1,1,216,0,2.271808," ","integrate(x^3*coth(b*x+a),x, algorithm=""fricas"")","-\frac{b^{4} x^{4} - 4 \, b^{3} x^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - 12 \, b^{2} x^{2} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 12 \, b^{2} x^{2} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 4 \, a^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + 24 \, b x {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 24 \, b x {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 24 \, {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 24 \, {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{4 \, b^{4}}"," ",0,"-1/4*(b^4*x^4 - 4*b^3*x^3*log(cosh(b*x + a) + sinh(b*x + a) + 1) - 12*b^2*x^2*dilog(cosh(b*x + a) + sinh(b*x + a)) - 12*b^2*x^2*dilog(-cosh(b*x + a) - sinh(b*x + a)) + 4*a^3*log(cosh(b*x + a) + sinh(b*x + a) - 1) + 24*b*x*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 24*b*x*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) - 4*(b^3*x^3 + a^3)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 24*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 24*polylog(4, -cosh(b*x + a) - sinh(b*x + a)))/b^4","C",0
2,1,168,0,0.626524," ","integrate(x^2*coth(b*x+a),x, algorithm=""fricas"")","-\frac{b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - 6 \, b x {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, b x {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 3 \, a^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 6 \, {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{3 \, b^{3}}"," ",0,"-1/3*(b^3*x^3 - 3*b^2*x^2*log(cosh(b*x + a) + sinh(b*x + a) + 1) - 6*b*x*dilog(cosh(b*x + a) + sinh(b*x + a)) - 6*b*x*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 3*a^2*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 3*(b^2*x^2 - a^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*polylog(3, -cosh(b*x + a) - sinh(b*x + a)))/b^3","C",0
3,1,112,0,1.364965," ","integrate(x*coth(b*x+a),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - 2 \, b x \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 2 \, a \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 2 \, {\left(b x + a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 2 \, {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 2 \, {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*x^2 - 2*b*x*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 2*a*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 2*(b*x + a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 2*dilog(cosh(b*x + a) + sinh(b*x + a)) - 2*dilog(-cosh(b*x + a) - sinh(b*x + a)))/b^2","B",0
4,0,0,0,0.446477," ","integrate(coth(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)}{x}, x\right)"," ",0,"integral(coth(b*x + a)/x, x)","F",0
5,0,0,0,0.458776," ","integrate(coth(b*x+a)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)}{x^{2}}, x\right)"," ",0,"integral(coth(b*x + a)/x^2, x)","F",0
6,1,632,0,0.545185," ","integrate(x^3*coth(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{4} x^{4} - 8 \, a^{3} - {\left(b^{4} x^{4} - 8 \, b^{3} x^{3} - 8 \, a^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{4} x^{4} - 8 \, b^{3} x^{3} - 8 \, a^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{4} x^{4} - 8 \, b^{3} x^{3} - 8 \, a^{3}\right)} \sinh\left(b x + a\right)^{2} - 24 \, {\left(b x \cosh\left(b x + a\right)^{2} + 2 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b x \sinh\left(b x + a\right)^{2} - b x\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 24 \, {\left(b x \cosh\left(b x + a\right)^{2} + 2 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b x \sinh\left(b x + a\right)^{2} - b x\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 12 \, {\left(b^{2} x^{2} \cosh\left(b x + a\right)^{2} + 2 \, b^{2} x^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{2} x^{2} \sinh\left(b x + a\right)^{2} - b^{2} x^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - 12 \, {\left(a^{2} \cosh\left(b x + a\right)^{2} + 2 \, a^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + a^{2} \sinh\left(b x + a\right)^{2} - a^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + 12 \, {\left(b^{2} x^{2} - {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} x^{2} - a^{2}\right)} \sinh\left(b x + a\right)^{2} - a^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 24 \, {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} - 1\right)} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 24 \, {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} - 1\right)} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{4 \, {\left(b^{4} \cosh\left(b x + a\right)^{2} + 2 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{4} \sinh\left(b x + a\right)^{2} - b^{4}\right)}}"," ",0,"-1/4*(b^4*x^4 - 8*a^3 - (b^4*x^4 - 8*b^3*x^3 - 8*a^3)*cosh(b*x + a)^2 - 2*(b^4*x^4 - 8*b^3*x^3 - 8*a^3)*cosh(b*x + a)*sinh(b*x + a) - (b^4*x^4 - 8*b^3*x^3 - 8*a^3)*sinh(b*x + a)^2 - 24*(b*x*cosh(b*x + a)^2 + 2*b*x*cosh(b*x + a)*sinh(b*x + a) + b*x*sinh(b*x + a)^2 - b*x)*dilog(cosh(b*x + a) + sinh(b*x + a)) - 24*(b*x*cosh(b*x + a)^2 + 2*b*x*cosh(b*x + a)*sinh(b*x + a) + b*x*sinh(b*x + a)^2 - b*x)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 12*(b^2*x^2*cosh(b*x + a)^2 + 2*b^2*x^2*cosh(b*x + a)*sinh(b*x + a) + b^2*x^2*sinh(b*x + a)^2 - b^2*x^2)*log(cosh(b*x + a) + sinh(b*x + a) + 1) - 12*(a^2*cosh(b*x + a)^2 + 2*a^2*cosh(b*x + a)*sinh(b*x + a) + a^2*sinh(b*x + a)^2 - a^2)*log(cosh(b*x + a) + sinh(b*x + a) - 1) + 12*(b^2*x^2 - (b^2*x^2 - a^2)*cosh(b*x + a)^2 - 2*(b^2*x^2 - a^2)*cosh(b*x + a)*sinh(b*x + a) - (b^2*x^2 - a^2)*sinh(b*x + a)^2 - a^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 24*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1)*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 24*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1)*polylog(3, -cosh(b*x + a) - sinh(b*x + a)))/(b^4*cosh(b*x + a)^2 + 2*b^4*cosh(b*x + a)*sinh(b*x + a) + b^4*sinh(b*x + a)^2 - b^4)","C",0
7,1,453,0,0.469371," ","integrate(x^2*coth(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{3} x^{3} - {\left(b^{3} x^{3} - 6 \, b^{2} x^{2} + 6 \, a^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} x^{3} - 6 \, b^{2} x^{2} + 6 \, a^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{3} x^{3} - 6 \, b^{2} x^{2} + 6 \, a^{2}\right)} \sinh\left(b x + a\right)^{2} + 6 \, a^{2} - 6 \, {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} - 1\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} - 1\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 6 \, {\left(b x \cosh\left(b x + a\right)^{2} + 2 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b x \sinh\left(b x + a\right)^{2} - b x\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 6 \, {\left(a \cosh\left(b x + a\right)^{2} + 2 \, a \cosh\left(b x + a\right) \sinh\left(b x + a\right) + a \sinh\left(b x + a\right)^{2} - a\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 6 \, {\left({\left(b x + a\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b x + a\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b x + a\right)} \sinh\left(b x + a\right)^{2} - b x - a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right)}{3 \, {\left(b^{3} \cosh\left(b x + a\right)^{2} + 2 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{3} \sinh\left(b x + a\right)^{2} - b^{3}\right)}}"," ",0,"-1/3*(b^3*x^3 - (b^3*x^3 - 6*b^2*x^2 + 6*a^2)*cosh(b*x + a)^2 - 2*(b^3*x^3 - 6*b^2*x^2 + 6*a^2)*cosh(b*x + a)*sinh(b*x + a) - (b^3*x^3 - 6*b^2*x^2 + 6*a^2)*sinh(b*x + a)^2 + 6*a^2 - 6*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1)*dilog(cosh(b*x + a) + sinh(b*x + a)) - 6*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 6*(b*x*cosh(b*x + a)^2 + 2*b*x*cosh(b*x + a)*sinh(b*x + a) + b*x*sinh(b*x + a)^2 - b*x)*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 6*(a*cosh(b*x + a)^2 + 2*a*cosh(b*x + a)*sinh(b*x + a) + a*sinh(b*x + a)^2 - a)*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 6*((b*x + a)*cosh(b*x + a)^2 + 2*(b*x + a)*cosh(b*x + a)*sinh(b*x + a) + (b*x + a)*sinh(b*x + a)^2 - b*x - a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1))/(b^3*cosh(b*x + a)^2 + 2*b^3*cosh(b*x + a)*sinh(b*x + a) + b^3*sinh(b*x + a)^2 - b^3)","B",0
8,1,189,0,0.457201," ","integrate(x*coth(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} x^{2} - {\left(b^{2} x^{2} - 4 \, b x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 4 \, b x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} x^{2} - 4 \, b x\right)} \sinh\left(b x + a\right)^{2} - 2 \, {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{2 \, \sinh\left(b x + a\right)}{\cosh\left(b x + a\right) - \sinh\left(b x + a\right)}\right)}{2 \, {\left(b^{2} \cosh\left(b x + a\right)^{2} + 2 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{2} \sinh\left(b x + a\right)^{2} - b^{2}\right)}}"," ",0,"-1/2*(b^2*x^2 - (b^2*x^2 - 4*b*x)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 4*b*x)*cosh(b*x + a)*sinh(b*x + a) - (b^2*x^2 - 4*b*x)*sinh(b*x + a)^2 - 2*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1)*log(2*sinh(b*x + a)/(cosh(b*x + a) - sinh(b*x + a))))/(b^2*cosh(b*x + a)^2 + 2*b^2*cosh(b*x + a)*sinh(b*x + a) + b^2*sinh(b*x + a)^2 - b^2)","B",0
9,0,0,0,0.454985," ","integrate(coth(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(coth(b*x + a)^2/x, x)","F",0
10,0,0,0,0.454830," ","integrate(coth(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(coth(b*x + a)^2/x^2, x)","F",0
11,1,1985,0,0.480208," ","integrate(x^3*coth(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{4} x^{4} + {\left(b^{4} x^{4} - 2 \, a^{4} + 12 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{4} x^{4} - 2 \, a^{4} + 12 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{4} x^{4} - 2 \, a^{4} + 12 \, b^{2} x^{2} - 12 \, a^{2}\right)} \sinh\left(b x + a\right)^{4} - 2 \, a^{4} - 2 \, {\left(b^{4} x^{4} - 4 \, b^{3} x^{3} - 2 \, a^{4} + 6 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{4} x^{4} - 4 \, b^{3} x^{3} - 2 \, a^{4} + 6 \, b^{2} x^{2} - 3 \, {\left(b^{4} x^{4} - 2 \, a^{4} + 12 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right)^{2} - 12 \, a^{2}\right)} \sinh\left(b x + a\right)^{2} - 12 \, a^{2} - 12 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} x^{2} + 1\right)} \sinh\left(b x + a\right)^{4} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 3 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 12 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} x^{2} + 1\right)} \sinh\left(b x + a\right)^{4} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 3 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 4 \, {\left(b^{3} x^{3} + {\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} x^{3} + 3 \, b x\right)} \sinh\left(b x + a\right)^{4} - 2 \, {\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} x^{3} - 3 \, {\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)^{2} + 3 \, b x\right)} \sinh\left(b x + a\right)^{2} + 3 \, b x + 4 \, {\left({\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 4 \, {\left({\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(a^{3} + 3 \, a\right)} \sinh\left(b x + a\right)^{4} + a^{3} - 2 \, {\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(a^{3} - 3 \, {\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right)^{2} + 3 \, a\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right)^{3} - {\left(a^{3} + 3 \, a\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 3 \, a\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 4 \, {\left(b^{3} x^{3} + {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \sinh\left(b x + a\right)^{4} + a^{3} - 2 \, {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} x^{3} + a^{3} - 3 \, {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right)^{2} + 3 \, b x + 3 \, a\right)} \sinh\left(b x + a\right)^{2} + 3 \, b x + 4 \, {\left({\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + a^{3} + 3 \, b x + 3 \, a\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 3 \, a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 24 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 24 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 24 \, {\left(b x \cosh\left(b x + a\right)^{4} + 4 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b x \sinh\left(b x + a\right)^{4} - 2 \, b x \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} - b x\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left(b x \cosh\left(b x + a\right)^{3} - b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 24 \, {\left(b x \cosh\left(b x + a\right)^{4} + 4 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b x \sinh\left(b x + a\right)^{4} - 2 \, b x \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} - b x\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left(b x \cosh\left(b x + a\right)^{3} - b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 4 \, {\left({\left(b^{4} x^{4} - 2 \, a^{4} + 12 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{4} x^{4} - 4 \, b^{3} x^{3} - 2 \, a^{4} + 6 \, b^{2} x^{2} - 12 \, a^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)}{4 \, {\left(b^{4} \cosh\left(b x + a\right)^{4} + 4 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{4} \sinh\left(b x + a\right)^{4} - 2 \, b^{4} \cosh\left(b x + a\right)^{2} + b^{4} + 2 \, {\left(3 \, b^{4} \cosh\left(b x + a\right)^{2} - b^{4}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b^{4} \cosh\left(b x + a\right)^{3} - b^{4} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/4*(b^4*x^4 + (b^4*x^4 - 2*a^4 + 12*b^2*x^2 - 12*a^2)*cosh(b*x + a)^4 + 4*(b^4*x^4 - 2*a^4 + 12*b^2*x^2 - 12*a^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^4*x^4 - 2*a^4 + 12*b^2*x^2 - 12*a^2)*sinh(b*x + a)^4 - 2*a^4 - 2*(b^4*x^4 - 4*b^3*x^3 - 2*a^4 + 6*b^2*x^2 - 12*a^2)*cosh(b*x + a)^2 - 2*(b^4*x^4 - 4*b^3*x^3 - 2*a^4 + 6*b^2*x^2 - 3*(b^4*x^4 - 2*a^4 + 12*b^2*x^2 - 12*a^2)*cosh(b*x + a)^2 - 12*a^2)*sinh(b*x + a)^2 - 12*a^2 - 12*((b^2*x^2 + 1)*cosh(b*x + a)^4 + 4*(b^2*x^2 + 1)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*x^2 + 1)*sinh(b*x + a)^4 + b^2*x^2 - 2*(b^2*x^2 + 1)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 3*(b^2*x^2 + 1)*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 4*((b^2*x^2 + 1)*cosh(b*x + a)^3 - (b^2*x^2 + 1)*cosh(b*x + a))*sinh(b*x + a) + 1)*dilog(cosh(b*x + a) + sinh(b*x + a)) - 12*((b^2*x^2 + 1)*cosh(b*x + a)^4 + 4*(b^2*x^2 + 1)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*x^2 + 1)*sinh(b*x + a)^4 + b^2*x^2 - 2*(b^2*x^2 + 1)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 3*(b^2*x^2 + 1)*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 4*((b^2*x^2 + 1)*cosh(b*x + a)^3 - (b^2*x^2 + 1)*cosh(b*x + a))*sinh(b*x + a) + 1)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 4*(b^3*x^3 + (b^3*x^3 + 3*b*x)*cosh(b*x + a)^4 + 4*(b^3*x^3 + 3*b*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*x^3 + 3*b*x)*sinh(b*x + a)^4 - 2*(b^3*x^3 + 3*b*x)*cosh(b*x + a)^2 - 2*(b^3*x^3 - 3*(b^3*x^3 + 3*b*x)*cosh(b*x + a)^2 + 3*b*x)*sinh(b*x + a)^2 + 3*b*x + 4*((b^3*x^3 + 3*b*x)*cosh(b*x + a)^3 - (b^3*x^3 + 3*b*x)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 4*((a^3 + 3*a)*cosh(b*x + a)^4 + 4*(a^3 + 3*a)*cosh(b*x + a)*sinh(b*x + a)^3 + (a^3 + 3*a)*sinh(b*x + a)^4 + a^3 - 2*(a^3 + 3*a)*cosh(b*x + a)^2 - 2*(a^3 - 3*(a^3 + 3*a)*cosh(b*x + a)^2 + 3*a)*sinh(b*x + a)^2 + 4*((a^3 + 3*a)*cosh(b*x + a)^3 - (a^3 + 3*a)*cosh(b*x + a))*sinh(b*x + a) + 3*a)*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 4*(b^3*x^3 + (b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a)^4 + 4*(b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*x^3 + a^3 + 3*b*x + 3*a)*sinh(b*x + a)^4 + a^3 - 2*(b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a)^2 - 2*(b^3*x^3 + a^3 - 3*(b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a)^2 + 3*b*x + 3*a)*sinh(b*x + a)^2 + 3*b*x + 4*((b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a)^3 - (b^3*x^3 + a^3 + 3*b*x + 3*a)*cosh(b*x + a))*sinh(b*x + a) + 3*a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 24*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 24*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*polylog(4, -cosh(b*x + a) - sinh(b*x + a)) + 24*(b*x*cosh(b*x + a)^4 + 4*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + b*x*sinh(b*x + a)^4 - 2*b*x*cosh(b*x + a)^2 + 2*(3*b*x*cosh(b*x + a)^2 - b*x)*sinh(b*x + a)^2 + b*x + 4*(b*x*cosh(b*x + a)^3 - b*x*cosh(b*x + a))*sinh(b*x + a))*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 24*(b*x*cosh(b*x + a)^4 + 4*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + b*x*sinh(b*x + a)^4 - 2*b*x*cosh(b*x + a)^2 + 2*(3*b*x*cosh(b*x + a)^2 - b*x)*sinh(b*x + a)^2 + b*x + 4*(b*x*cosh(b*x + a)^3 - b*x*cosh(b*x + a))*sinh(b*x + a))*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + 4*((b^4*x^4 - 2*a^4 + 12*b^2*x^2 - 12*a^2)*cosh(b*x + a)^3 - (b^4*x^4 - 4*b^3*x^3 - 2*a^4 + 6*b^2*x^2 - 12*a^2)*cosh(b*x + a))*sinh(b*x + a))/(b^4*cosh(b*x + a)^4 + 4*b^4*cosh(b*x + a)*sinh(b*x + a)^3 + b^4*sinh(b*x + a)^4 - 2*b^4*cosh(b*x + a)^2 + b^4 + 2*(3*b^4*cosh(b*x + a)^2 - b^4)*sinh(b*x + a)^2 + 4*(b^4*cosh(b*x + a)^3 - b^4*cosh(b*x + a))*sinh(b*x + a))","C",0
12,1,1467,0,0.522980," ","integrate(x^2*coth(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{3} x^{3} + {\left(b^{3} x^{3} + 2 \, a^{3} + 6 \, b x + 6 \, a\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} x^{3} + 2 \, a^{3} + 6 \, b x + 6 \, a\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} x^{3} + 2 \, a^{3} + 6 \, b x + 6 \, a\right)} \sinh\left(b x + a\right)^{4} + 2 \, a^{3} - 2 \, {\left(b^{3} x^{3} - 3 \, b^{2} x^{2} + 2 \, a^{3} + 3 \, b x + 6 \, a\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} x^{3} - 3 \, b^{2} x^{2} + 2 \, a^{3} - 3 \, {\left(b^{3} x^{3} + 2 \, a^{3} + 6 \, b x + 6 \, a\right)} \cosh\left(b x + a\right)^{2} + 3 \, b x + 6 \, a\right)} \sinh\left(b x + a\right)^{2} - 6 \, {\left(b x \cosh\left(b x + a\right)^{4} + 4 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b x \sinh\left(b x + a\right)^{4} - 2 \, b x \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} - b x\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left(b x \cosh\left(b x + a\right)^{3} - b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, {\left(b x \cosh\left(b x + a\right)^{4} + 4 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b x \sinh\left(b x + a\right)^{4} - 2 \, b x \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} - b x\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left(b x \cosh\left(b x + a\right)^{3} - b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 3 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} x^{2} + 1\right)} \sinh\left(b x + a\right)^{4} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 3 \, {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - 3 \, {\left({\left(a^{2} + 1\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(a^{2} + 1\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(a^{2} + 1\right)} \sinh\left(b x + a\right)^{4} - 2 \, {\left(a^{2} + 1\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 1\right)} \cosh\left(b x + a\right)^{2} - a^{2} - 1\right)} \sinh\left(b x + a\right)^{2} + a^{2} + 4 \, {\left({\left(a^{2} + 1\right)} \cosh\left(b x + a\right)^{3} - {\left(a^{2} + 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 3 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} x^{2} - a^{2}\right)} \sinh\left(b x + a\right)^{4} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)^{2} - a^{2}\right)} \sinh\left(b x + a\right)^{2} - a^{2} + 4 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 6 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 4 \, {\left({\left(b^{3} x^{3} + 2 \, a^{3} + 6 \, b x + 6 \, a\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} x^{3} - 3 \, b^{2} x^{2} + 2 \, a^{3} + 3 \, b x + 6 \, a\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 6 \, a}{3 \, {\left(b^{3} \cosh\left(b x + a\right)^{4} + 4 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{3} \sinh\left(b x + a\right)^{4} - 2 \, b^{3} \cosh\left(b x + a\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(b x + a\right)^{2} - b^{3}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b^{3} \cosh\left(b x + a\right)^{3} - b^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/3*(b^3*x^3 + (b^3*x^3 + 2*a^3 + 6*b*x + 6*a)*cosh(b*x + a)^4 + 4*(b^3*x^3 + 2*a^3 + 6*b*x + 6*a)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*x^3 + 2*a^3 + 6*b*x + 6*a)*sinh(b*x + a)^4 + 2*a^3 - 2*(b^3*x^3 - 3*b^2*x^2 + 2*a^3 + 3*b*x + 6*a)*cosh(b*x + a)^2 - 2*(b^3*x^3 - 3*b^2*x^2 + 2*a^3 - 3*(b^3*x^3 + 2*a^3 + 6*b*x + 6*a)*cosh(b*x + a)^2 + 3*b*x + 6*a)*sinh(b*x + a)^2 - 6*(b*x*cosh(b*x + a)^4 + 4*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + b*x*sinh(b*x + a)^4 - 2*b*x*cosh(b*x + a)^2 + 2*(3*b*x*cosh(b*x + a)^2 - b*x)*sinh(b*x + a)^2 + b*x + 4*(b*x*cosh(b*x + a)^3 - b*x*cosh(b*x + a))*sinh(b*x + a))*dilog(cosh(b*x + a) + sinh(b*x + a)) - 6*(b*x*cosh(b*x + a)^4 + 4*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + b*x*sinh(b*x + a)^4 - 2*b*x*cosh(b*x + a)^2 + 2*(3*b*x*cosh(b*x + a)^2 - b*x)*sinh(b*x + a)^2 + b*x + 4*(b*x*cosh(b*x + a)^3 - b*x*cosh(b*x + a))*sinh(b*x + a))*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 3*((b^2*x^2 + 1)*cosh(b*x + a)^4 + 4*(b^2*x^2 + 1)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*x^2 + 1)*sinh(b*x + a)^4 + b^2*x^2 - 2*(b^2*x^2 + 1)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 3*(b^2*x^2 + 1)*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 4*((b^2*x^2 + 1)*cosh(b*x + a)^3 - (b^2*x^2 + 1)*cosh(b*x + a))*sinh(b*x + a) + 1)*log(cosh(b*x + a) + sinh(b*x + a) + 1) - 3*((a^2 + 1)*cosh(b*x + a)^4 + 4*(a^2 + 1)*cosh(b*x + a)*sinh(b*x + a)^3 + (a^2 + 1)*sinh(b*x + a)^4 - 2*(a^2 + 1)*cosh(b*x + a)^2 + 2*(3*(a^2 + 1)*cosh(b*x + a)^2 - a^2 - 1)*sinh(b*x + a)^2 + a^2 + 4*((a^2 + 1)*cosh(b*x + a)^3 - (a^2 + 1)*cosh(b*x + a))*sinh(b*x + a) + 1)*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 3*((b^2*x^2 - a^2)*cosh(b*x + a)^4 + 4*(b^2*x^2 - a^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*x^2 - a^2)*sinh(b*x + a)^4 + b^2*x^2 - 2*(b^2*x^2 - a^2)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 3*(b^2*x^2 - a^2)*cosh(b*x + a)^2 - a^2)*sinh(b*x + a)^2 - a^2 + 4*((b^2*x^2 - a^2)*cosh(b*x + a)^3 - (b^2*x^2 - a^2)*cosh(b*x + a))*sinh(b*x + a))*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + 4*((b^3*x^3 + 2*a^3 + 6*b*x + 6*a)*cosh(b*x + a)^3 - (b^3*x^3 - 3*b^2*x^2 + 2*a^3 + 3*b*x + 6*a)*cosh(b*x + a))*sinh(b*x + a) + 6*a)/(b^3*cosh(b*x + a)^4 + 4*b^3*cosh(b*x + a)*sinh(b*x + a)^3 + b^3*sinh(b*x + a)^4 - 2*b^3*cosh(b*x + a)^2 + b^3 + 2*(3*b^3*cosh(b*x + a)^2 - b^3)*sinh(b*x + a)^2 + 4*(b^3*cosh(b*x + a)^3 - b^3*cosh(b*x + a))*sinh(b*x + a))","C",0
13,1,975,0,0.520468," ","integrate(x*coth(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(b^{2} x^{2} - 2 \, a^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} x^{2} - 2 \, a^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} x^{2} - 2 \, a^{2}\right)} \sinh\left(b x + a\right)^{4} + b^{2} x^{2} - 2 \, {\left(b^{2} x^{2} - 2 \, a^{2} - 2 \, b x - 1\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} x^{2} - 3 \, {\left(b^{2} x^{2} - 2 \, a^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, a^{2} - 2 \, b x - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, a^{2} - 2 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 2 \, {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{2} - 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} - \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 2 \, {\left(b x \cosh\left(b x + a\right)^{4} + 4 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b x \sinh\left(b x + a\right)^{4} - 2 \, b x \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} - b x\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left(b x \cosh\left(b x + a\right)^{3} - b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 2 \, {\left(a \cosh\left(b x + a\right)^{4} + 4 \, a \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + a \sinh\left(b x + a\right)^{4} - 2 \, a \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, a \cosh\left(b x + a\right)^{2} - a\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(a \cosh\left(b x + a\right)^{3} - a \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + a\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 2 \, {\left({\left(b x + a\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b x + a\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b x + a\right)} \sinh\left(b x + a\right)^{4} - 2 \, {\left(b x + a\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(b x + a\right)} \cosh\left(b x + a\right)^{2} - b x - a\right)} \sinh\left(b x + a\right)^{2} + b x + 4 \, {\left({\left(b x + a\right)} \cosh\left(b x + a\right)^{3} - {\left(b x + a\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b^{2} x^{2} - 2 \, a^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - 2 \, a^{2} - 2 \, b x - 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) - 2}{2 \, {\left(b^{2} \cosh\left(b x + a\right)^{4} + 4 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{2} \sinh\left(b x + a\right)^{4} - 2 \, b^{2} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(b x + a\right)^{2} - b^{2}\right)} \sinh\left(b x + a\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(b x + a\right)^{3} - b^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/2*((b^2*x^2 - 2*a^2)*cosh(b*x + a)^4 + 4*(b^2*x^2 - 2*a^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*x^2 - 2*a^2)*sinh(b*x + a)^4 + b^2*x^2 - 2*(b^2*x^2 - 2*a^2 - 2*b*x - 1)*cosh(b*x + a)^2 - 2*(b^2*x^2 - 3*(b^2*x^2 - 2*a^2)*cosh(b*x + a)^2 - 2*a^2 - 2*b*x - 1)*sinh(b*x + a)^2 - 2*a^2 - 2*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*dilog(cosh(b*x + a) + sinh(b*x + a)) - 2*(cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^2 - 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 - cosh(b*x + a))*sinh(b*x + a) + 1)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - 2*(b*x*cosh(b*x + a)^4 + 4*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + b*x*sinh(b*x + a)^4 - 2*b*x*cosh(b*x + a)^2 + 2*(3*b*x*cosh(b*x + a)^2 - b*x)*sinh(b*x + a)^2 + b*x + 4*(b*x*cosh(b*x + a)^3 - b*x*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 2*(a*cosh(b*x + a)^4 + 4*a*cosh(b*x + a)*sinh(b*x + a)^3 + a*sinh(b*x + a)^4 - 2*a*cosh(b*x + a)^2 + 2*(3*a*cosh(b*x + a)^2 - a)*sinh(b*x + a)^2 + 4*(a*cosh(b*x + a)^3 - a*cosh(b*x + a))*sinh(b*x + a) + a)*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 2*((b*x + a)*cosh(b*x + a)^4 + 4*(b*x + a)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*x + a)*sinh(b*x + a)^4 - 2*(b*x + a)*cosh(b*x + a)^2 + 2*(3*(b*x + a)*cosh(b*x + a)^2 - b*x - a)*sinh(b*x + a)^2 + b*x + 4*((b*x + a)*cosh(b*x + a)^3 - (b*x + a)*cosh(b*x + a))*sinh(b*x + a) + a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 4*((b^2*x^2 - 2*a^2)*cosh(b*x + a)^3 - (b^2*x^2 - 2*a^2 - 2*b*x - 1)*cosh(b*x + a))*sinh(b*x + a) - 2)/(b^2*cosh(b*x + a)^4 + 4*b^2*cosh(b*x + a)*sinh(b*x + a)^3 + b^2*sinh(b*x + a)^4 - 2*b^2*cosh(b*x + a)^2 + 2*(3*b^2*cosh(b*x + a)^2 - b^2)*sinh(b*x + a)^2 + b^2 + 4*(b^2*cosh(b*x + a)^3 - b^2*cosh(b*x + a))*sinh(b*x + a))","B",0
14,0,0,0,0.478980," ","integrate(coth(b*x+a)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)^{3}}{x}, x\right)"," ",0,"integral(coth(b*x + a)^3/x, x)","F",0
15,0,0,0,0.443001," ","integrate(coth(b*x+a)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(b x + a\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(coth(b*x + a)^3/x^2, x)","F",0
16,1,304,0,0.511639," ","integrate((d*x+c)^3/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, d^{3} f^{4} x^{4} + 4 \, c^{3} f^{3} + 6 \, c^{2} d f^{2} + 6 \, c d^{2} f + 4 \, {\left(2 \, c d^{2} f^{4} + d^{3} f^{3}\right)} x^{3} + 3 \, d^{3} + 6 \, {\left(2 \, c^{2} d f^{4} + 2 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + 2 \, {\left(4 \, c^{3} f^{4} + 6 \, c^{2} d f^{3} + 6 \, c d^{2} f^{2} + 3 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right) + {\left(2 \, d^{3} f^{4} x^{4} - 4 \, c^{3} f^{3} - 6 \, c^{2} d f^{2} - 6 \, c d^{2} f + 4 \, {\left(2 \, c d^{2} f^{4} - d^{3} f^{3}\right)} x^{3} - 3 \, d^{3} + 6 \, {\left(2 \, c^{2} d f^{4} - 2 \, c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 2 \, {\left(4 \, c^{3} f^{4} - 6 \, c^{2} d f^{3} - 6 \, c d^{2} f^{2} - 3 \, d^{3} f\right)} x\right)} \sinh\left(f x + e\right)}{16 \, {\left(a f^{4} \cosh\left(f x + e\right) + a f^{4} \sinh\left(f x + e\right)\right)}}"," ",0,"1/16*((2*d^3*f^4*x^4 + 4*c^3*f^3 + 6*c^2*d*f^2 + 6*c*d^2*f + 4*(2*c*d^2*f^4 + d^3*f^3)*x^3 + 3*d^3 + 6*(2*c^2*d*f^4 + 2*c*d^2*f^3 + d^3*f^2)*x^2 + 2*(4*c^3*f^4 + 6*c^2*d*f^3 + 6*c*d^2*f^2 + 3*d^3*f)*x)*cosh(f*x + e) + (2*d^3*f^4*x^4 - 4*c^3*f^3 - 6*c^2*d*f^2 - 6*c*d^2*f + 4*(2*c*d^2*f^4 - d^3*f^3)*x^3 - 3*d^3 + 6*(2*c^2*d*f^4 - 2*c*d^2*f^3 - d^3*f^2)*x^2 + 2*(4*c^3*f^4 - 6*c^2*d*f^3 - 6*c*d^2*f^2 - 3*d^3*f)*x)*sinh(f*x + e))/(a*f^4*cosh(f*x + e) + a*f^4*sinh(f*x + e))","A",0
17,1,192,0,0.410978," ","integrate((d*x+c)^2/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(4 \, d^{2} f^{3} x^{3} + 6 \, c^{2} f^{2} + 6 \, c d f + 6 \, {\left(2 \, c d f^{3} + d^{2} f^{2}\right)} x^{2} + 3 \, d^{2} + 6 \, {\left(2 \, c^{2} f^{3} + 2 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right) + {\left(4 \, d^{2} f^{3} x^{3} - 6 \, c^{2} f^{2} - 6 \, c d f + 6 \, {\left(2 \, c d f^{3} - d^{2} f^{2}\right)} x^{2} - 3 \, d^{2} + 6 \, {\left(2 \, c^{2} f^{3} - 2 \, c d f^{2} - d^{2} f\right)} x\right)} \sinh\left(f x + e\right)}{24 \, {\left(a f^{3} \cosh\left(f x + e\right) + a f^{3} \sinh\left(f x + e\right)\right)}}"," ",0,"1/24*((4*d^2*f^3*x^3 + 6*c^2*f^2 + 6*c*d*f + 6*(2*c*d*f^3 + d^2*f^2)*x^2 + 3*d^2 + 6*(2*c^2*f^3 + 2*c*d*f^2 + d^2*f)*x)*cosh(f*x + e) + (4*d^2*f^3*x^3 - 6*c^2*f^2 - 6*c*d*f + 6*(2*c*d*f^3 - d^2*f^2)*x^2 - 3*d^2 + 6*(2*c^2*f^3 - 2*c*d*f^2 - d^2*f)*x)*sinh(f*x + e))/(a*f^3*cosh(f*x + e) + a*f^3*sinh(f*x + e))","A",0
18,1,101,0,0.386860," ","integrate((d*x+c)/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, d f^{2} x^{2} + 2 \, c f + 2 \, {\left(2 \, c f^{2} + d f\right)} x + d\right)} \cosh\left(f x + e\right) + {\left(2 \, d f^{2} x^{2} - 2 \, c f + 2 \, {\left(2 \, c f^{2} - d f\right)} x - d\right)} \sinh\left(f x + e\right)}{8 \, {\left(a f^{2} \cosh\left(f x + e\right) + a f^{2} \sinh\left(f x + e\right)\right)}}"," ",0,"1/8*((2*d*f^2*x^2 + 2*c*f + 2*(2*c*f^2 + d*f)*x + d)*cosh(f*x + e) + (2*d*f^2*x^2 - 2*c*f + 2*(2*c*f^2 - d*f)*x - d)*sinh(f*x + e))/(a*f^2*cosh(f*x + e) + a*f^2*sinh(f*x + e))","A",0
19,1,75,0,0.396322," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","-\frac{{\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - \log\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) + Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - log(d*x + c))/(a*d)","A",0
20,1,216,0,0.398762," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - d\right)} \sinh\left(f x + e\right)}{{\left(a d^{3} x + a c d^{2}\right)} \cosh\left(f x + e\right) + {\left(a d^{3} x + a c d^{2}\right)} \sinh\left(f x + e\right)}"," ",0,"((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)*cosh(-2*(d*e - c*f)/d) + (d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-2*(d*e - c*f)/d) + ((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) + (d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - d)*sinh(f*x + e))/((a*d^3*x + a*c*d^2)*cosh(f*x + e) + (a*d^3*x + a*c*d^2)*sinh(f*x + e))","A",0
21,1,342,0,0.397286," ","integrate(1/(d*x+c)^3/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + {\left(d^{2} f x + c d f + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)\right)} \cosh\left(f x + e\right) - {\left(d^{2} f x + c d f - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - d^{2}\right)} \sinh\left(f x + e\right)}{2 \, {\left({\left(a d^{5} x^{2} + 2 \, a c d^{4} x + a c^{2} d^{3}\right)} \cosh\left(f x + e\right) + {\left(a d^{5} x^{2} + 2 \, a c d^{4} x + a c^{2} d^{3}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-1/2*(2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-2*(d*e - c*f)/d) + (d^2*f*x + c*d*f + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d))*cosh(f*x + e) - (d^2*f*x + c*d*f - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - d^2)*sinh(f*x + e))/((a*d^5*x^2 + 2*a*c*d^4*x + a*c^2*d^3)*cosh(f*x + e) + (a*d^5*x^2 + 2*a*c*d^4*x + a*c^2*d^3)*sinh(f*x + e))","A",0
22,1,571,0,0.402372," ","integrate((d*x+c)^3/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","\frac{128 \, d^{3} f^{3} x^{3} + 128 \, c^{3} f^{3} + 192 \, c^{2} d f^{2} + 192 \, c d^{2} f + 96 \, d^{3} + 192 \, {\left(2 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + {\left(32 \, d^{3} f^{4} x^{4} - 32 \, c^{3} f^{3} - 24 \, c^{2} d f^{2} - 12 \, c d^{2} f + 32 \, {\left(4 \, c d^{2} f^{4} - d^{3} f^{3}\right)} x^{3} - 3 \, d^{3} + 24 \, {\left(8 \, c^{2} d f^{4} - 4 \, c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 4 \, {\left(32 \, c^{3} f^{4} - 24 \, c^{2} d f^{3} - 12 \, c d^{2} f^{2} - 3 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(32 \, d^{3} f^{4} x^{4} + 32 \, c^{3} f^{3} + 24 \, c^{2} d f^{2} + 12 \, c d^{2} f + 32 \, {\left(4 \, c d^{2} f^{4} + d^{3} f^{3}\right)} x^{3} + 3 \, d^{3} + 24 \, {\left(8 \, c^{2} d f^{4} + 4 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + 4 \, {\left(32 \, c^{3} f^{4} + 24 \, c^{2} d f^{3} + 12 \, c d^{2} f^{2} + 3 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(32 \, d^{3} f^{4} x^{4} - 32 \, c^{3} f^{3} - 24 \, c^{2} d f^{2} - 12 \, c d^{2} f + 32 \, {\left(4 \, c d^{2} f^{4} - d^{3} f^{3}\right)} x^{3} - 3 \, d^{3} + 24 \, {\left(8 \, c^{2} d f^{4} - 4 \, c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 4 \, {\left(32 \, c^{3} f^{4} - 24 \, c^{2} d f^{3} - 12 \, c d^{2} f^{2} - 3 \, d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + 192 \, {\left(2 \, c^{2} d f^{3} + 2 \, c d^{2} f^{2} + d^{3} f\right)} x}{512 \, {\left(a^{2} f^{4} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{4} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a^{2} f^{4} \sinh\left(f x + e\right)^{2}\right)}}"," ",0,"1/512*(128*d^3*f^3*x^3 + 128*c^3*f^3 + 192*c^2*d*f^2 + 192*c*d^2*f + 96*d^3 + 192*(2*c*d^2*f^3 + d^3*f^2)*x^2 + (32*d^3*f^4*x^4 - 32*c^3*f^3 - 24*c^2*d*f^2 - 12*c*d^2*f + 32*(4*c*d^2*f^4 - d^3*f^3)*x^3 - 3*d^3 + 24*(8*c^2*d*f^4 - 4*c*d^2*f^3 - d^3*f^2)*x^2 + 4*(32*c^3*f^4 - 24*c^2*d*f^3 - 12*c*d^2*f^2 - 3*d^3*f)*x)*cosh(f*x + e)^2 + 2*(32*d^3*f^4*x^4 + 32*c^3*f^3 + 24*c^2*d*f^2 + 12*c*d^2*f + 32*(4*c*d^2*f^4 + d^3*f^3)*x^3 + 3*d^3 + 24*(8*c^2*d*f^4 + 4*c*d^2*f^3 + d^3*f^2)*x^2 + 4*(32*c^3*f^4 + 24*c^2*d*f^3 + 12*c*d^2*f^2 + 3*d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e) + (32*d^3*f^4*x^4 - 32*c^3*f^3 - 24*c^2*d*f^2 - 12*c*d^2*f + 32*(4*c*d^2*f^4 - d^3*f^3)*x^3 - 3*d^3 + 24*(8*c^2*d*f^4 - 4*c*d^2*f^3 - d^3*f^2)*x^2 + 4*(32*c^3*f^4 - 24*c^2*d*f^3 - 12*c*d^2*f^2 - 3*d^3*f)*x)*sinh(f*x + e)^2 + 192*(2*c^2*d*f^3 + 2*c*d^2*f^2 + d^3*f)*x)/(a^2*f^4*cosh(f*x + e)^2 + 2*a^2*f^4*cosh(f*x + e)*sinh(f*x + e) + a^2*f^4*sinh(f*x + e)^2)","B",0
23,1,359,0,0.417124," ","integrate((d*x+c)^2/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","\frac{96 \, d^{2} f^{2} x^{2} + 96 \, c^{2} f^{2} + 96 \, c d f + {\left(32 \, d^{2} f^{3} x^{3} - 24 \, c^{2} f^{2} - 12 \, c d f + 24 \, {\left(4 \, c d f^{3} - d^{2} f^{2}\right)} x^{2} - 3 \, d^{2} + 12 \, {\left(8 \, c^{2} f^{3} - 4 \, c d f^{2} - d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(32 \, d^{2} f^{3} x^{3} + 24 \, c^{2} f^{2} + 12 \, c d f + 24 \, {\left(4 \, c d f^{3} + d^{2} f^{2}\right)} x^{2} + 3 \, d^{2} + 12 \, {\left(8 \, c^{2} f^{3} + 4 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(32 \, d^{2} f^{3} x^{3} - 24 \, c^{2} f^{2} - 12 \, c d f + 24 \, {\left(4 \, c d f^{3} - d^{2} f^{2}\right)} x^{2} - 3 \, d^{2} + 12 \, {\left(8 \, c^{2} f^{3} - 4 \, c d f^{2} - d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + 48 \, d^{2} + 96 \, {\left(2 \, c d f^{2} + d^{2} f\right)} x}{384 \, {\left(a^{2} f^{3} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a^{2} f^{3} \sinh\left(f x + e\right)^{2}\right)}}"," ",0,"1/384*(96*d^2*f^2*x^2 + 96*c^2*f^2 + 96*c*d*f + (32*d^2*f^3*x^3 - 24*c^2*f^2 - 12*c*d*f + 24*(4*c*d*f^3 - d^2*f^2)*x^2 - 3*d^2 + 12*(8*c^2*f^3 - 4*c*d*f^2 - d^2*f)*x)*cosh(f*x + e)^2 + 2*(32*d^2*f^3*x^3 + 24*c^2*f^2 + 12*c*d*f + 24*(4*c*d*f^3 + d^2*f^2)*x^2 + 3*d^2 + 12*(8*c^2*f^3 + 4*c*d*f^2 + d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e) + (32*d^2*f^3*x^3 - 24*c^2*f^2 - 12*c*d*f + 24*(4*c*d*f^3 - d^2*f^2)*x^2 - 3*d^2 + 12*(8*c^2*f^3 - 4*c*d*f^2 - d^2*f)*x)*sinh(f*x + e)^2 + 48*d^2 + 96*(2*c*d*f^2 + d^2*f)*x)/(a^2*f^3*cosh(f*x + e)^2 + 2*a^2*f^3*cosh(f*x + e)*sinh(f*x + e) + a^2*f^3*sinh(f*x + e)^2)","B",0
24,1,190,0,0.394586," ","integrate((d*x+c)/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","\frac{16 \, d f x + {\left(8 \, d f^{2} x^{2} - 4 \, c f + 4 \, {\left(4 \, c f^{2} - d f\right)} x - d\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(8 \, d f^{2} x^{2} + 4 \, c f + 4 \, {\left(4 \, c f^{2} + d f\right)} x + d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(8 \, d f^{2} x^{2} - 4 \, c f + 4 \, {\left(4 \, c f^{2} - d f\right)} x - d\right)} \sinh\left(f x + e\right)^{2} + 16 \, c f + 8 \, d}{64 \, {\left(a^{2} f^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a^{2} f^{2} \sinh\left(f x + e\right)^{2}\right)}}"," ",0,"1/64*(16*d*f*x + (8*d*f^2*x^2 - 4*c*f + 4*(4*c*f^2 - d*f)*x - d)*cosh(f*x + e)^2 + 2*(8*d*f^2*x^2 + 4*c*f + 4*(4*c*f^2 + d*f)*x + d)*cosh(f*x + e)*sinh(f*x + e) + (8*d*f^2*x^2 - 4*c*f + 4*(4*c*f^2 - d*f)*x - d)*sinh(f*x + e)^2 + 16*c*f + 8*d)/(a^2*f^2*cosh(f*x + e)^2 + 2*a^2*f^2*cosh(f*x + e)*sinh(f*x + e) + a^2*f^2*sinh(f*x + e)^2)","A",0
25,1,137,0,0.412873," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - \log\left(d x + c\right)}{4 \, a^{2} d}"," ",0,"-1/4*(2*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + 2*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - Ei(-4*(d*f*x + c*f)/d)*sinh(-4*(d*e - c*f)/d) - log(d*x + c))/(a^2*d)","A",0
26,1,615,0,0.410278," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{2} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{2} \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\left(2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - d\right)} \cosh\left(f x + e\right)^{2} + {\left(2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) - d\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right)\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + d}{2 \, {\left({\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} d^{3} x + a^{2} c d^{2}\right)} \sinh\left(f x + e\right)^{2}\right)}}"," ",0,"1/2*(2*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)^2*sinh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(f*x + e)^2*sinh(-4*(d*e - c*f)/d) + (2*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) - d)*cosh(f*x + e)^2 + (2*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + 2*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*sinh(-4*(d*e - c*f)/d) - d)*sinh(f*x + e)^2 + 4*((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-2*(d*e - c*f)/d) - (d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-4*(d*e - c*f)/d) + ((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - (d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d))*cosh(f*x + e))*sinh(f*x + e) + d)/((a^2*d^3*x + a^2*c*d^2)*cosh(f*x + e)^2 + 2*(a^2*d^3*x + a^2*c*d^2)*cosh(f*x + e)*sinh(f*x + e) + (a^2*d^3*x + a^2*c*d^2)*sinh(f*x + e)^2)","A",0
27,1,844,0,0.403686," ","integrate((d*x+c)^3/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{16 \, {\left(54 \, d^{3} f^{4} x^{4} + 36 \, c^{3} f^{3} + 18 \, c^{2} d f^{2} + 6 \, c d^{2} f + 36 \, {\left(6 \, c d^{2} f^{4} + d^{3} f^{3}\right)} x^{3} + d^{3} + 18 \, {\left(18 \, c^{2} d f^{4} + 6 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + 6 \, {\left(36 \, c^{3} f^{4} + 18 \, c^{2} d f^{3} + 6 \, c d^{2} f^{2} + d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{3} + 48 \, {\left(54 \, d^{3} f^{4} x^{4} + 36 \, c^{3} f^{3} + 18 \, c^{2} d f^{2} + 6 \, c d^{2} f + 36 \, {\left(6 \, c d^{2} f^{4} + d^{3} f^{3}\right)} x^{3} + d^{3} + 18 \, {\left(18 \, c^{2} d f^{4} + 6 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + 6 \, {\left(36 \, c^{3} f^{4} + 18 \, c^{2} d f^{3} + 6 \, c d^{2} f^{2} + d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + 16 \, {\left(54 \, d^{3} f^{4} x^{4} - 36 \, c^{3} f^{3} - 18 \, c^{2} d f^{2} - 6 \, c d^{2} f + 36 \, {\left(6 \, c d^{2} f^{4} - d^{3} f^{3}\right)} x^{3} - d^{3} + 18 \, {\left(18 \, c^{2} d f^{4} - 6 \, c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 6 \, {\left(36 \, c^{3} f^{4} - 18 \, c^{2} d f^{3} - 6 \, c d^{2} f^{2} - d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{3} + 81 \, {\left(32 \, d^{3} f^{3} x^{3} + 32 \, c^{3} f^{3} + 72 \, c^{2} d f^{2} + 84 \, c d^{2} f + 45 \, d^{3} + 24 \, {\left(4 \, c d^{2} f^{3} + 3 \, d^{3} f^{2}\right)} x^{2} + 12 \, {\left(8 \, c^{2} d f^{3} + 12 \, c d^{2} f^{2} + 7 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right) + 3 \, {\left(2592 \, d^{3} f^{3} x^{3} + 2592 \, c^{3} f^{3} + 3240 \, c^{2} d f^{2} + 2916 \, c d^{2} f + 1377 \, d^{3} + 648 \, {\left(12 \, c d^{2} f^{3} + 5 \, d^{3} f^{2}\right)} x^{2} + 16 \, {\left(54 \, d^{3} f^{4} x^{4} - 36 \, c^{3} f^{3} - 18 \, c^{2} d f^{2} - 6 \, c d^{2} f + 36 \, {\left(6 \, c d^{2} f^{4} - d^{3} f^{3}\right)} x^{3} - d^{3} + 18 \, {\left(18 \, c^{2} d f^{4} - 6 \, c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 6 \, {\left(36 \, c^{3} f^{4} - 18 \, c^{2} d f^{3} - 6 \, c d^{2} f^{2} - d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} + 324 \, {\left(24 \, c^{2} d f^{3} + 20 \, c d^{2} f^{2} + 9 \, d^{3} f\right)} x\right)} \sinh\left(f x + e\right)}{27648 \, {\left(a^{3} f^{4} \cosh\left(f x + e\right)^{3} + 3 \, a^{3} f^{4} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, a^{3} f^{4} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + a^{3} f^{4} \sinh\left(f x + e\right)^{3}\right)}}"," ",0,"1/27648*(16*(54*d^3*f^4*x^4 + 36*c^3*f^3 + 18*c^2*d*f^2 + 6*c*d^2*f + 36*(6*c*d^2*f^4 + d^3*f^3)*x^3 + d^3 + 18*(18*c^2*d*f^4 + 6*c*d^2*f^3 + d^3*f^2)*x^2 + 6*(36*c^3*f^4 + 18*c^2*d*f^3 + 6*c*d^2*f^2 + d^3*f)*x)*cosh(f*x + e)^3 + 48*(54*d^3*f^4*x^4 + 36*c^3*f^3 + 18*c^2*d*f^2 + 6*c*d^2*f + 36*(6*c*d^2*f^4 + d^3*f^3)*x^3 + d^3 + 18*(18*c^2*d*f^4 + 6*c*d^2*f^3 + d^3*f^2)*x^2 + 6*(36*c^3*f^4 + 18*c^2*d*f^3 + 6*c*d^2*f^2 + d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e)^2 + 16*(54*d^3*f^4*x^4 - 36*c^3*f^3 - 18*c^2*d*f^2 - 6*c*d^2*f + 36*(6*c*d^2*f^4 - d^3*f^3)*x^3 - d^3 + 18*(18*c^2*d*f^4 - 6*c*d^2*f^3 - d^3*f^2)*x^2 + 6*(36*c^3*f^4 - 18*c^2*d*f^3 - 6*c*d^2*f^2 - d^3*f)*x)*sinh(f*x + e)^3 + 81*(32*d^3*f^3*x^3 + 32*c^3*f^3 + 72*c^2*d*f^2 + 84*c*d^2*f + 45*d^3 + 24*(4*c*d^2*f^3 + 3*d^3*f^2)*x^2 + 12*(8*c^2*d*f^3 + 12*c*d^2*f^2 + 7*d^3*f)*x)*cosh(f*x + e) + 3*(2592*d^3*f^3*x^3 + 2592*c^3*f^3 + 3240*c^2*d*f^2 + 2916*c*d^2*f + 1377*d^3 + 648*(12*c*d^2*f^3 + 5*d^3*f^2)*x^2 + 16*(54*d^3*f^4*x^4 - 36*c^3*f^3 - 18*c^2*d*f^2 - 6*c*d^2*f + 36*(6*c*d^2*f^4 - d^3*f^3)*x^3 - d^3 + 18*(18*c^2*d*f^4 - 6*c*d^2*f^3 - d^3*f^2)*x^2 + 6*(36*c^3*f^4 - 18*c^2*d*f^3 - 6*c*d^2*f^2 - d^3*f)*x)*cosh(f*x + e)^2 + 324*(24*c^2*d*f^3 + 20*c*d^2*f^2 + 9*d^3*f)*x)*sinh(f*x + e))/(a^3*f^4*cosh(f*x + e)^3 + 3*a^3*f^4*cosh(f*x + e)^2*sinh(f*x + e) + 3*a^3*f^4*cosh(f*x + e)*sinh(f*x + e)^2 + a^3*f^4*sinh(f*x + e)^3)","B",0
28,1,532,0,0.389718," ","integrate((d*x+c)^2/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(36 \, d^{2} f^{3} x^{3} + 18 \, c^{2} f^{2} + 6 \, c d f + 18 \, {\left(6 \, c d f^{3} + d^{2} f^{2}\right)} x^{2} + d^{2} + 6 \, {\left(18 \, c^{2} f^{3} + 6 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{3} + 24 \, {\left(36 \, d^{2} f^{3} x^{3} + 18 \, c^{2} f^{2} + 6 \, c d f + 18 \, {\left(6 \, c d f^{3} + d^{2} f^{2}\right)} x^{2} + d^{2} + 6 \, {\left(18 \, c^{2} f^{3} + 6 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + 8 \, {\left(36 \, d^{2} f^{3} x^{3} - 18 \, c^{2} f^{2} - 6 \, c d f + 18 \, {\left(6 \, c d f^{3} - d^{2} f^{2}\right)} x^{2} - d^{2} + 6 \, {\left(18 \, c^{2} f^{3} - 6 \, c d f^{2} - d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{3} + 81 \, {\left(8 \, d^{2} f^{2} x^{2} + 8 \, c^{2} f^{2} + 12 \, c d f + 7 \, d^{2} + 4 \, {\left(4 \, c d f^{2} + 3 \, d^{2} f\right)} x\right)} \cosh\left(f x + e\right) + 3 \, {\left(648 \, d^{2} f^{2} x^{2} + 648 \, c^{2} f^{2} + 540 \, c d f + 8 \, {\left(36 \, d^{2} f^{3} x^{3} - 18 \, c^{2} f^{2} - 6 \, c d f + 18 \, {\left(6 \, c d f^{3} - d^{2} f^{2}\right)} x^{2} - d^{2} + 6 \, {\left(18 \, c^{2} f^{3} - 6 \, c d f^{2} - d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} + 243 \, d^{2} + 108 \, {\left(12 \, c d f^{2} + 5 \, d^{2} f\right)} x\right)} \sinh\left(f x + e\right)}{6912 \, {\left(a^{3} f^{3} \cosh\left(f x + e\right)^{3} + 3 \, a^{3} f^{3} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, a^{3} f^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + a^{3} f^{3} \sinh\left(f x + e\right)^{3}\right)}}"," ",0,"1/6912*(8*(36*d^2*f^3*x^3 + 18*c^2*f^2 + 6*c*d*f + 18*(6*c*d*f^3 + d^2*f^2)*x^2 + d^2 + 6*(18*c^2*f^3 + 6*c*d*f^2 + d^2*f)*x)*cosh(f*x + e)^3 + 24*(36*d^2*f^3*x^3 + 18*c^2*f^2 + 6*c*d*f + 18*(6*c*d*f^3 + d^2*f^2)*x^2 + d^2 + 6*(18*c^2*f^3 + 6*c*d*f^2 + d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e)^2 + 8*(36*d^2*f^3*x^3 - 18*c^2*f^2 - 6*c*d*f + 18*(6*c*d*f^3 - d^2*f^2)*x^2 - d^2 + 6*(18*c^2*f^3 - 6*c*d*f^2 - d^2*f)*x)*sinh(f*x + e)^3 + 81*(8*d^2*f^2*x^2 + 8*c^2*f^2 + 12*c*d*f + 7*d^2 + 4*(4*c*d*f^2 + 3*d^2*f)*x)*cosh(f*x + e) + 3*(648*d^2*f^2*x^2 + 648*c^2*f^2 + 540*c*d*f + 8*(36*d^2*f^3*x^3 - 18*c^2*f^2 - 6*c*d*f + 18*(6*c*d*f^3 - d^2*f^2)*x^2 - d^2 + 6*(18*c^2*f^3 - 6*c*d*f^2 - d^2*f)*x)*cosh(f*x + e)^2 + 243*d^2 + 108*(12*c*d*f^2 + 5*d^2*f)*x)*sinh(f*x + e))/(a^3*f^3*cosh(f*x + e)^3 + 3*a^3*f^3*cosh(f*x + e)^2*sinh(f*x + e) + 3*a^3*f^3*cosh(f*x + e)*sinh(f*x + e)^2 + a^3*f^3*sinh(f*x + e)^3)","B",0
29,1,286,0,0.387414," ","integrate((d*x+c)/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(18 \, d f^{2} x^{2} + 6 \, c f + 6 \, {\left(6 \, c f^{2} + d f\right)} x + d\right)} \cosh\left(f x + e\right)^{3} + 12 \, {\left(18 \, d f^{2} x^{2} + 6 \, c f + 6 \, {\left(6 \, c f^{2} + d f\right)} x + d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + 4 \, {\left(18 \, d f^{2} x^{2} - 6 \, c f + 6 \, {\left(6 \, c f^{2} - d f\right)} x - d\right)} \sinh\left(f x + e\right)^{3} + 27 \, {\left(4 \, d f x + 4 \, c f + 3 \, d\right)} \cosh\left(f x + e\right) + 3 \, {\left(108 \, d f x + 4 \, {\left(18 \, d f^{2} x^{2} - 6 \, c f + 6 \, {\left(6 \, c f^{2} - d f\right)} x - d\right)} \cosh\left(f x + e\right)^{2} + 108 \, c f + 45 \, d\right)} \sinh\left(f x + e\right)}{1152 \, {\left(a^{3} f^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{3} f^{2} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, a^{3} f^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + a^{3} f^{2} \sinh\left(f x + e\right)^{3}\right)}}"," ",0,"1/1152*(4*(18*d*f^2*x^2 + 6*c*f + 6*(6*c*f^2 + d*f)*x + d)*cosh(f*x + e)^3 + 12*(18*d*f^2*x^2 + 6*c*f + 6*(6*c*f^2 + d*f)*x + d)*cosh(f*x + e)*sinh(f*x + e)^2 + 4*(18*d*f^2*x^2 - 6*c*f + 6*(6*c*f^2 - d*f)*x - d)*sinh(f*x + e)^3 + 27*(4*d*f*x + 4*c*f + 3*d)*cosh(f*x + e) + 3*(108*d*f*x + 4*(18*d*f^2*x^2 - 6*c*f + 6*(6*c*f^2 - d*f)*x - d)*cosh(f*x + e)^2 + 108*c*f + 45*d)*sinh(f*x + e))/(a^3*f^2*cosh(f*x + e)^3 + 3*a^3*f^2*cosh(f*x + e)^2*sinh(f*x + e) + 3*a^3*f^2*cosh(f*x + e)*sinh(f*x + e)^2 + a^3*f^2*sinh(f*x + e)^3)","A",0
30,1,195,0,0.398553," ","integrate(1/(d*x+c)/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","-\frac{3 \, {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 3 \, {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 3 \, {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) - \log\left(d x + c\right)}{8 \, a^{3} d}"," ",0,"-1/8*(3*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 3*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + Ei(-6*(d*f*x + c*f)/d)*cosh(-6*(d*e - c*f)/d) + 3*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - 3*Ei(-4*(d*f*x + c*f)/d)*sinh(-4*(d*e - c*f)/d) + Ei(-6*(d*f*x + c*f)/d)*sinh(-6*(d*e - c*f)/d) - log(d*x + c))/(a^3*d)","A",0
31,1,1162,0,0.406835," ","integrate(1/(d*x+c)^2/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{3} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 6 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{3} \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{3} \sinh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right)\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 6 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 6 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) - d\right)} \sinh\left(f x + e\right)^{3} + 9 \, {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right) \sinh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + {\left({\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right)\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{2} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 6 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{2} \sinh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(f x + e\right)^{2} \sinh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) + {\left(3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 6 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{4 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{4 \, {\left(d e - c f\right)}}{d}\right) + 3 \, {\left(d f x + c f\right)} {\rm Ei}\left(-\frac{6 \, {\left(d f x + c f\right)}}{d}\right) \cosh\left(-\frac{6 \, {\left(d e - c f\right)}}{d}\right) - d\right)} \cosh\left(f x + e\right)^{2} + d\right)} \sinh\left(f x + e\right)}{4 \, {\left({\left(a^{3} d^{3} x + a^{3} c d^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} d^{3} x + a^{3} c d^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, {\left(a^{3} d^{3} x + a^{3} c d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + {\left(a^{3} d^{3} x + a^{3} c d^{2}\right)} \sinh\left(f x + e\right)^{3}\right)}}"," ",0,"1/4*(3*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)^3*sinh(-2*(d*e - c*f)/d) - 6*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(f*x + e)^3*sinh(-4*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(f*x + e)^3*sinh(-6*(d*e - c*f)/d) + 3*((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + (d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(-6*(d*e - c*f)/d))*cosh(f*x + e)^3 + (3*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 6*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(-6*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*sinh(-2*(d*e - c*f)/d) - 6*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*sinh(-4*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*sinh(-6*(d*e - c*f)/d) - d)*sinh(f*x + e)^3 + 9*((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-4*(d*e - c*f)/d) + (d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(f*x + e)*sinh(-6*(d*e - c*f)/d) + ((d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 2*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + (d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(-6*(d*e - c*f)/d))*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(3*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(f*x + e)^2*sinh(-2*(d*e - c*f)/d) - 6*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(f*x + e)^2*sinh(-4*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(f*x + e)^2*sinh(-6*(d*e - c*f)/d) + (3*(d*f*x + c*f)*Ei(-2*(d*f*x + c*f)/d)*cosh(-2*(d*e - c*f)/d) - 6*(d*f*x + c*f)*Ei(-4*(d*f*x + c*f)/d)*cosh(-4*(d*e - c*f)/d) + 3*(d*f*x + c*f)*Ei(-6*(d*f*x + c*f)/d)*cosh(-6*(d*e - c*f)/d) - d)*cosh(f*x + e)^2 + d)*sinh(f*x + e))/((a^3*d^3*x + a^3*c*d^2)*cosh(f*x + e)^3 + 3*(a^3*d^3*x + a^3*c*d^2)*cosh(f*x + e)^2*sinh(f*x + e) + 3*(a^3*d^3*x + a^3*c*d^2)*cosh(f*x + e)*sinh(f*x + e)^2 + (a^3*d^3*x + a^3*c*d^2)*sinh(f*x + e)^3)","A",0
32,0,0,0,0.411220," ","integrate((d*x+c)^m*(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \coth\left(f x + e\right)^{2} + 2 \, a^{2} \coth\left(f x + e\right) + a^{2}\right)} {\left(d x + c\right)}^{m}, x\right)"," ",0,"integral((a^2*coth(f*x + e)^2 + 2*a^2*coth(f*x + e) + a^2)*(d*x + c)^m, x)","F",0
33,0,0,0,0.391599," ","integrate((d*x+c)^m*(a+a*coth(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \coth\left(f x + e\right) + a\right)} {\left(d x + c\right)}^{m}, x\right)"," ",0,"integral((a*coth(f*x + e) + a)*(d*x + c)^m, x)","F",0
34,1,148,0,0.399499," ","integrate((d*x+c)^m/(a+a*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(d m + d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) + 2 \, {\left(d f x + c f\right)} \cosh\left(m \log\left(d x + c\right)\right) + 2 \, {\left(d f x + c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{4 \, {\left(a d f m + a d f\right)}}"," ",0,"1/4*((d*m + d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) - (d*m + d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) + 2*(d*f*x + c*f)*cosh(m*log(d*x + c)) + 2*(d*f*x + c*f)*sinh(m*log(d*x + c)))/(a*d*f*m + a*d*f)","A",0
35,1,248,0,0.428899," ","integrate((d*x+c)^m/(a+a*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{4 \, f}{d}\right) + 4 \, d e - 4 \, c f}{d}\right) \Gamma\left(m + 1, \frac{4 \, {\left(d f x + c f\right)}}{d}\right) - 4 \, {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(d m + d\right)} \Gamma\left(m + 1, \frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{4 \, f}{d}\right) + 4 \, d e - 4 \, c f}{d}\right) + 4 \, {\left(d m + d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) - 4 \, {\left(d f x + c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 4 \, {\left(d f x + c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{16 \, {\left(a^{2} d f m + a^{2} d f\right)}}"," ",0,"-1/16*((d*m + d)*cosh((d*m*log(4*f/d) + 4*d*e - 4*c*f)/d)*gamma(m + 1, 4*(d*f*x + c*f)/d) - 4*(d*m + d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) - (d*m + d)*gamma(m + 1, 4*(d*f*x + c*f)/d)*sinh((d*m*log(4*f/d) + 4*d*e - 4*c*f)/d) + 4*(d*m + d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) - 4*(d*f*x + c*f)*cosh(m*log(d*x + c)) - 4*(d*f*x + c*f)*sinh(m*log(d*x + c)))/(a^2*d*f*m + a^2*d*f)","A",0
36,1,345,0,0.414451," ","integrate((d*x+c)^m/(a+a*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{6 \, f}{d}\right) + 6 \, d e - 6 \, c f}{d}\right) \Gamma\left(m + 1, \frac{6 \, {\left(d f x + c f\right)}}{d}\right) - 9 \, {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{4 \, f}{d}\right) + 4 \, d e - 4 \, c f}{d}\right) \Gamma\left(m + 1, \frac{4 \, {\left(d f x + c f\right)}}{d}\right) + 18 \, {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, {\left(d m + d\right)} \Gamma\left(m + 1, \frac{6 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{6 \, f}{d}\right) + 6 \, d e - 6 \, c f}{d}\right) + 9 \, {\left(d m + d\right)} \Gamma\left(m + 1, \frac{4 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{4 \, f}{d}\right) + 4 \, d e - 4 \, c f}{d}\right) - 18 \, {\left(d m + d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) + 12 \, {\left(d f x + c f\right)} \cosh\left(m \log\left(d x + c\right)\right) + 12 \, {\left(d f x + c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{96 \, {\left(a^{3} d f m + a^{3} d f\right)}}"," ",0,"1/96*(2*(d*m + d)*cosh((d*m*log(6*f/d) + 6*d*e - 6*c*f)/d)*gamma(m + 1, 6*(d*f*x + c*f)/d) - 9*(d*m + d)*cosh((d*m*log(4*f/d) + 4*d*e - 4*c*f)/d)*gamma(m + 1, 4*(d*f*x + c*f)/d) + 18*(d*m + d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) - 2*(d*m + d)*gamma(m + 1, 6*(d*f*x + c*f)/d)*sinh((d*m*log(6*f/d) + 6*d*e - 6*c*f)/d) + 9*(d*m + d)*gamma(m + 1, 4*(d*f*x + c*f)/d)*sinh((d*m*log(4*f/d) + 4*d*e - 4*c*f)/d) - 18*(d*m + d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) + 12*(d*f*x + c*f)*cosh(m*log(d*x + c)) + 12*(d*f*x + c*f)*sinh(m*log(d*x + c)))/(a^3*d*f*m + a^3*d*f)","A",0
37,1,488,0,0.433559," ","integrate((d*x+c)^3*(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a - b\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a - b\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a - b\right)} c^{3} f^{4} x + 24 \, b d^{3} {\rm polylog}\left(4, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 24 \, b d^{3} {\rm polylog}\left(4, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b c^{3} f^{3}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - 4 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) - 24 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 24 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right)}{4 \, f^{4}}"," ",0,"1/4*((a - b)*d^3*f^4*x^4 + 4*(a - b)*c*d^2*f^4*x^3 + 6*(a - b)*c^2*d*f^4*x^2 + 4*(a - b)*c^3*f^4*x + 24*b*d^3*polylog(4, cosh(f*x + e) + sinh(f*x + e)) + 24*b*d^3*polylog(4, -cosh(f*x + e) - sinh(f*x + e)) + 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*dilog(cosh(f*x + e) + sinh(f*x + e)) + 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*c^3*f^3)*log(cosh(f*x + e) + sinh(f*x + e) + 1) - 4*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-cosh(f*x + e) - sinh(f*x + e) + 1) - 24*(b*d^3*f*x + b*c*d^2*f)*polylog(3, cosh(f*x + e) + sinh(f*x + e)) - 24*(b*d^3*f*x + b*c*d^2*f)*polylog(3, -cosh(f*x + e) - sinh(f*x + e)))/f^4","C",0
38,1,303,0,0.431518," ","integrate((d*x+c)^2*(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a - b\right)} c d f^{3} x^{2} + 3 \, {\left(a - b\right)} c^{2} f^{3} x - 6 \, b d^{2} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 6 \, b d^{2} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 6 \, {\left(b d^{2} f x + b c d f\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 6 \, {\left(b d^{2} f x + b c d f\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right)}{3 \, f^{3}}"," ",0,"1/3*((a - b)*d^2*f^3*x^3 + 3*(a - b)*c*d*f^3*x^2 + 3*(a - b)*c^2*f^3*x - 6*b*d^2*polylog(3, cosh(f*x + e) + sinh(f*x + e)) - 6*b*d^2*polylog(3, -cosh(f*x + e) - sinh(f*x + e)) + 6*(b*d^2*f*x + b*c*d*f)*dilog(cosh(f*x + e) + sinh(f*x + e)) + 6*(b*d^2*f*x + b*c*d*f)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-cosh(f*x + e) - sinh(f*x + e) + 1))/f^3","C",0
39,1,156,0,0.411814," ","integrate((d*x+c)*(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} d f^{2} x^{2} + 2 \, {\left(a - b\right)} c f^{2} x + 2 \, b d {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 2 \, b d {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 2 \, {\left(b d f x + b c f\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - 2 \, {\left(b d e - b c f\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right)}{2 \, f^{2}}"," ",0,"1/2*((a - b)*d*f^2*x^2 + 2*(a - b)*c*f^2*x + 2*b*d*dilog(cosh(f*x + e) + sinh(f*x + e)) + 2*b*d*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 2*(b*d*f*x + b*c*f)*log(cosh(f*x + e) + sinh(f*x + e) + 1) - 2*(b*d*e - b*c*f)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 2*(b*d*f*x + b*d*e)*log(-cosh(f*x + e) - sinh(f*x + e) + 1))/f^2","B",0
40,0,0,0,0.394448," ","integrate((a+b*coth(f*x+e))/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \coth\left(f x + e\right) + a}{d x + c}, x\right)"," ",0,"integral((b*coth(f*x + e) + a)/(d*x + c), x)","F",0
41,0,0,0,0.424650," ","integrate((a+b*coth(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \coth\left(f x + e\right) + a}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b*coth(f*x + e) + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
42,1,3239,0,0.500430," ","integrate((d*x+c)^3*(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} d f^{4} x^{2} + 4 \, a b d^{3} e^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{3} f^{4} x - 8 \, b^{2} d^{3} e^{3} - 8 \, {\left(2 \, a b c^{3} e - b^{2} c^{3}\right)} f^{3} + 24 \, {\left(a b c^{2} d e^{2} - b^{2} c^{2} d e\right)} f^{2} - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, a b d^{3} e^{4} - 16 \, a b c^{3} e f^{3} - 8 \, b^{2} d^{3} e^{3} - 4 \, {\left(2 \, b^{2} d^{3} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d^{2} f^{4}\right)} x^{3} + 24 \, {\left(a b c^{2} d e^{2} - b^{2} c^{2} d e\right)} f^{2} - 6 \, {\left(4 \, b^{2} c d^{2} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} d f^{4}\right)} x^{2} - 8 \, {\left(2 \, a b c d^{2} e^{3} - 3 \, b^{2} c d^{2} e^{2}\right)} f - 4 \, {\left(6 \, b^{2} c^{2} d f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, a b d^{3} e^{4} - 16 \, a b c^{3} e f^{3} - 8 \, b^{2} d^{3} e^{3} - 4 \, {\left(2 \, b^{2} d^{3} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d^{2} f^{4}\right)} x^{3} + 24 \, {\left(a b c^{2} d e^{2} - b^{2} c^{2} d e\right)} f^{2} - 6 \, {\left(4 \, b^{2} c d^{2} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} d f^{4}\right)} x^{2} - 8 \, {\left(2 \, a b c d^{2} e^{3} - 3 \, b^{2} c d^{2} e^{2}\right)} f - 4 \, {\left(6 \, b^{2} c^{2} d f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, a b d^{3} e^{4} - 16 \, a b c^{3} e f^{3} - 8 \, b^{2} d^{3} e^{3} - 4 \, {\left(2 \, b^{2} d^{3} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d^{2} f^{4}\right)} x^{3} + 24 \, {\left(a b c^{2} d e^{2} - b^{2} c^{2} d e\right)} f^{2} - 6 \, {\left(4 \, b^{2} c d^{2} f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} d f^{4}\right)} x^{2} - 8 \, {\left(2 \, a b c d^{2} e^{3} - 3 \, b^{2} c d^{2} e^{2}\right)} f - 4 \, {\left(6 \, b^{2} c^{2} d f^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{3} f^{4}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 8 \, {\left(2 \, a b c d^{2} e^{3} - 3 \, b^{2} c d^{2} e^{2}\right)} f + 24 \, {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f - {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 24 \, {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f - {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d^{3} f^{2} x^{2} + a b c^{2} d f^{2} + b^{2} c d^{2} f + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a b c d^{2} f^{2} + b^{2} d^{3} f\right)} x\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 4 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} + 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} + 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} + 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b c^{3} f^{3} + 3 \, b^{2} c^{2} d f^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - 4 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{3} e^{3} - 2 \, a b c^{3} f^{3} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c^{2} d e - b^{2} c^{2} d\right)} f^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 4 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b c^{2} d e f^{2} - 3 \, b^{2} d^{3} e^{2} + 3 \, {\left(2 \, a b c d^{2} f^{3} + b^{2} d^{3} f^{2}\right)} x^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left(a b c d^{2} e^{2} - b^{2} c d^{2} e\right)} f + 6 \, {\left(a b c^{2} d f^{3} + b^{2} c d^{2} f^{2}\right)} x\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) - 48 \, {\left(a b d^{3} \cosh\left(f x + e\right)^{2} + 2 \, a b d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d^{3} \sinh\left(f x + e\right)^{2} - a b d^{3}\right)} {\rm polylog}\left(4, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 48 \, {\left(a b d^{3} \cosh\left(f x + e\right)^{2} + 2 \, a b d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d^{3} \sinh\left(f x + e\right)^{2} - a b d^{3}\right)} {\rm polylog}\left(4, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) - 24 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3} - {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 24 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3} - {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{3} f x + 2 \, a b c d^{2} f + b^{2} d^{3}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right)}{4 \, {\left(f^{4} \cosh\left(f x + e\right)^{2} + 2 \, f^{4} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f^{4} \sinh\left(f x + e\right)^{2} - f^{4}\right)}}"," ",0,"-1/4*((a^2 - 2*a*b + b^2)*d^3*f^4*x^4 + 4*(a^2 - 2*a*b + b^2)*c*d^2*f^4*x^3 + 6*(a^2 - 2*a*b + b^2)*c^2*d*f^4*x^2 + 4*a*b*d^3*e^4 + 4*(a^2 - 2*a*b + b^2)*c^3*f^4*x - 8*b^2*d^3*e^3 - 8*(2*a*b*c^3*e - b^2*c^3)*f^3 + 24*(a*b*c^2*d*e^2 - b^2*c^2*d*e)*f^2 - ((a^2 - 2*a*b + b^2)*d^3*f^4*x^4 + 4*a*b*d^3*e^4 - 16*a*b*c^3*e*f^3 - 8*b^2*d^3*e^3 - 4*(2*b^2*d^3*f^3 - (a^2 - 2*a*b + b^2)*c*d^2*f^4)*x^3 + 24*(a*b*c^2*d*e^2 - b^2*c^2*d*e)*f^2 - 6*(4*b^2*c*d^2*f^3 - (a^2 - 2*a*b + b^2)*c^2*d*f^4)*x^2 - 8*(2*a*b*c*d^2*e^3 - 3*b^2*c*d^2*e^2)*f - 4*(6*b^2*c^2*d*f^3 - (a^2 - 2*a*b + b^2)*c^3*f^4)*x)*cosh(f*x + e)^2 - 2*((a^2 - 2*a*b + b^2)*d^3*f^4*x^4 + 4*a*b*d^3*e^4 - 16*a*b*c^3*e*f^3 - 8*b^2*d^3*e^3 - 4*(2*b^2*d^3*f^3 - (a^2 - 2*a*b + b^2)*c*d^2*f^4)*x^3 + 24*(a*b*c^2*d*e^2 - b^2*c^2*d*e)*f^2 - 6*(4*b^2*c*d^2*f^3 - (a^2 - 2*a*b + b^2)*c^2*d*f^4)*x^2 - 8*(2*a*b*c*d^2*e^3 - 3*b^2*c*d^2*e^2)*f - 4*(6*b^2*c^2*d*f^3 - (a^2 - 2*a*b + b^2)*c^3*f^4)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2 - 2*a*b + b^2)*d^3*f^4*x^4 + 4*a*b*d^3*e^4 - 16*a*b*c^3*e*f^3 - 8*b^2*d^3*e^3 - 4*(2*b^2*d^3*f^3 - (a^2 - 2*a*b + b^2)*c*d^2*f^4)*x^3 + 24*(a*b*c^2*d*e^2 - b^2*c^2*d*e)*f^2 - 6*(4*b^2*c*d^2*f^3 - (a^2 - 2*a*b + b^2)*c^2*d*f^4)*x^2 - 8*(2*a*b*c*d^2*e^3 - 3*b^2*c*d^2*e^2)*f - 4*(6*b^2*c^2*d*f^3 - (a^2 - 2*a*b + b^2)*c^3*f^4)*x)*sinh(f*x + e)^2 - 8*(2*a*b*c*d^2*e^3 - 3*b^2*c*d^2*e^2)*f + 24*(a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f - (a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cosh(f*x + e)^2 - 2*(a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*sinh(f*x + e)^2 + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*dilog(cosh(f*x + e) + sinh(f*x + e)) + 24*(a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f - (a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cosh(f*x + e)^2 - 2*(a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d^3*f^2*x^2 + a*b*c^2*d*f^2 + b^2*c*d^2*f + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*sinh(f*x + e)^2 + (2*a*b*c*d^2*f^2 + b^2*d^3*f)*x)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 4*(2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 + 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - (2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 + 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 + 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^3*f^3*x^3 + 2*a*b*c^3*f^3 + 3*b^2*c^2*d*f^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*sinh(f*x + e)^2 + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*log(cosh(f*x + e) + sinh(f*x + e) + 1) - 4*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - (2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*cosh(f*x + e)^2 - 2*(2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^3*e^3 - 2*a*b*c^3*f^3 - 3*b^2*d^3*e^2 + 3*(2*a*b*c^2*d*e - b^2*c^2*d)*f^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*sinh(f*x + e)^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 4*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - (2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*c^2*d*e*f^2 - 3*b^2*d^3*e^2 + 3*(2*a*b*c*d^2*f^3 + b^2*d^3*f^2)*x^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*sinh(f*x + e)^2 - 6*(a*b*c*d^2*e^2 - b^2*c*d^2*e)*f + 6*(a*b*c^2*d*f^3 + b^2*c*d^2*f^2)*x)*log(-cosh(f*x + e) - sinh(f*x + e) + 1) - 48*(a*b*d^3*cosh(f*x + e)^2 + 2*a*b*d^3*cosh(f*x + e)*sinh(f*x + e) + a*b*d^3*sinh(f*x + e)^2 - a*b*d^3)*polylog(4, cosh(f*x + e) + sinh(f*x + e)) - 48*(a*b*d^3*cosh(f*x + e)^2 + 2*a*b*d^3*cosh(f*x + e)*sinh(f*x + e) + a*b*d^3*sinh(f*x + e)^2 - a*b*d^3)*polylog(4, -cosh(f*x + e) - sinh(f*x + e)) - 24*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3 - (2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cosh(f*x + e)^2 - 2*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*sinh(f*x + e)^2)*polylog(3, cosh(f*x + e) + sinh(f*x + e)) - 24*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3 - (2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cosh(f*x + e)^2 - 2*(2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^3*f*x + 2*a*b*c*d^2*f + b^2*d^3)*sinh(f*x + e)^2)*polylog(3, -cosh(f*x + e) - sinh(f*x + e)))/(f^4*cosh(f*x + e)^2 + 2*f^4*cosh(f*x + e)*sinh(f*x + e) + f^4*sinh(f*x + e)^2 - f^4)","C",0
43,1,1854,0,0.453021," ","integrate((d*x+c)^2*(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c d f^{3} x^{2} - 4 \, a b d^{2} e^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} f^{3} x + 6 \, b^{2} d^{2} e^{2} - 6 \, {\left(2 \, a b c^{2} e - b^{2} c^{2}\right)} f^{2} - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{2} f^{3} x^{3} - 4 \, a b d^{2} e^{3} - 12 \, a b c^{2} e f^{2} + 6 \, b^{2} d^{2} e^{2} - 3 \, {\left(2 \, b^{2} d^{2} f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d f^{3}\right)} x^{2} + 12 \, {\left(a b c d e^{2} - b^{2} c d e\right)} f - 3 \, {\left(4 \, b^{2} c d f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{2} f^{3} x^{3} - 4 \, a b d^{2} e^{3} - 12 \, a b c^{2} e f^{2} + 6 \, b^{2} d^{2} e^{2} - 3 \, {\left(2 \, b^{2} d^{2} f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d f^{3}\right)} x^{2} + 12 \, {\left(a b c d e^{2} - b^{2} c d e\right)} f - 3 \, {\left(4 \, b^{2} c d f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d^{2} f^{3} x^{3} - 4 \, a b d^{2} e^{3} - 12 \, a b c^{2} e f^{2} + 6 \, b^{2} d^{2} e^{2} - 3 \, {\left(2 \, b^{2} d^{2} f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c d f^{3}\right)} x^{2} + 12 \, {\left(a b c d e^{2} - b^{2} c d e\right)} f - 3 \, {\left(4 \, b^{2} c d f^{2} - {\left(a^{2} - 2 \, a b + b^{2}\right)} c^{2} f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left(a b c d e^{2} - b^{2} c d e\right)} f + 6 \, {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2} - {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 6 \, {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2} - {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d^{2} f x + 2 \, a b c d f + b^{2} d^{2}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 6 \, {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} + b^{2} c d f - {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} + b^{2} c d f + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} + b^{2} c d f + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d^{2} f^{2} x^{2} + a b c^{2} f^{2} + b^{2} c d f + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 6 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d^{2} e^{2} + a b c^{2} f^{2} - b^{2} d^{2} e - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \sinh\left(f x + e\right)^{2} - {\left(2 \, a b c d e - b^{2} c d\right)} f\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 6 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e - {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d^{2} f^{2} x^{2} - a b d^{2} e^{2} + 2 \, a b c d e f + b^{2} d^{2} e + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a b c d f^{2} + b^{2} d^{2} f\right)} x\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) + 12 \, {\left(a b d^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d^{2} \sinh\left(f x + e\right)^{2} - a b d^{2}\right)} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 12 \, {\left(a b d^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d^{2} \sinh\left(f x + e\right)^{2} - a b d^{2}\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right)}{3 \, {\left(f^{3} \cosh\left(f x + e\right)^{2} + 2 \, f^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f^{3} \sinh\left(f x + e\right)^{2} - f^{3}\right)}}"," ",0,"-1/3*((a^2 - 2*a*b + b^2)*d^2*f^3*x^3 + 3*(a^2 - 2*a*b + b^2)*c*d*f^3*x^2 - 4*a*b*d^2*e^3 + 3*(a^2 - 2*a*b + b^2)*c^2*f^3*x + 6*b^2*d^2*e^2 - 6*(2*a*b*c^2*e - b^2*c^2)*f^2 - ((a^2 - 2*a*b + b^2)*d^2*f^3*x^3 - 4*a*b*d^2*e^3 - 12*a*b*c^2*e*f^2 + 6*b^2*d^2*e^2 - 3*(2*b^2*d^2*f^2 - (a^2 - 2*a*b + b^2)*c*d*f^3)*x^2 + 12*(a*b*c*d*e^2 - b^2*c*d*e)*f - 3*(4*b^2*c*d*f^2 - (a^2 - 2*a*b + b^2)*c^2*f^3)*x)*cosh(f*x + e)^2 - 2*((a^2 - 2*a*b + b^2)*d^2*f^3*x^3 - 4*a*b*d^2*e^3 - 12*a*b*c^2*e*f^2 + 6*b^2*d^2*e^2 - 3*(2*b^2*d^2*f^2 - (a^2 - 2*a*b + b^2)*c*d*f^3)*x^2 + 12*(a*b*c*d*e^2 - b^2*c*d*e)*f - 3*(4*b^2*c*d*f^2 - (a^2 - 2*a*b + b^2)*c^2*f^3)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2 - 2*a*b + b^2)*d^2*f^3*x^3 - 4*a*b*d^2*e^3 - 12*a*b*c^2*e*f^2 + 6*b^2*d^2*e^2 - 3*(2*b^2*d^2*f^2 - (a^2 - 2*a*b + b^2)*c*d*f^3)*x^2 + 12*(a*b*c*d*e^2 - b^2*c*d*e)*f - 3*(4*b^2*c*d*f^2 - (a^2 - 2*a*b + b^2)*c^2*f^3)*x)*sinh(f*x + e)^2 + 12*(a*b*c*d*e^2 - b^2*c*d*e)*f + 6*(2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2 - (2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*cosh(f*x + e)^2 - 2*(2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*sinh(f*x + e)^2)*dilog(cosh(f*x + e) + sinh(f*x + e)) + 6*(2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2 - (2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*cosh(f*x + e)^2 - 2*(2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d^2*f*x + 2*a*b*c*d*f + b^2*d^2)*sinh(f*x + e)^2)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 6*(a*b*d^2*f^2*x^2 + a*b*c^2*f^2 + b^2*c*d*f - (a*b*d^2*f^2*x^2 + a*b*c^2*f^2 + b^2*c*d*f + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cosh(f*x + e)^2 - 2*(a*b*d^2*f^2*x^2 + a*b*c^2*f^2 + b^2*c*d*f + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d^2*f^2*x^2 + a*b*c^2*f^2 + b^2*c*d*f + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*sinh(f*x + e)^2 + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 6*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*cosh(f*x + e)^2 - 2*(a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d^2*e^2 + a*b*c^2*f^2 - b^2*d^2*e - (2*a*b*c*d*e - b^2*c*d)*f)*sinh(f*x + e)^2 - (2*a*b*c*d*e - b^2*c*d)*f)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 6*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e - (a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cosh(f*x + e)^2 - 2*(a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d^2*f^2*x^2 - a*b*d^2*e^2 + 2*a*b*c*d*e*f + b^2*d^2*e + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*sinh(f*x + e)^2 + (2*a*b*c*d*f^2 + b^2*d^2*f)*x)*log(-cosh(f*x + e) - sinh(f*x + e) + 1) + 12*(a*b*d^2*cosh(f*x + e)^2 + 2*a*b*d^2*cosh(f*x + e)*sinh(f*x + e) + a*b*d^2*sinh(f*x + e)^2 - a*b*d^2)*polylog(3, cosh(f*x + e) + sinh(f*x + e)) + 12*(a*b*d^2*cosh(f*x + e)^2 + 2*a*b*d^2*cosh(f*x + e)*sinh(f*x + e) + a*b*d^2*sinh(f*x + e)^2 - a*b*d^2)*polylog(3, -cosh(f*x + e) - sinh(f*x + e)))/(f^3*cosh(f*x + e)^2 + 2*f^3*cosh(f*x + e)*sinh(f*x + e) + f^3*sinh(f*x + e)^2 - f^3)","C",0
44,1,851,0,0.439644," ","integrate((d*x+c)*(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - 2 \, a b + b^{2}\right)} d f^{2} x^{2} + 4 \, a b d e^{2} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} c f^{2} x - 4 \, b^{2} d e - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d f^{2} x^{2} + 4 \, a b d e^{2} - 8 \, a b c e f - 4 \, b^{2} d e - 2 \, {\left(2 \, b^{2} d f - {\left(a^{2} - 2 \, a b + b^{2}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d f^{2} x^{2} + 4 \, a b d e^{2} - 8 \, a b c e f - 4 \, b^{2} d e - 2 \, {\left(2 \, b^{2} d f - {\left(a^{2} - 2 \, a b + b^{2}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d f^{2} x^{2} + 4 \, a b d e^{2} - 8 \, a b c e f - 4 \, b^{2} d e - 2 \, {\left(2 \, b^{2} d f - {\left(a^{2} - 2 \, a b + b^{2}\right)} c f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left(2 \, a b c e - b^{2} c\right)} f - 4 \, {\left(a b d \cosh\left(f x + e\right)^{2} + 2 \, a b d \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d \sinh\left(f x + e\right)^{2} - a b d\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 4 \, {\left(a b d \cosh\left(f x + e\right)^{2} + 2 \, a b d \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b d \sinh\left(f x + e\right)^{2} - a b d\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 2 \, {\left(2 \, a b d f x + 2 \, a b c f + b^{2} d - {\left(2 \, a b d f x + 2 \, a b c f + b^{2} d\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d f x + 2 \, a b c f + b^{2} d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d f x + 2 \, a b c f + b^{2} d\right)} \sinh\left(f x + e\right)^{2}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a b d e - 2 \, a b c f - b^{2} d - {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, a b d e - 2 \, a b c f - b^{2} d\right)} \sinh\left(f x + e\right)^{2}\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 4 \, {\left(a b d f x + a b d e - {\left(a b d f x + a b d e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(a b d f x + a b d e\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(a b d f x + a b d e\right)} \sinh\left(f x + e\right)^{2}\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right)}{2 \, {\left(f^{2} \cosh\left(f x + e\right)^{2} + 2 \, f^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f^{2} \sinh\left(f x + e\right)^{2} - f^{2}\right)}}"," ",0,"-1/2*((a^2 - 2*a*b + b^2)*d*f^2*x^2 + 4*a*b*d*e^2 + 2*(a^2 - 2*a*b + b^2)*c*f^2*x - 4*b^2*d*e - ((a^2 - 2*a*b + b^2)*d*f^2*x^2 + 4*a*b*d*e^2 - 8*a*b*c*e*f - 4*b^2*d*e - 2*(2*b^2*d*f - (a^2 - 2*a*b + b^2)*c*f^2)*x)*cosh(f*x + e)^2 - 2*((a^2 - 2*a*b + b^2)*d*f^2*x^2 + 4*a*b*d*e^2 - 8*a*b*c*e*f - 4*b^2*d*e - 2*(2*b^2*d*f - (a^2 - 2*a*b + b^2)*c*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2 - 2*a*b + b^2)*d*f^2*x^2 + 4*a*b*d*e^2 - 8*a*b*c*e*f - 4*b^2*d*e - 2*(2*b^2*d*f - (a^2 - 2*a*b + b^2)*c*f^2)*x)*sinh(f*x + e)^2 - 4*(2*a*b*c*e - b^2*c)*f - 4*(a*b*d*cosh(f*x + e)^2 + 2*a*b*d*cosh(f*x + e)*sinh(f*x + e) + a*b*d*sinh(f*x + e)^2 - a*b*d)*dilog(cosh(f*x + e) + sinh(f*x + e)) - 4*(a*b*d*cosh(f*x + e)^2 + 2*a*b*d*cosh(f*x + e)*sinh(f*x + e) + a*b*d*sinh(f*x + e)^2 - a*b*d)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 2*(2*a*b*d*f*x + 2*a*b*c*f + b^2*d - (2*a*b*d*f*x + 2*a*b*c*f + b^2*d)*cosh(f*x + e)^2 - 2*(2*a*b*d*f*x + 2*a*b*c*f + b^2*d)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d*f*x + 2*a*b*c*f + b^2*d)*sinh(f*x + e)^2)*log(cosh(f*x + e) + sinh(f*x + e) + 1) - 2*(2*a*b*d*e - 2*a*b*c*f - b^2*d - (2*a*b*d*e - 2*a*b*c*f - b^2*d)*cosh(f*x + e)^2 - 2*(2*a*b*d*e - 2*a*b*c*f - b^2*d)*cosh(f*x + e)*sinh(f*x + e) - (2*a*b*d*e - 2*a*b*c*f - b^2*d)*sinh(f*x + e)^2)*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 4*(a*b*d*f*x + a*b*d*e - (a*b*d*f*x + a*b*d*e)*cosh(f*x + e)^2 - 2*(a*b*d*f*x + a*b*d*e)*cosh(f*x + e)*sinh(f*x + e) - (a*b*d*f*x + a*b*d*e)*sinh(f*x + e)^2)*log(-cosh(f*x + e) - sinh(f*x + e) + 1))/(f^2*cosh(f*x + e)^2 + 2*f^2*cosh(f*x + e)*sinh(f*x + e) + f^2*sinh(f*x + e)^2 - f^2)","B",0
45,0,0,0,0.408934," ","integrate((a+b*coth(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \coth\left(f x + e\right)^{2} + 2 \, a b \coth\left(f x + e\right) + a^{2}}{d x + c}, x\right)"," ",0,"integral((b^2*coth(f*x + e)^2 + 2*a*b*coth(f*x + e) + a^2)/(d*x + c), x)","F",0
46,0,0,0,0.426279," ","integrate((a+b*coth(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \coth\left(f x + e\right)^{2} + 2 \, a b \coth\left(f x + e\right) + a^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^2*coth(f*x + e)^2 + 2*a*b*coth(f*x + e) + a^2)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
47,1,11137,0,0.664027," ","integrate((d*x+c)^3*(a+b*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4} x^{2} - 24 \, a b^{2} d^{3} e^{3} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4} x + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 8 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e f^{3} - 4 \, {\left(6 \, a b^{2} d^{3} f^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(12 \, a b^{2} c d^{2} f^{3} + 2 \, b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(18 \, a b^{2} c^{2} d f^{3} + 6 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 8 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e f^{3} - 4 \, {\left(6 \, a b^{2} d^{3} f^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(12 \, a b^{2} c d^{2} f^{3} + 2 \, b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(18 \, a b^{2} c^{2} d f^{3} + 6 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 8 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e f^{3} - 4 \, {\left(6 \, a b^{2} d^{3} f^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(12 \, a b^{2} c d^{2} f^{3} + 2 \, b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(18 \, a b^{2} c^{2} d f^{3} + 6 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(3 \, a b^{2} c^{3} - {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e\right)} f^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - b^{3} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 4 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{3}\right)} f^{3} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4} - {\left(3 \, a b^{2} - b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 6 \, {\left(12 \, a b^{2} c^{2} d e - b^{3} c^{2} d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(3 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4} + 3 \, {\left(3 \, a b^{2} - b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 4 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{3}\right)} f^{3} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4} - {\left(3 \, a b^{2} - b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 6 \, {\left(12 \, a b^{2} c^{2} d e - b^{3} c^{2} d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 8 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e f^{3} - 4 \, {\left(6 \, a b^{2} d^{3} f^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(12 \, a b^{2} c d^{2} f^{3} + 2 \, b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(18 \, a b^{2} c^{2} d f^{3} + 6 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(3 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4} + 3 \, {\left(3 \, a b^{2} - b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f + 12 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 12 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, a b^{2} c d^{2} f + b^{3} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{4} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 9 \, a b^{2} c^{2} d f^{2} + 3 \, b^{3} c d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 4 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 2 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 4 \, {\left({\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right)^{3} - {\left(9 \, a b^{2} d^{3} e^{2} - 3 \, b^{3} d^{3} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} f^{3} + 3 \, {\left(3 \, a b^{2} c^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e\right)} f^{2} - 3 \, {\left(6 \, a b^{2} c d^{2} e - b^{3} c d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{4} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} - 9 \, a b^{2} d^{3} e^{2} + 3 \, b^{3} d^{3} e + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e f^{2} + 3 \, {\left(3 \, a b^{2} d^{3} f^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 3 \, {\left(6 \, a b^{2} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{2}\right)} f + 3 \, {\left(6 \, a b^{2} c d^{2} f^{2} + b^{3} d^{3} f + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) + 24 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{3}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(4, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 24 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{3}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d^{3} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(4, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) - 24 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f + {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f - 3 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 24 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f + {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f - 3 \, {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{3} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 4 \, {\left({\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 8 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e f^{3} - 4 \, {\left(6 \, a b^{2} d^{3} f^{3} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4}\right)} x^{3} - 12 \, {\left(6 \, a b^{2} c^{2} d e - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(12 \, a b^{2} c d^{2} f^{3} + 2 \, b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(18 \, a b^{2} c^{2} d f^{3} + 6 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} - 24 \, a b^{2} d^{3} e^{3} + 12 \, b^{3} d^{3} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{3} e^{4} - 4 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{3} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{3}\right)} f^{3} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d^{2} f^{4} - {\left(3 \, a b^{2} - b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 6 \, {\left(12 \, a b^{2} c^{2} d e - b^{3} c^{2} d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} d e^{2}\right)} f^{2} - 6 \, {\left(b^{3} d^{3} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} d f^{4} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 8 \, {\left(9 \, a b^{2} c d^{2} e^{2} - 3 \, b^{3} c d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} c d^{2} e^{3}\right)} f - 4 \, {\left(3 \, b^{3} c d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{3} f^{4} + 3 \, {\left(3 \, a b^{2} - b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{4 \, {\left(f^{4} \cosh\left(f x + e\right)^{4} + 4 \, f^{4} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f^{4} \sinh\left(f x + e\right)^{4} - 2 \, f^{4} \cosh\left(f x + e\right)^{2} + f^{4} + 2 \, {\left(3 \, f^{4} \cosh\left(f x + e\right)^{2} - f^{4}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f^{4} \cosh\left(f x + e\right)^{3} - f^{4} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4*x^3 + 6*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4*x^2 - 24*a*b^2*d^3*e^3 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4*x + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 8*(3*a^2*b + b^3)*c^3*e*f^3 - 4*(6*a*b^2*d^3*f^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4)*x^3 - 12*(6*a*b^2*c^2*d*e - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(12*a*b^2*c*d^2*f^3 + 2*b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(18*a*b^2*c^2*d*f^3 + 6*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4)*x)*cosh(f*x + e)^4 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 8*(3*a^2*b + b^3)*c^3*e*f^3 - 4*(6*a*b^2*d^3*f^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4)*x^3 - 12*(6*a*b^2*c^2*d*e - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(12*a*b^2*c*d^2*f^3 + 2*b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(18*a*b^2*c^2*d*f^3 + 6*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 8*(3*a^2*b + b^3)*c^3*e*f^3 - 4*(6*a*b^2*d^3*f^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4)*x^3 - 12*(6*a*b^2*c^2*d*e - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(12*a*b^2*c*d^2*f^3 + 2*b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(18*a*b^2*c^2*d*f^3 + 6*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4)*x)*sinh(f*x + e)^4 + 8*(3*a*b^2*c^3 - (3*a^2*b + b^3)*c^3*e)*f^3 - 12*(6*a*b^2*c^2*d*e - b^3*c^2*d - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 4*(2*(3*a^2*b + b^3)*c^3*e - (3*a*b^2 + b^3)*c^3)*f^3 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4 - (3*a*b^2 - b^3)*d^3*f^3)*x^3 - 6*(12*a*b^2*c^2*d*e - b^3*c^2*d - 2*(3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4 + 2*(3*a*b^2 - b^3)*c*d^2*f^3)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(3*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4 + 3*(3*a*b^2 - b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 4*(2*(3*a^2*b + b^3)*c^3*e - (3*a*b^2 + b^3)*c^3)*f^3 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4 - (3*a*b^2 - b^3)*d^3*f^3)*x^3 - 6*(12*a*b^2*c^2*d*e - b^3*c^2*d - 2*(3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4 + 2*(3*a*b^2 - b^3)*c*d^2*f^3)*x^2 - 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 8*(3*a^2*b + b^3)*c^3*e*f^3 - 4*(6*a*b^2*d^3*f^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4)*x^3 - 12*(6*a*b^2*c^2*d*e - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(12*a*b^2*c*d^2*f^3 + 2*b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(18*a*b^2*c^2*d*f^3 + 6*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4)*x)*cosh(f*x + e)^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(3*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4 + 3*(3*a*b^2 - b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f + 12*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^4 - 2*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 - 3*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x + 4*(((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e))*sinh(f*x + e))*dilog(cosh(f*x + e) + sinh(f*x + e)) + 12*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^4 - 2*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 - 3*((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x + 4*(((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^3*f^2*x^2 + 6*a*b^2*c*d^2*f + b^3*d^3 + (3*a^2*b + b^3)*c^2*d*f^2 + 2*(3*a*b^2*d^3*f + (3*a^2*b + b^3)*c*d^2*f^2)*x)*cosh(f*x + e))*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 4*((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + ((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^4 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 - 2*((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 - 3*((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x + 4*(((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^3*f^3*x^3 + 9*a*b^2*c^2*d*f^2 + 3*b^3*c*d^2*f + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 4*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + (9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e)^4 + 4*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*sinh(f*x + e)^4 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 2*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e)^2 - 2*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e)^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*sinh(f*x + e)^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f + 4*((9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e)^3 - (9*a*b^2*d^3*e^2 - 3*b^3*d^3*e - (3*a^2*b + b^3)*d^3*e^3 + (3*a^2*b + b^3)*c^3*f^3 + 3*(3*a*b^2*c^2*d - (3*a^2*b + b^3)*c^2*d*e)*f^2 - 3*(6*a*b^2*c*d^2*e - b^3*c*d^2 - (3*a^2*b + b^3)*c*d^2*e^2)*f)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 4*((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + ((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^4 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 - 2*((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 - 3*((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x + 4*(((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^3*f^3*x^3 - 9*a*b^2*d^3*e^2 + 3*b^3*d^3*e + (3*a^2*b + b^3)*d^3*e^3 + 3*(3*a^2*b + b^3)*c^2*d*e*f^2 + 3*(3*a*b^2*d^3*f^2 + (3*a^2*b + b^3)*c*d^2*f^3)*x^2 + 3*(6*a*b^2*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^2)*f + 3*(6*a*b^2*c*d^2*f^2 + b^3*d^3*f + (3*a^2*b + b^3)*c^2*d*f^3)*x)*cosh(f*x + e))*sinh(f*x + e))*log(-cosh(f*x + e) - sinh(f*x + e) + 1) + 24*((3*a^2*b + b^3)*d^3*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d^3*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d^3*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d^3*cosh(f*x + e)^2 + (3*a^2*b + b^3)*d^3 + 2*(3*(3*a^2*b + b^3)*d^3*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d^3)*sinh(f*x + e)^2 + 4*((3*a^2*b + b^3)*d^3*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d^3*cosh(f*x + e))*sinh(f*x + e))*polylog(4, cosh(f*x + e) + sinh(f*x + e)) + 24*((3*a^2*b + b^3)*d^3*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d^3*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d^3*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d^3*cosh(f*x + e)^2 + (3*a^2*b + b^3)*d^3 + 2*(3*(3*a^2*b + b^3)*d^3*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d^3)*sinh(f*x + e)^2 + 4*((3*a^2*b + b^3)*d^3*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d^3*cosh(f*x + e))*sinh(f*x + e))*polylog(4, -cosh(f*x + e) - sinh(f*x + e)) - 24*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f + (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*sinh(f*x + e)^4 - 2*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f - 3*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^3 - (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e))*polylog(3, cosh(f*x + e) + sinh(f*x + e)) - 24*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f + (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*sinh(f*x + e)^4 - 2*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f - 3*(3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e)^3 - (3*a*b^2*d^3 + (3*a^2*b + b^3)*d^3*f*x + (3*a^2*b + b^3)*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e))*polylog(3, -cosh(f*x + e) - sinh(f*x + e)) + 4*(((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 8*(3*a^2*b + b^3)*c^3*e*f^3 - 4*(6*a*b^2*d^3*f^3 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4)*x^3 - 12*(6*a*b^2*c^2*d*e - (3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(12*a*b^2*c*d^2*f^3 + 2*b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(18*a*b^2*c^2*d*f^3 + 6*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4)*x)*cosh(f*x + e)^3 - ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^3*f^4*x^4 - 24*a*b^2*d^3*e^3 + 12*b^3*d^3*e^2 + 2*(3*a^2*b + b^3)*d^3*e^4 - 4*(2*(3*a^2*b + b^3)*c^3*e - (3*a*b^2 + b^3)*c^3)*f^3 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d^2*f^4 - (3*a*b^2 - b^3)*d^3*f^3)*x^3 - 6*(12*a*b^2*c^2*d*e - b^3*c^2*d - 2*(3*a^2*b + b^3)*c^2*d*e^2)*f^2 - 6*(b^3*d^3*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*d*f^4 + 2*(3*a*b^2 - b^3)*c*d^2*f^3)*x^2 + 8*(9*a*b^2*c*d^2*e^2 - 3*b^3*c*d^2*e - (3*a^2*b + b^3)*c*d^2*e^3)*f - 4*(3*b^3*c*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^3*f^4 + 3*(3*a*b^2 - b^3)*c^2*d*f^3)*x)*cosh(f*x + e))*sinh(f*x + e))/(f^4*cosh(f*x + e)^4 + 4*f^4*cosh(f*x + e)*sinh(f*x + e)^3 + f^4*sinh(f*x + e)^4 - 2*f^4*cosh(f*x + e)^2 + f^4 + 2*(3*f^4*cosh(f*x + e)^2 - f^4)*sinh(f*x + e)^2 + 4*(f^4*cosh(f*x + e)^3 - f^4*cosh(f*x + e))*sinh(f*x + e))","C",0
48,1,6356,0,0.620310," ","integrate((d*x+c)^2*(a+b*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3} x^{2} + 18 \, a b^{2} d^{2} e^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3} x - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(6 \, a b^{2} c d e - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(12 \, a b^{2} c d f^{2} + 2 \, b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(6 \, a b^{2} c d e - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(12 \, a b^{2} c d f^{2} + 2 \, b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(6 \, a b^{2} c d e - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(12 \, a b^{2} c d f^{2} + 2 \, b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{4} + 6 \, {\left(3 \, a b^{2} c^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e\right)} f^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 3 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{2}\right)} f^{2} + 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3} - {\left(3 \, a b^{2} - b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 3 \, {\left(12 \, a b^{2} c d e - b^{3} c d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 3 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{2}\right)} f^{2} + 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3} - {\left(3 \, a b^{2} - b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(6 \, a b^{2} c d e - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(12 \, a b^{2} c d f^{2} + 2 \, b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(12 \, a b^{2} c d e - b^{3} c d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left(6 \, a b^{2} c d e - b^{3} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f + 6 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{4} + {\left(3 \, a^{2} b + b^{3}\right)} c d f - 2 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f - 3 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 6 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{4} + {\left(3 \, a^{2} b + b^{3}\right)} c d f - 2 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f - 3 \, {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f x + {\left(3 \, a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} c d f + b^{3} d^{2} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - 3 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f + 4 \, {\left({\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right)^{3} - {\left(6 \, a b^{2} d^{2} e - b^{3} d^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} - 2 \, {\left(3 \, a b^{2} c d - {\left(3 \, a^{2} b + b^{3}\right)} c d e\right)} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, a b^{2} d^{2} e - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(3 \, a b^{2} d^{2} f + {\left(3 \, a^{2} b + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) - 6 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(3, \cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) - 6 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 4 \, {\left({\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 6 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e f^{2} - 3 \, {\left(6 \, a b^{2} d^{2} f^{2} - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3}\right)} x^{2} - 6 \, {\left(6 \, a b^{2} c d e - {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(12 \, a b^{2} c d f^{2} + 2 \, b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 18 \, a b^{2} d^{2} e^{2} - 6 \, b^{3} d^{2} e - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{3} - 3 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} e - {\left(3 \, a b^{2} + b^{3}\right)} c^{2}\right)} f^{2} + 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c d f^{3} - {\left(3 \, a b^{2} - b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 3 \, {\left(12 \, a b^{2} c d e - b^{3} c d - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} c d e^{2}\right)} f - 3 \, {\left(b^{3} d^{2} f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c^{2} f^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{3 \, {\left(f^{3} \cosh\left(f x + e\right)^{4} + 4 \, f^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f^{3} \sinh\left(f x + e\right)^{4} - 2 \, f^{3} \cosh\left(f x + e\right)^{2} + f^{3} + 2 \, {\left(3 \, f^{3} \cosh\left(f x + e\right)^{2} - f^{3}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f^{3} \cosh\left(f x + e\right)^{3} - f^{3} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3*x^2 + 18*a*b^2*d^2*e^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3*x - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 6*(3*a^2*b + b^3)*c^2*e*f^2 - 3*(6*a*b^2*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3)*x^2 - 6*(6*a*b^2*c*d*e - (3*a^2*b + b^3)*c*d*e^2)*f - 3*(12*a*b^2*c*d*f^2 + 2*b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3)*x)*cosh(f*x + e)^4 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 6*(3*a^2*b + b^3)*c^2*e*f^2 - 3*(6*a*b^2*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3)*x^2 - 6*(6*a*b^2*c*d*e - (3*a^2*b + b^3)*c*d*e^2)*f - 3*(12*a*b^2*c*d*f^2 + 2*b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 6*(3*a^2*b + b^3)*c^2*e*f^2 - 3*(6*a*b^2*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3)*x^2 - 6*(6*a*b^2*c*d*e - (3*a^2*b + b^3)*c*d*e^2)*f - 3*(12*a*b^2*c*d*f^2 + 2*b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3)*x)*sinh(f*x + e)^4 + 6*(3*a*b^2*c^2 - (3*a^2*b + b^3)*c^2*e)*f^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 3*(2*(3*a^2*b + b^3)*c^2*e - (3*a*b^2 + b^3)*c^2)*f^2 + 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3 - (3*a*b^2 - b^3)*d^2*f^2)*x^2 - 3*(12*a*b^2*c*d*e - b^3*c*d - 2*(3*a^2*b + b^3)*c*d*e^2)*f - 3*(b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3 + 2*(3*a*b^2 - b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 3*(2*(3*a^2*b + b^3)*c^2*e - (3*a*b^2 + b^3)*c^2)*f^2 + 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3 - (3*a*b^2 - b^3)*d^2*f^2)*x^2 - 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 6*(3*a^2*b + b^3)*c^2*e*f^2 - 3*(6*a*b^2*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3)*x^2 - 6*(6*a*b^2*c*d*e - (3*a^2*b + b^3)*c*d*e^2)*f - 3*(12*a*b^2*c*d*f^2 + 2*b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3)*x)*cosh(f*x + e)^2 - 3*(12*a*b^2*c*d*e - b^3*c*d - 2*(3*a^2*b + b^3)*c*d*e^2)*f - 3*(b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3 + 2*(3*a*b^2 - b^3)*c*d*f^2)*x)*sinh(f*x + e)^2 - 6*(6*a*b^2*c*d*e - b^3*c*d - (3*a^2*b + b^3)*c*d*e^2)*f + 6*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*sinh(f*x + e)^4 + (3*a^2*b + b^3)*c*d*f - 2*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f - 3*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^3 - (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*dilog(cosh(f*x + e) + sinh(f*x + e)) + 6*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*sinh(f*x + e)^4 + (3*a^2*b + b^3)*c*d*f - 2*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f - 3*(3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e)^3 - (3*a*b^2*d^2 + (3*a^2*b + b^3)*d^2*f*x + (3*a^2*b + b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 3*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*sinh(f*x + e)^4 - 2*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 - 3*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*sinh(f*x + e)^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x + 4*(((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*c*d*f + b^3*d^2 + (3*a^2*b + b^3)*c^2*f^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) - 3*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 + (6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e)^4 + 4*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*sinh(f*x + e)^4 - 2*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e)^2 - 2*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 3*(6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*sinh(f*x + e)^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f + 4*((6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e)^3 - (6*a*b^2*d^2*e - b^3*d^2 - (3*a^2*b + b^3)*d^2*e^2 - (3*a^2*b + b^3)*c^2*f^2 - 2*(3*a*b^2*c*d - (3*a^2*b + b^3)*c*d*e)*f)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 3*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*sinh(f*x + e)^4 - 2*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f - 3*((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*sinh(f*x + e)^2 + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x + 4*(((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d^2*f^2*x^2 + 6*a*b^2*d^2*e - (3*a^2*b + b^3)*d^2*e^2 + 2*(3*a^2*b + b^3)*c*d*e*f + 2*(3*a*b^2*d^2*f + (3*a^2*b + b^3)*c*d*f^2)*x)*cosh(f*x + e))*sinh(f*x + e))*log(-cosh(f*x + e) - sinh(f*x + e) + 1) - 6*((3*a^2*b + b^3)*d^2*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d^2*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d^2*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d^2*cosh(f*x + e)^2 + (3*a^2*b + b^3)*d^2 + 2*(3*(3*a^2*b + b^3)*d^2*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d^2)*sinh(f*x + e)^2 + 4*((3*a^2*b + b^3)*d^2*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d^2*cosh(f*x + e))*sinh(f*x + e))*polylog(3, cosh(f*x + e) + sinh(f*x + e)) - 6*((3*a^2*b + b^3)*d^2*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d^2*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d^2*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d^2*cosh(f*x + e)^2 + (3*a^2*b + b^3)*d^2 + 2*(3*(3*a^2*b + b^3)*d^2*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d^2)*sinh(f*x + e)^2 + 4*((3*a^2*b + b^3)*d^2*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d^2*cosh(f*x + e))*sinh(f*x + e))*polylog(3, -cosh(f*x + e) - sinh(f*x + e)) + 4*(((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 6*(3*a^2*b + b^3)*c^2*e*f^2 - 3*(6*a*b^2*d^2*f^2 - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3)*x^2 - 6*(6*a*b^2*c*d*e - (3*a^2*b + b^3)*c*d*e^2)*f - 3*(12*a*b^2*c*d*f^2 + 2*b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3)*x)*cosh(f*x + e)^3 - ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d^2*f^3*x^3 + 18*a*b^2*d^2*e^2 - 6*b^3*d^2*e - 2*(3*a^2*b + b^3)*d^2*e^3 - 3*(2*(3*a^2*b + b^3)*c^2*e - (3*a*b^2 + b^3)*c^2)*f^2 + 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*d*f^3 - (3*a*b^2 - b^3)*d^2*f^2)*x^2 - 3*(12*a*b^2*c*d*e - b^3*c*d - 2*(3*a^2*b + b^3)*c*d*e^2)*f - 3*(b^3*d^2*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c^2*f^3 + 2*(3*a*b^2 - b^3)*c*d*f^2)*x)*cosh(f*x + e))*sinh(f*x + e))/(f^3*cosh(f*x + e)^4 + 4*f^3*cosh(f*x + e)*sinh(f*x + e)^3 + f^3*sinh(f*x + e)^4 - 2*f^3*cosh(f*x + e)^2 + f^3 + 2*(3*f^3*cosh(f*x + e)^2 - f^3)*sinh(f*x + e)^2 + 4*(f^3*cosh(f*x + e)^3 - f^3*cosh(f*x + e))*sinh(f*x + e))","C",0
49,1,2907,0,0.535547," ","integrate((d*x+c)*(a+b*coth(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2} x + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 4 \, {\left(3 \, a^{2} b + b^{3}\right)} c e f - 2 \, {\left(6 \, a b^{2} d f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 4 \, {\left(3 \, a^{2} b + b^{3}\right)} c e f - 2 \, {\left(6 \, a b^{2} d f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 4 \, {\left(3 \, a^{2} b + b^{3}\right)} c e f - 2 \, {\left(6 \, a b^{2} d f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{4} + 2 \, b^{3} d + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + b^{3} d + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 2 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c e - {\left(3 \, a b^{2} + b^{3}\right)} c\right)} f + 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2} - {\left(3 \, a b^{2} - b^{3}\right)} d f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + b^{3} d + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 3 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 4 \, {\left(3 \, a^{2} b + b^{3}\right)} c e f - 2 \, {\left(6 \, a b^{2} d f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c e - {\left(3 \, a b^{2} + b^{3}\right)} c\right)} f + 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2} - {\left(3 \, a b^{2} - b^{3}\right)} d f\right)} x\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, a b^{2} c - {\left(3 \, a^{2} b + b^{3}\right)} c e\right)} f + 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d\right)} \sinh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} d \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} - {\left(3 \, a^{2} b + b^{3}\right)} d\right)} \sinh\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 2 \, {\left({\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(f x + e\right)^{4} + 3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f - 2 \, {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f - 3 \, {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 2 \, {\left({\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(f x + e\right)^{4} + 3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f - 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f - 3 \, {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b^{2} d - {\left(3 \, a^{2} b + b^{3}\right)} d e + {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1\right) + 2 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \sinh\left(f x + e\right)^{4} + {\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e - 3 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(3 \, a^{2} b + b^{3}\right)} d f x + {\left(3 \, a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right) + 1\right) + 4 \, {\left({\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 4 \, {\left(3 \, a^{2} b + b^{3}\right)} c e f - 2 \, {\left(6 \, a b^{2} d f - {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{3} - {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d f^{2} x^{2} - 12 \, a b^{2} d e + b^{3} d + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} d e^{2} - 2 \, {\left(2 \, {\left(3 \, a^{2} b + b^{3}\right)} c e - {\left(3 \, a b^{2} + b^{3}\right)} c\right)} f + 2 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} c f^{2} - {\left(3 \, a b^{2} - b^{3}\right)} d f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{2 \, {\left(f^{2} \cosh\left(f x + e\right)^{4} + 4 \, f^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f^{2} \sinh\left(f x + e\right)^{4} - 2 \, f^{2} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f^{2} \cosh\left(f x + e\right)^{2} - f^{2}\right)} \sinh\left(f x + e\right)^{2} + f^{2} + 4 \, {\left(f^{2} \cosh\left(f x + e\right)^{3} - f^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2*x + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(3*a^2*b + b^3)*d*e^2 - 4*(3*a^2*b + b^3)*c*e*f - 2*(6*a*b^2*d*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2)*x)*cosh(f*x + e)^4 + 4*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(3*a^2*b + b^3)*d*e^2 - 4*(3*a^2*b + b^3)*c*e*f - 2*(6*a*b^2*d*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2)*x)*cosh(f*x + e)*sinh(f*x + e)^3 + ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(3*a^2*b + b^3)*d*e^2 - 4*(3*a^2*b + b^3)*c*e*f - 2*(6*a*b^2*d*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2)*x)*sinh(f*x + e)^4 + 2*b^3*d + 2*(3*a^2*b + b^3)*d*e^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + b^3*d + 2*(3*a^2*b + b^3)*d*e^2 - 2*(2*(3*a^2*b + b^3)*c*e - (3*a*b^2 + b^3)*c)*f + 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2 - (3*a*b^2 - b^3)*d*f)*x)*cosh(f*x + e)^2 - 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + b^3*d + 2*(3*a^2*b + b^3)*d*e^2 - 3*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(3*a^2*b + b^3)*d*e^2 - 4*(3*a^2*b + b^3)*c*e*f - 2*(6*a*b^2*d*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2)*x)*cosh(f*x + e)^2 - 2*(2*(3*a^2*b + b^3)*c*e - (3*a*b^2 + b^3)*c)*f + 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2 - (3*a*b^2 - b^3)*d*f)*x)*sinh(f*x + e)^2 + 4*(3*a*b^2*c - (3*a^2*b + b^3)*c*e)*f + 2*((3*a^2*b + b^3)*d*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d*cosh(f*x + e)^2 + 2*(3*(3*a^2*b + b^3)*d*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d)*sinh(f*x + e)^2 + (3*a^2*b + b^3)*d + 4*((3*a^2*b + b^3)*d*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d*cosh(f*x + e))*sinh(f*x + e))*dilog(cosh(f*x + e) + sinh(f*x + e)) + 2*((3*a^2*b + b^3)*d*cosh(f*x + e)^4 + 4*(3*a^2*b + b^3)*d*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a^2*b + b^3)*d*sinh(f*x + e)^4 - 2*(3*a^2*b + b^3)*d*cosh(f*x + e)^2 + 2*(3*(3*a^2*b + b^3)*d*cosh(f*x + e)^2 - (3*a^2*b + b^3)*d)*sinh(f*x + e)^2 + (3*a^2*b + b^3)*d + 4*((3*a^2*b + b^3)*d*cosh(f*x + e)^3 - (3*a^2*b + b^3)*d*cosh(f*x + e))*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 2*((3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*sinh(f*x + e)^4 + 3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f - 2*(3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f - 3*(3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^3 - (3*a*b^2*d + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*c*f)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 2*((3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^4 + 4*(3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)*sinh(f*x + e)^3 + (3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*sinh(f*x + e)^4 + 3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f - 2*(3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^2 - 2*(3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f - 3*(3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*((3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e)^3 - (3*a*b^2*d - (3*a^2*b + b^3)*d*e + (3*a^2*b + b^3)*c*f)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) - 1) + 2*(((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e)^4 + 4*((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e)*sinh(f*x + e)^3 + ((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*sinh(f*x + e)^4 + (3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e - 2*((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e)^2 - 2*((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e - 3*((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e)^3 - ((3*a^2*b + b^3)*d*f*x + (3*a^2*b + b^3)*d*e)*cosh(f*x + e))*sinh(f*x + e))*log(-cosh(f*x + e) - sinh(f*x + e) + 1) + 4*(((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + 2*(3*a^2*b + b^3)*d*e^2 - 4*(3*a^2*b + b^3)*c*e*f - 2*(6*a*b^2*d*f - (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2)*x)*cosh(f*x + e)^3 - ((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*f^2*x^2 - 12*a*b^2*d*e + b^3*d + 2*(3*a^2*b + b^3)*d*e^2 - 2*(2*(3*a^2*b + b^3)*c*e - (3*a*b^2 + b^3)*c)*f + 2*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*c*f^2 - (3*a*b^2 - b^3)*d*f)*x)*cosh(f*x + e))*sinh(f*x + e))/(f^2*cosh(f*x + e)^4 + 4*f^2*cosh(f*x + e)*sinh(f*x + e)^3 + f^2*sinh(f*x + e)^4 - 2*f^2*cosh(f*x + e)^2 + 2*(3*f^2*cosh(f*x + e)^2 - f^2)*sinh(f*x + e)^2 + f^2 + 4*(f^2*cosh(f*x + e)^3 - f^2*cosh(f*x + e))*sinh(f*x + e))","B",0
50,0,0,0,0.430150," ","integrate((a+b*coth(f*x+e))^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \coth\left(f x + e\right)^{3} + 3 \, a b^{2} \coth\left(f x + e\right)^{2} + 3 \, a^{2} b \coth\left(f x + e\right) + a^{3}}{d x + c}, x\right)"," ",0,"integral((b^3*coth(f*x + e)^3 + 3*a*b^2*coth(f*x + e)^2 + 3*a^2*b*coth(f*x + e) + a^3)/(d*x + c), x)","F",0
51,0,0,0,0.457253," ","integrate((a+b*coth(f*x+e))^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \coth\left(f x + e\right)^{3} + 3 \, a b^{2} \coth\left(f x + e\right)^{2} + 3 \, a^{2} b \coth\left(f x + e\right) + a^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral((b^3*coth(f*x + e)^3 + 3*a*b^2*coth(f*x + e)^2 + 3*a^2*b*coth(f*x + e) + a^3)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
52,1,730,0,0.451197," ","integrate((d*x+c)^3/(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a + b\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a + b\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a + b\right)} c^{3} f^{4} x - 24 \, b d^{3} {\rm polylog}\left(4, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 24 \, b d^{3} {\rm polylog}\left(4, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 4 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) + 4 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) + 24 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 24 \, {\left(b d^{3} f x + b c d^{2} f\right)} {\rm polylog}\left(3, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right)}{4 \, {\left(a^{2} - b^{2}\right)} f^{4}}"," ",0,"1/4*((a + b)*d^3*f^4*x^4 + 4*(a + b)*c*d^2*f^4*x^3 + 6*(a + b)*c^2*d*f^4*x^2 + 4*(a + b)*c^3*f^4*x - 24*b*d^3*polylog(4, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 24*b*d^3*polylog(4, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 4*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) + 4*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) + 24*(b*d^3*f*x + b*c*d^2*f)*polylog(3, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 24*(b*d^3*f*x + b*c*d^2*f)*polylog(3, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))))/((a^2 - b^2)*f^4)","C",0
53,1,492,0,0.441097," ","integrate((d*x+c)^2/(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a + b\right)} c d f^{3} x^{2} + 3 \, {\left(a + b\right)} c^{2} f^{3} x + 6 \, b d^{2} {\rm polylog}\left(3, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 6 \, b d^{2} {\rm polylog}\left(3, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 6 \, {\left(b d^{2} f x + b c d f\right)} {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 6 \, {\left(b d^{2} f x + b c d f\right)} {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right)}{3 \, {\left(a^{2} - b^{2}\right)} f^{3}}"," ",0,"1/3*((a + b)*d^2*f^3*x^3 + 3*(a + b)*c*d*f^3*x^2 + 3*(a + b)*c^2*f^3*x + 6*b*d^2*polylog(3, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 6*b*d^2*polylog(3, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 6*(b*d^2*f*x + b*c*d*f)*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 6*(b*d^2*f*x + b*c*d*f)*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1))/((a^2 - b^2)*f^3)","C",0
54,1,300,0,0.455248," ","integrate((d*x+c)/(a+b*coth(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} d f^{2} x^{2} + 2 \, {\left(a + b\right)} c f^{2} x - 2 \, b d {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 2 \, b d {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 2 \, {\left(b d e - b c f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) + 2 \, {\left(b d e - b c f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 2 \, {\left(b d f x + b d e\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 2 \, {\left(b d f x + b d e\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right)}{2 \, {\left(a^{2} - b^{2}\right)} f^{2}}"," ",0,"1/2*((a + b)*d*f^2*x^2 + 2*(a + b)*c*f^2*x - 2*b*d*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 2*b*d*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 2*(b*d*e - b*c*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) + 2*(b*d*e - b*c*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 2*(b*d*f*x + b*d*e)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 2*(b*d*f*x + b*d*e)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1))/((a^2 - b^2)*f^2)","B",0
55,0,0,0,0.393838," ","integrate(1/(d*x+c)/(a+b*coth(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \coth\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*coth(f*x + e)), x)","F",0
56,0,0,0,0.402764," ","integrate(1/(d*x+c)^2/(a+b*coth(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \coth\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*coth(f*x + e)), x)","F",0
57,1,6171,0,0.570825," ","integrate((d*x+c)^3/(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d^{2} f^{4} x^{3} + 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} d f^{4} x^{2} + 4 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{3} f^{4} x - 4 \, {\left(a^{2} b - a b^{2}\right)} d^{3} e^{4} - 8 \, {\left(a b^{2} - b^{3}\right)} d^{3} e^{3} + 8 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c^{3} e + {\left(a b^{2} - b^{3}\right)} c^{3}\right)} f^{3} - 24 \, {\left({\left(a^{2} b - a b^{2}\right)} c^{2} d e^{2} + {\left(a b^{2} - b^{3}\right)} c^{2} d e\right)} f^{2} - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{3} f^{4} x^{4} - 4 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{4} + 16 \, {\left(a^{2} b + a b^{2}\right)} c^{3} e f^{3} - 8 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{3} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d^{2} f^{4} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 24 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d e^{2} + {\left(a b^{2} + b^{3}\right)} c^{2} d e\right)} f^{2} + 6 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} d f^{4} - 4 \, {\left(a b^{2} + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 8 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} e^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} c d^{2} e^{2}\right)} f + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{3} f^{4} - 6 \, {\left(a b^{2} + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{3} f^{4} x^{4} - 4 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{4} + 16 \, {\left(a^{2} b + a b^{2}\right)} c^{3} e f^{3} - 8 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{3} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d^{2} f^{4} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 24 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d e^{2} + {\left(a b^{2} + b^{3}\right)} c^{2} d e\right)} f^{2} + 6 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} d f^{4} - 4 \, {\left(a b^{2} + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 8 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} e^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} c d^{2} e^{2}\right)} f + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{3} f^{4} - 6 \, {\left(a b^{2} + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{3} f^{4} x^{4} - 4 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{4} + 16 \, {\left(a^{2} b + a b^{2}\right)} c^{3} e f^{3} - 8 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{3} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d^{2} f^{4} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{3} f^{3}\right)} x^{3} - 24 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d e^{2} + {\left(a b^{2} + b^{3}\right)} c^{2} d e\right)} f^{2} + 6 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} d f^{4} - 4 \, {\left(a b^{2} + b^{3}\right)} c d^{2} f^{3}\right)} x^{2} + 8 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} e^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} c d^{2} e^{2}\right)} f + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{3} f^{4} - 6 \, {\left(a b^{2} + b^{3}\right)} c^{2} d f^{3}\right)} x\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} e^{3} + 3 \, {\left(a b^{2} - b^{3}\right)} c d^{2} e^{2}\right)} f - 24 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b - a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} - b^{3}\right)} c d^{2} f - {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} - b^{3}\right)} d^{3} f\right)} x\right)} {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 24 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b - a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} - b^{3}\right)} c d^{2} f - {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{3} f^{2} x^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} d f^{2} - {\left(a b^{2} + b^{3}\right)} c d^{2} f + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} + b^{3}\right)} d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f^{2} - {\left(a b^{2} - b^{3}\right)} d^{3} f\right)} x\right)} {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 4 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b - a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} - b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c^{2} d e + {\left(a b^{2} - b^{3}\right)} c^{2} d\right)} f^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) + 4 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b - a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} - b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c^{2} d e + {\left(a b^{2} - b^{3}\right)} c^{2} d\right)} f^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left(a^{2} b + a b^{2}\right)} c^{3} f^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e + {\left(a b^{2} + b^{3}\right)} c^{2} d\right)} f^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} - b^{3}\right)} c d^{2} e\right)} f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 4 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} - b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} - b^{3}\right)} d^{3} f^{2}\right)} x^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} - b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} - b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 4 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} - b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} - b^{3}\right)} d^{3} f^{2}\right)} x^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + a b^{2}\right)} c^{2} d e f^{2} + 3 \, {\left(a b^{2} + b^{3}\right)} d^{3} e^{2} + 3 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f^{3} - {\left(a b^{2} + b^{3}\right)} d^{3} f^{2}\right)} x^{2} - 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} + b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b + a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} + b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c d^{2} e^{2} + {\left(a b^{2} - b^{3}\right)} c d^{2} e\right)} f + 6 \, {\left({\left(a^{2} b - a b^{2}\right)} c^{2} d f^{3} - {\left(a b^{2} - b^{3}\right)} c d^{2} f^{2}\right)} x\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{3} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d^{3} \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d^{3}\right)} {\rm polylog}\left(4, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{3} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d^{3} \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d^{3}\right)} {\rm polylog}\left(4, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 24 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f - {\left(a b^{2} - b^{3}\right)} d^{3} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm polylog}\left(3, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 24 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b - a b^{2}\right)} c d^{2} f - {\left(a b^{2} - b^{3}\right)} d^{3} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{3} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d^{2} f - {\left(a b^{2} + b^{3}\right)} d^{3}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm polylog}\left(3, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right)}{4 \, {\left({\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{4} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{4} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{4} \sinh\left(f x + e\right)^{2} - {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} f^{4}\right)}}"," ",0,"-1/4*((a^3 + a^2*b - a*b^2 - b^3)*d^3*f^4*x^4 + 4*(a^3 + a^2*b - a*b^2 - b^3)*c*d^2*f^4*x^3 + 6*(a^3 + a^2*b - a*b^2 - b^3)*c^2*d*f^4*x^2 + 4*(a^3 + a^2*b - a*b^2 - b^3)*c^3*f^4*x - 4*(a^2*b - a*b^2)*d^3*e^4 - 8*(a*b^2 - b^3)*d^3*e^3 + 8*(2*(a^2*b - a*b^2)*c^3*e + (a*b^2 - b^3)*c^3)*f^3 - 24*((a^2*b - a*b^2)*c^2*d*e^2 + (a*b^2 - b^3)*c^2*d*e)*f^2 - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^3*f^4*x^4 - 4*(a^2*b + a*b^2)*d^3*e^4 + 16*(a^2*b + a*b^2)*c^3*e*f^3 - 8*(a*b^2 + b^3)*d^3*e^3 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d^2*f^4 - 2*(a*b^2 + b^3)*d^3*f^3)*x^3 - 24*((a^2*b + a*b^2)*c^2*d*e^2 + (a*b^2 + b^3)*c^2*d*e)*f^2 + 6*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*d*f^4 - 4*(a*b^2 + b^3)*c*d^2*f^3)*x^2 + 8*(2*(a^2*b + a*b^2)*c*d^2*e^3 + 3*(a*b^2 + b^3)*c*d^2*e^2)*f + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^3*f^4 - 6*(a*b^2 + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)^2 - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^3*f^4*x^4 - 4*(a^2*b + a*b^2)*d^3*e^4 + 16*(a^2*b + a*b^2)*c^3*e*f^3 - 8*(a*b^2 + b^3)*d^3*e^3 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d^2*f^4 - 2*(a*b^2 + b^3)*d^3*f^3)*x^3 - 24*((a^2*b + a*b^2)*c^2*d*e^2 + (a*b^2 + b^3)*c^2*d*e)*f^2 + 6*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*d*f^4 - 4*(a*b^2 + b^3)*c*d^2*f^3)*x^2 + 8*(2*(a^2*b + a*b^2)*c*d^2*e^3 + 3*(a*b^2 + b^3)*c*d^2*e^2)*f + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^3*f^4 - 6*(a*b^2 + b^3)*c^2*d*f^3)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^3*f^4*x^4 - 4*(a^2*b + a*b^2)*d^3*e^4 + 16*(a^2*b + a*b^2)*c^3*e*f^3 - 8*(a*b^2 + b^3)*d^3*e^3 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d^2*f^4 - 2*(a*b^2 + b^3)*d^3*f^3)*x^3 - 24*((a^2*b + a*b^2)*c^2*d*e^2 + (a*b^2 + b^3)*c^2*d*e)*f^2 + 6*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*d*f^4 - 4*(a*b^2 + b^3)*c*d^2*f^3)*x^2 + 8*(2*(a^2*b + a*b^2)*c*d^2*e^3 + 3*(a*b^2 + b^3)*c*d^2*e^2)*f + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^3*f^4 - 6*(a*b^2 + b^3)*c^2*d*f^3)*x)*sinh(f*x + e)^2 + 8*(2*(a^2*b - a*b^2)*c*d^2*e^3 + 3*(a*b^2 - b^3)*c*d^2*e^2)*f - 24*((a^2*b - a*b^2)*d^3*f^2*x^2 + (a^2*b - a*b^2)*c^2*d*f^2 - (a*b^2 - b^3)*c*d^2*f - ((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*sinh(f*x + e)^2 + (2*(a^2*b - a*b^2)*c*d^2*f^2 - (a*b^2 - b^3)*d^3*f)*x)*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 24*((a^2*b - a*b^2)*d^3*f^2*x^2 + (a^2*b - a*b^2)*c^2*d*f^2 - (a*b^2 - b^3)*c*d^2*f - ((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^3*f^2*x^2 + (a^2*b + a*b^2)*c^2*d*f^2 - (a*b^2 + b^3)*c*d^2*f + (2*(a^2*b + a*b^2)*c*d^2*f^2 - (a*b^2 + b^3)*d^3*f)*x)*sinh(f*x + e)^2 + (2*(a^2*b - a*b^2)*c*d^2*f^2 - (a*b^2 - b^3)*d^3*f)*x)*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 4*(2*(a^2*b - a*b^2)*d^3*e^3 - 2*(a^2*b - a*b^2)*c^3*f^3 + 3*(a*b^2 - b^3)*d^3*e^2 + 3*(2*(a^2*b - a*b^2)*c^2*d*e + (a*b^2 - b^3)*c^2*d)*f^2 - (2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*sinh(f*x + e)^2 - 6*((a^2*b - a*b^2)*c*d^2*e^2 + (a*b^2 - b^3)*c*d^2*e)*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) + 4*(2*(a^2*b - a*b^2)*d^3*e^3 - 2*(a^2*b - a*b^2)*c^3*f^3 + 3*(a*b^2 - b^3)*d^3*e^2 + 3*(2*(a^2*b - a*b^2)*c^2*d*e + (a*b^2 - b^3)*c^2*d)*f^2 - (2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*e^3 - 2*(a^2*b + a*b^2)*c^3*f^3 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c^2*d*e + (a*b^2 + b^3)*c^2*d)*f^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f)*sinh(f*x + e)^2 - 6*((a^2*b - a*b^2)*c*d^2*e^2 + (a*b^2 - b^3)*c*d^2*e)*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 4*(2*(a^2*b - a*b^2)*d^3*f^3*x^3 + 2*(a^2*b - a*b^2)*d^3*e^3 + 6*(a^2*b - a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 - b^3)*d^3*e^2 + 3*(2*(a^2*b - a*b^2)*c*d^2*f^3 - (a*b^2 - b^3)*d^3*f^2)*x^2 - (2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^2 - 6*((a^2*b - a*b^2)*c*d^2*e^2 + (a*b^2 - b^3)*c*d^2*e)*f + 6*((a^2*b - a*b^2)*c^2*d*f^3 - (a*b^2 - b^3)*c*d^2*f^2)*x)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 4*(2*(a^2*b - a*b^2)*d^3*f^3*x^3 + 2*(a^2*b - a*b^2)*d^3*e^3 + 6*(a^2*b - a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 - b^3)*d^3*e^2 + 3*(2*(a^2*b - a*b^2)*c*d^2*f^3 - (a*b^2 - b^3)*d^3*f^2)*x^2 - (2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*f^3*x^3 + 2*(a^2*b + a*b^2)*d^3*e^3 + 6*(a^2*b + a*b^2)*c^2*d*e*f^2 + 3*(a*b^2 + b^3)*d^3*e^2 + 3*(2*(a^2*b + a*b^2)*c*d^2*f^3 - (a*b^2 + b^3)*d^3*f^2)*x^2 - 6*((a^2*b + a*b^2)*c*d^2*e^2 + (a*b^2 + b^3)*c*d^2*e)*f + 6*((a^2*b + a*b^2)*c^2*d*f^3 - (a*b^2 + b^3)*c*d^2*f^2)*x)*sinh(f*x + e)^2 - 6*((a^2*b - a*b^2)*c*d^2*e^2 + (a*b^2 - b^3)*c*d^2*e)*f + 6*((a^2*b - a*b^2)*c^2*d*f^3 - (a*b^2 - b^3)*c*d^2*f^2)*x)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) + 48*((a^2*b + a*b^2)*d^3*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d^3*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d^3*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d^3)*polylog(4, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 48*((a^2*b + a*b^2)*d^3*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d^3*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d^3*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d^3)*polylog(4, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 24*(2*(a^2*b - a*b^2)*d^3*f*x + 2*(a^2*b - a*b^2)*c*d^2*f - (a*b^2 - b^3)*d^3 - (2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*sinh(f*x + e)^2)*polylog(3, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 24*(2*(a^2*b - a*b^2)*d^3*f*x + 2*(a^2*b - a*b^2)*c*d^2*f - (a*b^2 - b^3)*d^3 - (2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^3*f*x + 2*(a^2*b + a*b^2)*c*d^2*f - (a*b^2 + b^3)*d^3)*sinh(f*x + e)^2)*polylog(3, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))))/((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^4*cosh(f*x + e)^2 + 2*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^4*cosh(f*x + e)*sinh(f*x + e) + (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^4*sinh(f*x + e)^2 - (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*f^4)","C",0
58,1,3702,0,0.501615," ","integrate((d*x+c)^2/(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} f^{3} x^{3} + 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d f^{3} x^{2} + 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} f^{3} x + 4 \, {\left(a^{2} b - a b^{2}\right)} d^{2} e^{3} + 6 \, {\left(a b^{2} - b^{3}\right)} d^{2} e^{2} + 6 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c^{2} e + {\left(a b^{2} - b^{3}\right)} c^{2}\right)} f^{2} - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{2} f^{3} x^{3} + 4 \, {\left(a^{2} b + a b^{2}\right)} d^{2} e^{3} + 12 \, {\left(a^{2} b + a b^{2}\right)} c^{2} e f^{2} + 6 \, {\left(a b^{2} + b^{3}\right)} d^{2} e^{2} + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d f^{3} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 12 \, {\left({\left(a^{2} b + a b^{2}\right)} c d e^{2} + {\left(a b^{2} + b^{3}\right)} c d e\right)} f + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} f^{3} - 4 \, {\left(a b^{2} + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{2} f^{3} x^{3} + 4 \, {\left(a^{2} b + a b^{2}\right)} d^{2} e^{3} + 12 \, {\left(a^{2} b + a b^{2}\right)} c^{2} e f^{2} + 6 \, {\left(a b^{2} + b^{3}\right)} d^{2} e^{2} + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d f^{3} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 12 \, {\left({\left(a^{2} b + a b^{2}\right)} c d e^{2} + {\left(a b^{2} + b^{3}\right)} c d e\right)} f + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} f^{3} - 4 \, {\left(a b^{2} + b^{3}\right)} c d f^{2}\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d^{2} f^{3} x^{3} + 4 \, {\left(a^{2} b + a b^{2}\right)} d^{2} e^{3} + 12 \, {\left(a^{2} b + a b^{2}\right)} c^{2} e f^{2} + 6 \, {\left(a b^{2} + b^{3}\right)} d^{2} e^{2} + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c d f^{3} - 2 \, {\left(a b^{2} + b^{3}\right)} d^{2} f^{2}\right)} x^{2} - 12 \, {\left({\left(a^{2} b + a b^{2}\right)} c d e^{2} + {\left(a b^{2} + b^{3}\right)} c d e\right)} f + 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c^{2} f^{3} - 4 \, {\left(a b^{2} + b^{3}\right)} c d f^{2}\right)} x\right)} \sinh\left(f x + e\right)^{2} - 12 \, {\left({\left(a^{2} b - a b^{2}\right)} c d e^{2} + {\left(a b^{2} - b^{3}\right)} c d e\right)} f - 6 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b - a b^{2}\right)} c d f - {\left(a b^{2} - b^{3}\right)} d^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 6 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b - a b^{2}\right)} c d f - {\left(a b^{2} - b^{3}\right)} d^{2} - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{2} b + a b^{2}\right)} c d f - {\left(a b^{2} + b^{3}\right)} d^{2}\right)} \sinh\left(f x + e\right)^{2}\right)} {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b - a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} - b^{3}\right)} d^{2} e - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \sinh\left(f x + e\right)^{2} - {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d e + {\left(a b^{2} - b^{3}\right)} c d\right)} f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b - a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} - b^{3}\right)} d^{2} e - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + {\left(a^{2} b + a b^{2}\right)} c^{2} f^{2} + {\left(a b^{2} + b^{3}\right)} d^{2} e - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d e + {\left(a b^{2} + b^{3}\right)} c d\right)} f\right)} \sinh\left(f x + e\right)^{2} - {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d e + {\left(a b^{2} - b^{3}\right)} c d\right)} f\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b - a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} c d e f - {\left(a b^{2} - b^{3}\right)} d^{2} e - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d f^{2} - {\left(a b^{2} - b^{3}\right)} d^{2} f\right)} x\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 6 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b - a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} c d e f - {\left(a b^{2} - b^{3}\right)} d^{2} e - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d^{2} f^{2} x^{2} - {\left(a^{2} b + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} c d e f - {\left(a b^{2} + b^{3}\right)} d^{2} e + {\left(2 \, {\left(a^{2} b + a b^{2}\right)} c d f^{2} - {\left(a b^{2} + b^{3}\right)} d^{2} f\right)} x\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c d f^{2} - {\left(a b^{2} - b^{3}\right)} d^{2} f\right)} x\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 12 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d^{2} \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d^{2}\right)} {\rm polylog}\left(3, \sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) - 12 \, {\left({\left(a^{2} b + a b^{2}\right)} d^{2} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d^{2} \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d^{2}\right)} {\rm polylog}\left(3, -\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right)}{3 \, {\left({\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{3} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{3} \sinh\left(f x + e\right)^{2} - {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} f^{3}\right)}}"," ",0,"-1/3*((a^3 + a^2*b - a*b^2 - b^3)*d^2*f^3*x^3 + 3*(a^3 + a^2*b - a*b^2 - b^3)*c*d*f^3*x^2 + 3*(a^3 + a^2*b - a*b^2 - b^3)*c^2*f^3*x + 4*(a^2*b - a*b^2)*d^2*e^3 + 6*(a*b^2 - b^3)*d^2*e^2 + 6*(2*(a^2*b - a*b^2)*c^2*e + (a*b^2 - b^3)*c^2)*f^2 - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^2*f^3*x^3 + 4*(a^2*b + a*b^2)*d^2*e^3 + 12*(a^2*b + a*b^2)*c^2*e*f^2 + 6*(a*b^2 + b^3)*d^2*e^2 + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d*f^3 - 2*(a*b^2 + b^3)*d^2*f^2)*x^2 - 12*((a^2*b + a*b^2)*c*d*e^2 + (a*b^2 + b^3)*c*d*e)*f + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*f^3 - 4*(a*b^2 + b^3)*c*d*f^2)*x)*cosh(f*x + e)^2 - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^2*f^3*x^3 + 4*(a^2*b + a*b^2)*d^2*e^3 + 12*(a^2*b + a*b^2)*c^2*e*f^2 + 6*(a*b^2 + b^3)*d^2*e^2 + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d*f^3 - 2*(a*b^2 + b^3)*d^2*f^2)*x^2 - 12*((a^2*b + a*b^2)*c*d*e^2 + (a*b^2 + b^3)*c*d*e)*f + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*f^3 - 4*(a*b^2 + b^3)*c*d*f^2)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d^2*f^3*x^3 + 4*(a^2*b + a*b^2)*d^2*e^3 + 12*(a^2*b + a*b^2)*c^2*e*f^2 + 6*(a*b^2 + b^3)*d^2*e^2 + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*d*f^3 - 2*(a*b^2 + b^3)*d^2*f^2)*x^2 - 12*((a^2*b + a*b^2)*c*d*e^2 + (a*b^2 + b^3)*c*d*e)*f + 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c^2*f^3 - 4*(a*b^2 + b^3)*c*d*f^2)*x)*sinh(f*x + e)^2 - 12*((a^2*b - a*b^2)*c*d*e^2 + (a*b^2 - b^3)*c*d*e)*f - 6*(2*(a^2*b - a*b^2)*d^2*f*x + 2*(a^2*b - a*b^2)*c*d*f - (a*b^2 - b^3)*d^2 - (2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*sinh(f*x + e)^2)*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 6*(2*(a^2*b - a*b^2)*d^2*f*x + 2*(a^2*b - a*b^2)*c*d*f - (a*b^2 - b^3)*d^2 - (2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d^2*f*x + 2*(a^2*b + a*b^2)*c*d*f - (a*b^2 + b^3)*d^2)*sinh(f*x + e)^2)*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 6*((a^2*b - a*b^2)*d^2*e^2 + (a^2*b - a*b^2)*c^2*f^2 + (a*b^2 - b^3)*d^2*e - ((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*sinh(f*x + e)^2 - (2*(a^2*b - a*b^2)*c*d*e + (a*b^2 - b^3)*c*d)*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) - 6*((a^2*b - a*b^2)*d^2*e^2 + (a^2*b - a*b^2)*c^2*f^2 + (a*b^2 - b^3)*d^2*e - ((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^2*e^2 + (a^2*b + a*b^2)*c^2*f^2 + (a*b^2 + b^3)*d^2*e - (2*(a^2*b + a*b^2)*c*d*e + (a*b^2 + b^3)*c*d)*f)*sinh(f*x + e)^2 - (2*(a^2*b - a*b^2)*c*d*e + (a*b^2 - b^3)*c*d)*f)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 6*((a^2*b - a*b^2)*d^2*f^2*x^2 - (a^2*b - a*b^2)*d^2*e^2 + 2*(a^2*b - a*b^2)*c*d*e*f - (a*b^2 - b^3)*d^2*e - ((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*sinh(f*x + e)^2 + (2*(a^2*b - a*b^2)*c*d*f^2 - (a*b^2 - b^3)*d^2*f)*x)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 6*((a^2*b - a*b^2)*d^2*f^2*x^2 - (a^2*b - a*b^2)*d^2*e^2 + 2*(a^2*b - a*b^2)*c*d*e*f - (a*b^2 - b^3)*d^2*e - ((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d^2*f^2*x^2 - (a^2*b + a*b^2)*d^2*e^2 + 2*(a^2*b + a*b^2)*c*d*e*f - (a*b^2 + b^3)*d^2*e + (2*(a^2*b + a*b^2)*c*d*f^2 - (a*b^2 + b^3)*d^2*f)*x)*sinh(f*x + e)^2 + (2*(a^2*b - a*b^2)*c*d*f^2 - (a*b^2 - b^3)*d^2*f)*x)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 12*((a^2*b + a*b^2)*d^2*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d^2*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d^2*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d^2)*polylog(3, sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) - 12*((a^2*b + a*b^2)*d^2*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d^2*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d^2*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d^2)*polylog(3, -sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))))/((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^3*cosh(f*x + e)^2 + 2*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^3*cosh(f*x + e)*sinh(f*x + e) + (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^3*sinh(f*x + e)^2 - (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*f^3)","C",0
59,1,1797,0,0.460298," ","integrate((d*x+c)/(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d f^{2} x^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c f^{2} x - 4 \, {\left(a^{2} b - a b^{2}\right)} d e^{2} - 4 \, {\left(a b^{2} - b^{3}\right)} d e - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d f^{2} x^{2} - 4 \, {\left(a^{2} b + a b^{2}\right)} d e^{2} + 8 \, {\left(a^{2} b + a b^{2}\right)} c e f - 4 \, {\left(a b^{2} + b^{3}\right)} d e + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c f^{2} - 2 \, {\left(a b^{2} + b^{3}\right)} d f\right)} x\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d f^{2} x^{2} - 4 \, {\left(a^{2} b + a b^{2}\right)} d e^{2} + 8 \, {\left(a^{2} b + a b^{2}\right)} c e f - 4 \, {\left(a b^{2} + b^{3}\right)} d e + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c f^{2} - 2 \, {\left(a b^{2} + b^{3}\right)} d f\right)} x\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d f^{2} x^{2} - 4 \, {\left(a^{2} b + a b^{2}\right)} d e^{2} + 8 \, {\left(a^{2} b + a b^{2}\right)} c e f - 4 \, {\left(a b^{2} + b^{3}\right)} d e + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} c f^{2} - 2 \, {\left(a b^{2} + b^{3}\right)} d f\right)} x\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} c e + {\left(a b^{2} - b^{3}\right)} c\right)} f + 4 \, {\left({\left(a^{2} b + a b^{2}\right)} d \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} {\rm Li}_2\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 4 \, {\left({\left(a^{2} b + a b^{2}\right)} d \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{2} b + a b^{2}\right)} d \sinh\left(f x + e\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} {\rm Li}_2\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)}\right) + 2 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d e - 2 \, {\left(a^{2} b - a b^{2}\right)} c f - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \sinh\left(f x + e\right)^{2} + {\left(a b^{2} - b^{3}\right)} d\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) + 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) + 2 \, {\left(2 \, {\left(a^{2} b - a b^{2}\right)} d e - 2 \, {\left(a^{2} b - a b^{2}\right)} c f - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d e - 2 \, {\left(a^{2} b + a b^{2}\right)} c f + {\left(a b^{2} + b^{3}\right)} d\right)} \sinh\left(f x + e\right)^{2} + {\left(a b^{2} - b^{3}\right)} d\right)} \log\left(2 \, {\left(a + b\right)} \cosh\left(f x + e\right) + 2 \, {\left(a + b\right)} \sinh\left(f x + e\right) - 2 \, {\left(a - b\right)} \sqrt{\frac{a + b}{a - b}}\right) - 4 \, {\left({\left(a^{2} b - a b^{2}\right)} d f x + {\left(a^{2} b - a b^{2}\right)} d e - {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \sinh\left(f x + e\right)^{2}\right)} \log\left(\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right) - 4 \, {\left({\left(a^{2} b - a b^{2}\right)} d f x + {\left(a^{2} b - a b^{2}\right)} d e - {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) - {\left({\left(a^{2} b + a b^{2}\right)} d f x + {\left(a^{2} b + a b^{2}\right)} d e\right)} \sinh\left(f x + e\right)^{2}\right)} \log\left(-\sqrt{\frac{a + b}{a - b}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 1\right)}{2 \, {\left({\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{2} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a^{5} + a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4} + b^{5}\right)} f^{2} \sinh\left(f x + e\right)^{2} - {\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} f^{2}\right)}}"," ",0,"-1/2*((a^3 + a^2*b - a*b^2 - b^3)*d*f^2*x^2 + 2*(a^3 + a^2*b - a*b^2 - b^3)*c*f^2*x - 4*(a^2*b - a*b^2)*d*e^2 - 4*(a*b^2 - b^3)*d*e - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*f^2*x^2 - 4*(a^2*b + a*b^2)*d*e^2 + 8*(a^2*b + a*b^2)*c*e*f - 4*(a*b^2 + b^3)*d*e + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*f^2 - 2*(a*b^2 + b^3)*d*f)*x)*cosh(f*x + e)^2 - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*f^2*x^2 - 4*(a^2*b + a*b^2)*d*e^2 + 8*(a^2*b + a*b^2)*c*e*f - 4*(a*b^2 + b^3)*d*e + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*f^2 - 2*(a*b^2 + b^3)*d*f)*x)*cosh(f*x + e)*sinh(f*x + e) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*f^2*x^2 - 4*(a^2*b + a*b^2)*d*e^2 + 8*(a^2*b + a*b^2)*c*e*f - 4*(a*b^2 + b^3)*d*e + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*c*f^2 - 2*(a*b^2 + b^3)*d*f)*x)*sinh(f*x + e)^2 + 4*(2*(a^2*b - a*b^2)*c*e + (a*b^2 - b^3)*c)*f + 4*((a^2*b + a*b^2)*d*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d)*dilog(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 4*((a^2*b + a*b^2)*d*cosh(f*x + e)^2 + 2*(a^2*b + a*b^2)*d*cosh(f*x + e)*sinh(f*x + e) + (a^2*b + a*b^2)*d*sinh(f*x + e)^2 - (a^2*b - a*b^2)*d)*dilog(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e))) + 2*(2*(a^2*b - a*b^2)*d*e - 2*(a^2*b - a*b^2)*c*f - (2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*sinh(f*x + e)^2 + (a*b^2 - b^3)*d)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) + 2*(a - b)*sqrt((a + b)/(a - b))) + 2*(2*(a^2*b - a*b^2)*d*e - 2*(a^2*b - a*b^2)*c*f - (2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*cosh(f*x + e)^2 - 2*(2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*cosh(f*x + e)*sinh(f*x + e) - (2*(a^2*b + a*b^2)*d*e - 2*(a^2*b + a*b^2)*c*f + (a*b^2 + b^3)*d)*sinh(f*x + e)^2 + (a*b^2 - b^3)*d)*log(2*(a + b)*cosh(f*x + e) + 2*(a + b)*sinh(f*x + e) - 2*(a - b)*sqrt((a + b)/(a - b))) - 4*((a^2*b - a*b^2)*d*f*x + (a^2*b - a*b^2)*d*e - ((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*sinh(f*x + e)^2)*log(sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1) - 4*((a^2*b - a*b^2)*d*f*x + (a^2*b - a*b^2)*d*e - ((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*cosh(f*x + e)^2 - 2*((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*cosh(f*x + e)*sinh(f*x + e) - ((a^2*b + a*b^2)*d*f*x + (a^2*b + a*b^2)*d*e)*sinh(f*x + e)^2)*log(-sqrt((a + b)/(a - b))*(cosh(f*x + e) + sinh(f*x + e)) + 1))/((a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^2*cosh(f*x + e)^2 + 2*(a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^2*cosh(f*x + e)*sinh(f*x + e) + (a^5 + a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + a*b^4 + b^5)*f^2*sinh(f*x + e)^2 - (a^5 - a^4*b - 2*a^3*b^2 + 2*a^2*b^3 + a*b^4 - b^5)*f^2)","B",0
60,0,0,0,0.405469," ","integrate(1/(d*x+c)/(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} \coth\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \coth\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*coth(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*coth(f*x + e)), x)","F",0
61,0,0,0,0.415423," ","integrate(1/(d*x+c)^2/(a+b*coth(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \coth\left(f x + e\right)^{2} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} \coth\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*coth(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*coth(f*x + e)), x)","F",0
