I*b*c^2)*sinh((3*n - 1)*log(e)) + (6*I*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + 6*I*b*d^2*cosh(n*log(x))*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (-6*I*b*cosh((3*n - 1)*log(e)) - 6*I*b*sinh((3*n - 1)*log(e)))*polylog(3, I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (6*I*b*cosh((3*n - 1)*log(e)) + 6*I*b*sinh((3*n - 1)*log(e)))*polylog(3, -I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*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
76,1,646,0,0.419835," ","integrate((e*x)^(-1+n)*(a+b*sech(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} + 4 \, {\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)} \arctan\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) + {\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 + 4*((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)))*arctan(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*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
77,1,2964,0,0.535409," ","integrate((e*x)^(-1+2*n)*(a+b*sech(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} + {\left({\left(4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 4 i \, 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} + 4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(8 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 8 i \, 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(4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 4 i \, 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} + 4 i \, a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left({\left(-4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 4 i \, 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} - 4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-8 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 8 i \, 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(-4 i \, a b \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 4 i \, 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} - 4 i \, a b \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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({\left({\left(2 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(2 i \, 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) + i\right) - 2 \, {\left({\left({\left(-2 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, 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 i \, a b c + b^{2}\right)} \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-2 i \, 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) - i\right) + {\left(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 4 i \, 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} + {\left(-8 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 8 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-8 i \, a b d \cosh\left(n \log\left(x\right)\right) - 8 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-8 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 8 i \, 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(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 4 i \, 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(-4 i \, a b d \cosh\left(n \log\left(x\right)\right) - 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(-4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) - 4 i \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \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(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 4 i \, 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} + {\left(8 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 8 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(8 i \, a b d \cosh\left(n \log\left(x\right)\right) + 8 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(8 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 8 i \, 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(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 4 i \, 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(4 i \, a b d \cosh\left(n \log\left(x\right)\right) + 4 i \, a b c\right)} \sinh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + {\left(4 i \, a b d \cosh\left({\left(2 \, n - 1\right)} \log\left(e\right)\right) + 4 i \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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*I*a*b*cosh((2*n - 1)*log(e)) + 4*I*a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 4*I*a*b*cosh((2*n - 1)*log(e)) + (8*I*a*b*cosh((2*n - 1)*log(e)) + 8*I*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) + (4*I*a*b*cosh((2*n - 1)*log(e)) + 4*I*a*b*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 4*I*a*b*sinh((2*n - 1)*log(e)))*dilog(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + ((-4*I*a*b*cosh((2*n - 1)*log(e)) - 4*I*a*b*sinh((2*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 4*I*a*b*cosh((2*n - 1)*log(e)) + (-8*I*a*b*cosh((2*n - 1)*log(e)) - 8*I*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) + (-4*I*a*b*cosh((2*n - 1)*log(e)) - 4*I*a*b*sinh((2*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 4*I*a*b*sinh((2*n - 1)*log(e)))*dilog(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) - 2*(((2*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (2*I*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) + I) - 2*(((-2*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (-2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (-2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (-2*I*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*I*a*b*c + b^2)*cosh((2*n - 1)*log(e)) + (-2*I*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) - I) + (-4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh(n*log(x)) - 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh((2*n - 1)*log(e)) - 4*I*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 + (-8*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 8*I*a*b*c*cosh((2*n - 1)*log(e)) + (-8*I*a*b*d*cosh(n*log(x)) - 8*I*a*b*c)*sinh((2*n - 1)*log(e)) + (-8*I*a*b*d*cosh((2*n - 1)*log(e)) - 8*I*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) + (-4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) - 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh(n*log(x)) - 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh((2*n - 1)*log(e)) - 4*I*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 + (-4*I*a*b*d*cosh(n*log(x)) - 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (-4*I*a*b*d*cosh((2*n - 1)*log(e)) - 4*I*a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh(n*log(x)) + 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh((2*n - 1)*log(e)) + 4*I*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 + (8*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + 8*I*a*b*c*cosh((2*n - 1)*log(e)) + (8*I*a*b*d*cosh(n*log(x)) + 8*I*a*b*c)*sinh((2*n - 1)*log(e)) + (8*I*a*b*d*cosh((2*n - 1)*log(e)) + 8*I*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) + (4*I*a*b*d*cosh((2*n - 1)*log(e))*cosh(n*log(x)) + 4*I*a*b*c*cosh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh(n*log(x)) + 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh((2*n - 1)*log(e)) + 4*I*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 + (4*I*a*b*d*cosh(n*log(x)) + 4*I*a*b*c)*sinh((2*n - 1)*log(e)) + (4*I*a*b*d*cosh((2*n - 1)*log(e)) + 4*I*a*b*d*sinh((2*n - 1)*log(e)))*sinh(n*log(x)))*log(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*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
78,1,5493,0,0.607203," ","integrate((e*x)^(-1+3*n)*(a+b*sech(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} + {\left(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 \, {\left(-2 i \, 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) + {\left(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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} - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(24 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 \, {\left(-2 i \, 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) + {\left(24 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 24 i \, 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(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 \, {\left(-2 i \, 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) + {\left(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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} - 6 \, {\left(-2 i \, 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) + {\left(12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 \, {\left(2 i \, 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) + {\left(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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} - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-24 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 \, {\left(2 i \, 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) + {\left(-24 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 24 i \, 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(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 \, {\left(2 i \, 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) + {\left(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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} - 6 \, {\left(2 i \, 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) + {\left(-12 i \, a b d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left({\left({\left(6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b c^{2} + 6 \, 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} + {\left({\left(12 i \, a b c^{2} + 12 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b c^{2} + 12 \, 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(6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b c^{2} + 6 \, 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(6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b c^{2} + 6 \, 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) + i\right) + {\left({\left({\left(-6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b c^{2} + 6 \, 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} + {\left({\left(-12 i \, a b c^{2} + 12 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b c^{2} + 12 \, 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(-6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b c^{2} + 6 \, 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(-6 i \, a b c^{2} + 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b c^{2} + 6 \, 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) - i\right) + {\left(-6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(-6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(-6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 i \, 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(6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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} + {\left(-12 i \, 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} - 12 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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(12 i \, a b c^{2} - 12 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 12 i \, a b c^{2} - 12 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-24 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-24 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 12 \, 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(-6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(-6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 i \, 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(6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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(-6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 6 i \, 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(6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} + 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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(i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \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(6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 6 i \, 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(-6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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} + {\left(12 i \, 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} - 12 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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(-12 i \, a b c^{2} - 12 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 12 i \, a b c^{2} - 12 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(24 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 12 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(24 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 12 \, 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(6 i \, 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} - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) + {\left(6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 6 i \, 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(-6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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(6 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 6 i \, 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(-6 i \, a b c^{2} - 6 \, b^{2} c\right)} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(6 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right)^{2} - 6 i \, a b c^{2} - 6 \, b^{2} d \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} c\right)} \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) \cosh\left(n \log\left(x\right)\right) - 6 \, b^{2} d \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(12 i \, a b d^{2} \cosh\left(n \log\left(x\right)\right) - 6 \, 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(-i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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({\left(-12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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} - 12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(-24 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 24 i \, 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(-12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) - 12 i \, 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} - 12 i \, a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) + i \, \sinh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right)\right) + {\left({\left(12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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} + 12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + {\left(24 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 24 i \, 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(12 i \, a b \cosh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right) + 12 i \, 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} + 12 i \, a b \sinh\left({\left(3 \, n - 1\right)} \log\left(e\right)\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d \cosh\left(n \log\left(x\right)\right) + d \sinh\left(n \log\left(x\right)\right) + c\right) - i \, \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 + (12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*cosh((3*n - 1)*log(e)) - 6*(-2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d*cosh((3*n - 1)*log(e)) + 12*I*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 - 6*b^2*cosh((3*n - 1)*log(e)) + (24*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 12*b^2*cosh((3*n - 1)*log(e)) - 12*(-2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (24*I*a*b*d*cosh((3*n - 1)*log(e)) + 24*I*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) + (12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*cosh((3*n - 1)*log(e)) - 6*(-2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d*cosh((3*n - 1)*log(e)) + 12*I*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 - 6*(-2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d*cosh((3*n - 1)*log(e)) + 12*I*a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (-12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (-12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*cosh((3*n - 1)*log(e)) - 6*(2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d*cosh((3*n - 1)*log(e)) - 12*I*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 - 6*b^2*cosh((3*n - 1)*log(e)) + (-24*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 12*b^2*cosh((3*n - 1)*log(e)) - 12*(2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (-24*I*a*b*d*cosh((3*n - 1)*log(e)) - 24*I*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) + (-12*I*a*b*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*cosh((3*n - 1)*log(e)) - 6*(2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d*cosh((3*n - 1)*log(e)) - 12*I*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 - 6*(2*I*a*b*d*cosh(n*log(x)) + b^2)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d*cosh((3*n - 1)*log(e)) - 12*I*a*b*d*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*dilog(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + (((6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*c^2 + 6*b^2*c)*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((12*I*a*b*c^2 + 12*b^2*c)*cosh((3*n - 1)*log(e)) + (12*I*a*b*c^2 + 12*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) + ((6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*c^2 + 6*b^2*c)*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*c^2 + 6*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) + I) + (((-6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*c^2 + 6*b^2*c)*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + ((-12*I*a*b*c^2 + 12*b^2*c)*cosh((3*n - 1)*log(e)) + (-12*I*a*b*c^2 + 12*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) + ((-6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*c^2 + 6*b^2*c)*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + (-6*I*a*b*c^2 + 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*c^2 + 6*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) - I) + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e)) - 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*d^2*cosh(n*log(x))^2 + 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh(n*log(x)) - 6*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 + (-12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 12*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (-12*I*a*b*d^2*cosh((3*n - 1)*log(e)) - 12*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (12*I*a*b*c^2 - 12*b^2*c)*cosh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh(n*log(x))^2 + 12*I*a*b*c^2 - 12*b^2*d*cosh(n*log(x)) - 12*b^2*c)*sinh((3*n - 1)*log(e)) + (-24*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 12*b^2*d*cosh((3*n - 1)*log(e)) + (-24*I*a*b*d^2*cosh(n*log(x)) - 12*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) + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e)) - 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*d^2*cosh(n*log(x))^2 + 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh(n*log(x)) - 6*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 + (-6*I*a*b*d^2*cosh((3*n - 1)*log(e)) - 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (-6*I*a*b*d^2*cosh(n*log(x))^2 + 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (-12*I*a*b*d^2*cosh(n*log(x)) - 6*b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + (6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (6*I*a*b*d^2*cosh((3*n - 1)*log(e)) + 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (-6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*d^2*cosh(n*log(x))^2 - 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh(n*log(x)) - 6*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 + (12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 12*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (12*I*a*b*d^2*cosh((3*n - 1)*log(e)) + 12*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (-12*I*a*b*c^2 - 12*b^2*c)*cosh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh(n*log(x))^2 - 12*I*a*b*c^2 - 12*b^2*d*cosh(n*log(x)) - 12*b^2*c)*sinh((3*n - 1)*log(e)) + (24*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 12*b^2*d*cosh((3*n - 1)*log(e)) + (24*I*a*b*d^2*cosh(n*log(x)) - 12*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) + (6*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x))^2 - 6*b^2*d*cosh((3*n - 1)*log(e))*cosh(n*log(x)) + (6*I*a*b*d^2*cosh((3*n - 1)*log(e)) + 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (-6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*d^2*cosh(n*log(x))^2 - 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh(n*log(x)) - 6*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 + (6*I*a*b*d^2*cosh((3*n - 1)*log(e)) + 6*I*a*b*d^2*sinh((3*n - 1)*log(e)))*sinh(n*log(x))^2 + (-6*I*a*b*c^2 - 6*b^2*c)*cosh((3*n - 1)*log(e)) + (6*I*a*b*d^2*cosh(n*log(x))^2 - 6*I*a*b*c^2 - 6*b^2*d*cosh(n*log(x)) - 6*b^2*c)*sinh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh((3*n - 1)*log(e))*cosh(n*log(x)) - 6*b^2*d*cosh((3*n - 1)*log(e)) + (12*I*a*b*d^2*cosh(n*log(x)) - 6*b^2*d)*sinh((3*n - 1)*log(e)))*sinh(n*log(x)))*log(-I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + 1) + ((-12*I*a*b*cosh((3*n - 1)*log(e)) - 12*I*a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 12*I*a*b*cosh((3*n - 1)*log(e)) + (-24*I*a*b*cosh((3*n - 1)*log(e)) - 24*I*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) + (-12*I*a*b*cosh((3*n - 1)*log(e)) - 12*I*a*b*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 - 12*I*a*b*sinh((3*n - 1)*log(e)))*polylog(3, I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + I*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)) + ((12*I*a*b*cosh((3*n - 1)*log(e)) + 12*I*a*b*sinh((3*n - 1)*log(e)))*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 12*I*a*b*cosh((3*n - 1)*log(e)) + (24*I*a*b*cosh((3*n - 1)*log(e)) + 24*I*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) + (12*I*a*b*cosh((3*n - 1)*log(e)) + 12*I*a*b*sinh((3*n - 1)*log(e)))*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c)^2 + 12*I*a*b*sinh((3*n - 1)*log(e)))*polylog(3, -I*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) - I*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
79,1,511,0,0.435332," ","integrate((e*x)^(-1+n)/(a+b*sech(c+d*x^n)),x, algorithm=""fricas"")","\left[\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(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(a^{2} - 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 \cosh\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}, \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) + 2 \, {\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)} \arctan\left(-\frac{\sqrt{a^{2} - b^{2}} a \cosh\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 \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}} b}{a^{2} - b^{2}}\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}\right]"," ",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 + (b^2 + sqrt(-a^2 + b^2)*b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^2 - 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*cosh(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), ((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)) + 2*(sqrt(a^2 - b^2)*b*cosh((n - 1)*log(e)) + sqrt(a^2 - b^2)*b*sinh((n - 1)*log(e)))*arctan(-(sqrt(a^2 - b^2)*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 - b^2)*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 - b^2)*b)/(a^2 - b^2)) + ((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
80,1,1286,0,0.418026," ","integrate((e*x)^(-1+2*n)/(a+b*sech(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
81,1,2005,0,0.445118," ","integrate((e*x)^(-1+3*n)/(a+b*sech(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
82,1,3547,0,0.500274," ","integrate((e*x)^(-1+n)/(a+b*sech(c+d*x^n))^2,x, algorithm=""fricas"")","\left[\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(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(a^{2} - 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 \cosh\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)}, \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({\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)} \arctan\left(-\frac{\sqrt{a^{2} - b^{2}} a \cosh\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 \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}} b}{a^{2} - b^{2}}\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(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) + 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)}\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 + (b^2 + sqrt(-a^2 + b^2)*b)*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + (a^2 - 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*cosh(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)), ((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*(((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))*arctan(-(sqrt(a^2 - b^2)*a*cosh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 - b^2)*a*sinh(d*cosh(n*log(x)) + d*sinh(n*log(x)) + c) + sqrt(a^2 - b^2)*b)/(a^2 - b^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^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
83,1,9020,0,0.558729," ","integrate((e*x)^(-1+2*n)/(a+b*sech(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
84,-1,0,0,0.000000," ","integrate((e*x)^(-1+3*n)/(a+b*sech(c+d*x^n))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
